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I am in the process of revising my homework due for my class soon. Can we go over these problems below?

I am in the process of revising my homework due for my class soon. Can we go over these problems below?

2, 5, 8, 13, 15, 16, 17, 18, 21, 22, 23 , 31, 32, 33 through 40 are my trouble spots to begin with.


1.

Which of the following is the appropriate interpretation for when an event has a probability of 0?

a.We are absolutely certain that the event will not occur.

b.The event could occur in the long run.

c.The event is unlikely to occur and has a very small relative frequency.



2.

Biology course grades: We recorded the lab scores (in percent), quiz scores (in percent) and course grade (in percent) for 50 biology students. Then we generated the following scatterplots of the data.

Screen Shot 2018-05-12 at 4.28.04 PM.png




The se value for scatterplot 1 is 4.8% and for scatterplot 2 is 5.4%. Using the se value, which is a better predictor of a student's biology course grade: lab scores or quiz scores?

a.Quiz scores

b.Lab scores



3.

  1. Which values indicate that a linear model makes more accurate predictions?

a.Large se values

b.Small se values

c.Large r2 values

d.Small r2 values




4.

Screen Shot 2018-05-12 at 4.40.53 PM.png


The scatterplot above plots number of unemployed Americans (in thousands) against gross national product (in billions of U.S. dollars). The data were gathered in an economics study from 1947 to 1962 by J.W. Longley.

(Reference: J. W. Longley (1967) An appraisal of least-squares programs from the point of view of the user. Journal of the American Statistical Association, 62, 819-841.)

The correlation is 0.60

Which of the following is the most appropriate conclusion given this finding?


a.A higher GNP causes higher unemployment numbers.

b.Gross domestic product is a lurking variable.

c.U.S. Population is a lurking variable.




5.

Clinical depression is the most common mental illness in the United States,affecting 19 million adults each year (Source:NIMH,1999). Nearly 50% of individuals who experience a major episode will have a recurrence within 2-3 years. Researchers are interested in comparing therapeutic solutions that could delay or reduce the incidence of recurrence.


In a study conducted by the National Institutes of Health, 109 clinically depressed patients were separated into three groups, and each group was given one of two active drugs (imipramine or lithium) or no drug at all. For each patient, the dataset contains the treatment used, the outcome of the treatment,and several other interesting characteristics.


Below is a summary of the variables in our dataset. Use this to answer the questions below.

  • Hospt: The patient's hospital, represented by a code for each of the 5 hospitals 1, 2, 3, 4, 5, or 6
  • Treat: The treatment received by the patient (Lithium, Imipramine,or Placebo)
  • Outcome: Whether or not a recurrence occurred during the patient's treatment (Recurrence or No Recurrence)
  • Time: Either the time in days till the first recurrence, or if a recurrence did not occur, the length in days of the patient's participation in the study.
  • AcuteT: The time in days that the patient was depressed prior to the study.
  • Age: The age of the patient in years, when the patient entered the study.
  • Gender: The patient's gender (1 = Female, 2 = Male)

Examine each of the variables in the dataset as well as their descriptions above.

Which of the following variables is quantitative?

a.Hospt

b.Time

c.Gender

d.Time.




6.

A company in the United States produces packs of Pokemon cards. According to the company, 45% of the cards feature normal-type Pokemon, 25% feature fire-type Pokemon, 20% feature water-type Pokemon, and 10% feature electric-type Pokemon. In a pack of 40 cards, what is the expected count of water-type Pokemon?

a.8

b.It is impossible to tell because samples of 40 cards will vary.

c.4



7.

Suppose that a company prints baseball cards. They claim that 30% of the cards feature rookies, 60% feature veterans, and 10% feature All-Stars. We buy a pack of 50 cards. The pack contains 20 rookies, 28 veterans, and 2 All-Stars. We run a chi-square goodness-of-fit test. The chi-square test statistic is 3.6 with a P-value of 0.1653.

a.Nothing, the conditions for use of the chi-square distribution are not met.

b.We have strong evidence that the proportion of All-Stars featured in the cards is less than 10%.

c.We do not have enough evidence to reject the claim that the cards feature 30% rookies, 60% veterans, and 10% All-Stars.



8.

Colon and rectal cancer are less common in countries, like Italy, that consume a Mediterranean diet. The primary source of fat in the Mediterranean diet is olive oil. Italian researchers collected data on olive oil consumption and other diet-related information from a random sample of 1,953 patients with colon or rectal cancer and 4,154 patients admitted to the same hospitals for other, unrelated reasons. We conducted a chi-square test of independence with some of the data.


Here are the results. In this print-out results table, the observed count appears above the expected count in each cell.

Screen Shot 2018-05-12 at 4.49.14 PM.png



What can we conclude?

a.Nothing, because the conditions for use of the chi-square test are not met.

b.When we compare the different olive oil consumption levels, the differences in the distribution of cancer rates are not statistically significant.

c.We have strong evidence that olive oil consumption and the occurrence of these types of cancer are dependent.

d.Higher levels of olive oil consumption are associated with lower colon and rectal cancer rates. The association is statistically significant.

e.There is no statistically significant association between colon and rectal cancer and consumption of olive oil.


9.

A researcher wants to find out which type of pet is the most popular. She conducts a survey that asks this question of a random sample of U.S. adults in 2010 and a second independent sample in 2017. She then conducts a chi-square test of homogeneity to determine if there are statistically significant differences in the distribution of responses for these two years.


In this results table, the observed count appears above the expected count in each cell.

Screen Shot 2018-05-12 at 4.59.17 PM.png




If we included an exploratory data analysis with the test of homogeneity, the percentages most appropriate as part of this analysis for the Dog group are ________ .

a.193/517 compared to 324/517

b.193/1517 compared to 994/1998

c.193/1998 compared to 324/1998

d.193/994 compared to 324/1004




10.

Researchers studied 208 infants whose brains were temporarily deprived of oxygen due to complications at birth. When researchers detected oxygen deprivation, they randomly assigned babies to either usual care or to a whole-body cooling group. The goal was to see whether reducing body temperature for three days after birth increased the rate of survival without brain damage.

What is the purpose of including the "usual care" treatment in the experiment?

a.To provide a baseline for judging the survival rates of infants who received whole-body cooling

b.To make similar treatment groups so that a cause-and-effect relationship can be established

c.To control for the placebo effect and keep it from confounding the results



11.

Suppose we have a large group of people and record their body temperatures. We then make probability histograms with the data in the following two ways:

Method 1: With temperatures measured to the nearest degree Fahrenheit (°F)

Method 2: With temperatures measured to the nearest tenth degree Fahrenheit (0.1°F)

Which of the resulting probability histograms will fit a curve most closely?

a.Method 2

b.Method 1


12.


Which of the following probabilities is represented by the shaded region under the probability density curve?

Screen Shot 2018-05-12 at 5.08.14 PM.png


a.P( 75 ≤ X or X ≤ 83)

b.P( 75 ≤ X)

c.P(X ≤ 83)

d.P( 75 ≤ X ≤ 83)


13.

A classroom of students has their heights measured (in inches) for statistics investigation. The tallest student in the class is 71 inches tall. One student is assigned to record all the values. That student made a mistake when recording one of the values. When they meant to record the 71, they accidentally entered 711.

How will the mean and SD be affected by this mistake?

a.The mean and SD will be unaffected by the mistake.

b.The mean and SD will be decreased by the mistake.

c.The mean and SD will be increased by the mistake.



14.

This probability distribution gives the potential cost of routine maintenance and major repairs in the first 5 years you own a new car.


Screen Shot 2018-05-12 at 5.23.58 PM.png



What is the expected cost of routine maintenance and major repairs for the 1st 5 years you own the car? (Recall: the expected value is the mean.)

a.$505

b.$101

c.$1000




15.

In a study at West Virginia University Hospital, researchers investigated smoking behavior of cancer patients to establish a program to help patients stop smoking. They published the results in Smoking Behaviors Among Cancer Survivors (January 2009 issue of the Journal of Oncology Practice.) In this study, the researchers sent a 22-item survey to 1,000 cancer patients. They collected demographic information (age, sex, ethnicity, zip code, level of education), clinical and smoking history, and information about quitting smoking.

The questionnaire filled out by cancer patients at West Virginia University Hospital also asked patients if they were current smokers. The current smoker rate for female cancer patients was 11.6%. 95 female respondents were included in the analysis. For male cancer patients, the current smoker rate was 10.4%, and 67 male respondents were included in the analysis. Suppose that these current smoker rates are the true parameters for all cancer patients. Can we use a normal model for the sampling distribution of differences in proportions?

a.No, a normal model is not a good fit for this sampling distribution.

b.Yes, a normal model is a good fit for this sampling distribution.



16.

Data collected in the 2010 U.S. census showed that men represent 49.2% of the population and women represent 50.8% of the population.

A researcher plans to survey 5 rural hospitals and calculate the difference in sample proportions between male births and female births. At each hospital, the researcher will record the percentage of male births and the percentage of female births. Assume each hospital has about 100 births per year. We define the difference in sample proportions as "male" minus "female." The standard error is about 0.07.

Which sequence of sample differences is the most likely?

a.-0.016, -0.016, 0, -0.016, -0.016

b.0.017, 0.039, -0.010, -0.081, -0.005

c.0.12, 0, -0.25, -0.08, 0.23



17.

Figure A represents the weights for a sample of 26 pebbles, each weighed to the nearest gram.

Figure B represents the mean weights of a random sample of 3 pebbles each, with the mean weights rounded to the nearest gram.


Screen Shot 2018-05-12 at 5.25.44 PM.png


One value is circled in each distribution. What is the difference between what is represented by the X circled in A and the X circled in B?

Please select the best answer from the list below.

a.Figure A has a larger range of values than Figure B.

b.The X in Figure A is the weight for a single pebble, while the X in Figure B represents the average weight of 3 pebbles.

c.There is no difference since in both Figure A and Figure B, the X represents one pebble that weighs 6 grams.



18.

A nutritional scientist is investigating the effects of ketogenic dieting on lean body mass. They studied 50 college age men in a paired study: each pair matched on starting lean body mass, height, and race and divided into Groups A and B. Group A consumed a ketogenic diet while Group B consumed a traditional western diet.

Which type of hypothesis test should they use?

a.test for one population proportion

b.test for one population mean

c.test for a difference in two population proportions

d.test for a difference in two population means



19.

The SAT-Verbal scores of a sample of 300 students at a particular university had a mean of 592 and standard deviation of 73.

According to the university's reports, the SAT-Verbal scores of all its students had a mean of 580 and a standard deviation of 110.

Which of the following is a statistic?

a.580

b.300

c.110

d.592




20.

Researchers produced new fertilizer. They conducted an experiment to compare the new fertilizer to the old fertilizer. They divided tomato plants into two groups. They applied the new fertilizer to one group and the old fertilizer to another group. The variable is the number of tomatoes per plant on a randomly selected day.


Screen Shot 2018-05-12 at 5.29.45 PM.png


Which one of the following statements is valid?

a.The new formula of fertilizer works better. Plants with the new fertilizer had more tomatoes.

b.The average number of tomatoes per plant with the old fertilizer is higher than the average amount of tomatoes per plant with the new fertilizer.

c.We can make no conclusions from this data about which fertilizer is better because the two groups have a different number of plants.

d.The old formula of fertilizer was better because the plant with the most tomatoes was treated with the old fertilizer.



21.

Quit Smoking: The New England Journal of Medicine published the results of a double-blind, placebo-controlled experiment to study the effect of nicotine patches and the antidepressant bupropion on quitting smoking.

With the data from the experiment we calculate the sample difference in the "quit smoking" rates for the nicotine treatment group and the placebo group ("treatment" minus "placebo"). We get 0.8% = 0.008. Which of the following is an appropriate conclusion based on this finding?

a.Nicotine patches and the antidepressant bupropion work equally well on "quit smoking" rates.

b.Nicotine patches will produce a slightly higher success rate when compared to a placebo, but the difference is not statistically significant.

c.In this experiment, the placebo group had a higher success rate than the nicotine group by 0.8%.

d.In this experiment the nicotine treatment had a higher success rate than the placebo group, but the improvement was less than 1%.

 


22.

In 2011, the Institute of Medicine (IOM), a non-profit group affiliated with the US National Academy of Sciences, reviewed a study measuring bone quality and levels of vitamin-D in a random sample from bodies of 675 people who died in good health. 8.5% of the 82 bodies with low vitamin-D levels (below 50 nmol/L) had weak bones. Comparatively, 1% of the 593 bodies with regular vitamin-D levels had weak bones.

True or False? If the hypothesis test has P-value = 0.03, IOM researchers can conclude that low vitamin-D levels cause weak bones.

a.True

b.False



23.

A marketing student is estimating the average amount of money that students at a large university spent on sporting events last year. He asks a random sample of 50 students at one of the university football games how much they spent on sporting events last year. Using this data he computes a 90% confidence interval, which turns out to be ($217, $677).

Which one of the following conclusions is valid?

a.No conclusion can be drawn.

b.We can be 90% confident that the mean amount of money spent at sporting events last year by all the students at this university is between $217 and $677.

c.90% of the sample said they spent between $217 and $677 at sporting events last year.




24.

Weight of a rock: In a geology course, students are learning to use a balance scale to accurately weigh rocks. One student plans to weigh a rock 20 times and then calculate the average of the 20 measurements to estimate her rock's true weight. A second student plans to weigh a rock 5 times and calculate the average of the 5 measurements to estimate his rock's true weight.


Let's say that the student who collected 20 weight measurements came up with a mean weight of 27.1 g with a standard deviation of 2.3 grams. The critical T-value for a 95% (one-sample) confidence interval with df = 19 is 2.09.


Which of the following is the resulting 95% confidence interval?

a.(25.0, 29.2)

b.(26.6, 27.6)

c.(26.0, 28.2)


25.

In the article Colas, but not other carbonated beverages, are associated with low bone mineral density in older women: The Framingham Osteoporosis Study, researchers investigate the relationship between daily cola consumption and bone mineral density (American Journal of Clinical Nutrition 84: 936-942, 2006). The article reports:

" The mean BMD of those with daily cola intake was 3.7% lower at the femoral neck and 5.4% lower at Ward's area than those who consumed <1 serving cola per month. "

An objective of this study is to ________ .

a.estimate and compare means between two groups

b.test a claim about a difference in means between two groups

c.test a claim about a difference in proportions between two groups

d.estimate and compare proportions between two groups



26.

Race relations: A New York Times/CBS poll surveyed 1,027 adults nationwide about race relations in the United States. Of the sample, 61% responded that race relations in this country are generally bad. The 95% confidence interval is (0.58, 0.64). Which of the following is an appropriate interpretation of the 95% confidence interval?

http://www.nytimes.com/2015/05/05/us/negative-view-of-us-race-relations-grows-poll-finds.html?_r=0

a.We are 95% confident that the proportion of all Americans who say that race relations in this country are generally bad is between 58% and 64%.

b.Of the samples, 95% will have between 58% and 64% of respondents who say that race relations in this country are generally bad.

c.We are 95% confident that the proportion of the sample who say that race relations in this country are generally bad is between 58% and 64%.

d.There is a 95% probability that the proportion of all Americans who say that race relations in this country are generally bad is between 58% and 64%.




27.

River Frogs: Use the information and graph below to answer the question. A non-native species of snake appeared in a large southern swamp in 1995. Shortly thereafter, scientists noticed that a particular species of river frog began to decline exponentially. They suspected that the snakes were eating the frogs at an alarming rate. The scientists made an exponential model to predict the decline in the frog population. The points plotted below come from their exponential model. Note that t is measured in years, the value t = 0 corresponds to 1995, and y is the predicted number of remaining frogs in thousands.


Screen Shot 2018-05-12 at 4.40.44 PM.pngScreen Shot 2018-05-12 at 5.33.34 PM.png




Which of the following values could represent the size of the frog population for the year 2005, as shown in the graph above?

a.10,700

b.3,500

c.32,800

d.100,000



28.

Which one of the following histograms could represent a distribution of weights of babies for a large random sample of male newborns at a local hospital?

Screen Shot 2018-05-12 at 7.35.46 PM.png


a.II

b.I

c.III

d.IV



29.

  1. Recall the (make-believe) matched-pairs investigation of the effect of drinking two beers on reaction time in a driving simulator. We set a significance level of 5% and tested the following hypotheses.
  • H0: Drinking 2 beers has no effect on reaction time.
  • Ha: Drinking 2 beers slows reaction time.
  1. We defined µ as the mean of the difference in reaction time (before minus after) for all students at this college after drinking two beers. We rewrote the hypotheses in terms of µ.
  • H0: μ = 0
  • Ha: μ < 0

Identify the type I error.

a.Researchers conclude that drinking 2 beers slows reaction time, and this is true.

b.In reality drinking 2 beers does not have much of an impact on reaction time, but researchers conclude from this experiment that drinking 2 beers significantly slows reaction time.

c.Researchers conclude that drinking 2 beers does not significantly slow reaction time, but this is not really true.



30.

A newspaper article reported on differences between unemployment rates of U.S. military veterans and non-veterans. Data selected randomly from local veterans and non-veterans, shows a 1% difference. Sample sizes were large enough to give a P-value of 0.015.



What issue exists in concluding that the unemployment rate is significantly higher for U.S. veterans?

a.The groups were not chosen by random assignment.

b.The samples were self-selected.

c.The samples gathered cannot be expected to represent the larger populations of U.S. veterans and non-veterans.

d.A 1% difference is not statistically significant.



31.

The Scholastic Aptitude Test (SAT) is a standardized test for college admissions in the U.S. Scores on the SAT can range from 600 to 2400. Suppose that PrepIt! is a company that offers classes to help students prepare for the SAT exam. In their ad, PrepIt! claims to produce "statistically significant" increases in SAT scores. This claim comes from a study in which 427 PrepIt! students took the SAT before and after PrepIt! classes. These students are compared to 2,733 students who took the SAT twice, without any type of formal preparation between tries.


Screen Shot 2018-05-12 at 7.42.37 PM.png



Let's first try to determine if students who take PrepIt! classes significantly improve their SAT scores. Which of the following is the best approach to answering this question?


a.Use the difference in sample means (29 and 21) in a hypothesis test for a difference in two population means.

b.Use the difference in sample means (500 - 529) in a hypothesis test for a difference in two population means.

c.Use the sample mean 29 in a hypothesis test for a population mean.


32.

A criminal investigator conducts a study on the accuracy of fingerprint matching and recruits a random sample of 35 people to participate. Since this is a random sample of people, we don't expect the fingerprints to match the comparison print. In the general population, a score of 80 indicates no match. Scores greater than 80 indicate a match. If the mean score suggests a match, then the fingerprint matching criteria are not accurate.

The null hypothesis is that the mean match score is 80. The alternative hypothesis is that the mean match score is greater than 80.

The criminal investigator chooses a 5% level of significance. She performs the experiment and analyzes the results. She uses a t-test for a mean and obtains a p-value of 0.04.

Which of the following is a reasonable interpretation of her results?

a.She cannot reject the null hypothesis. This suggests that the fingerprint matching criteria could be accurate.

b.This proves that there is evidence that the mean match score is greater than 80. This suggests that the fingerprint matching criteria are not accurate.

c.If there is a treatment effect, the sample size was too small to detect it. This suggests that we need a larger sample to determine if the fingerprint matching criteria are not accurate.

d.This proves that there is evidence that the mean match score is equal to 80. This suggests that the fingerprint matching criteria is accurate.



33.

Gun rights vs. gun control: In a December 2014 report, "For the first time in more than two decades of Pew Research Center surveys, there is more support for gun rights than gun control." According to a Pew Research survey, 52% of Americans say that protecting gun rights is more important than controlling gun ownership. Gun rights advocates in a conservative city believe that the percentage is higher among city residents.

They survey 200 city residents and find that 130 say that protecting gun rights is more important than controlling gun ownership. What is the test statistic?

http://www.people-press.org/2014/12/10/growing-public-support-for-gun-rights/

a.Z = -3.85

b.Z = 3.85

c.Z = 3.68

d.Z = -3.68




34.

One population proportion test: Which of the following situations involves testing a claim about a single population proportion?

a.A certain prescription allergy medicine is supposed to contain an average of 245 parts per million (ppm) of a certain chemical. The manufacturer takes a sample to check whether the mean concentration is the required 245 ppm or not.

b.A recent study estimated that 20% of all college students in the United States smoke. The head of Health Services at Goodheart University suspects that the proportion of smokers may be lower there.

c.According to the College Board, which administers the SAT exam, the average score for females is lower than for males among graduating seniors in 2011. An educational researcher wants to test whether this is also true in her school district.

d.A Statistics student at Tacoma Community Colleges wants to determine whether there is a difference in the proportions of class meetings that male and female students attend.



35.

Toys intended for use by infants are regularly inspected to see if they contain illegal concentrations of lead (lead can cause brain damage in infants that consume it). This can be thought of as a hypothesis test with the following hypotheses.

H0: The toy is safe.

Ha: The toy is not safe.

Is the following statement a Type I or Type II error?

The sample suggests that the toy is safe, but it actually is not safe.

a.Type II

b.Type I



36.

A graduate student designs a research study. She hopes to show that the results of her experiment are statistically significant.

What type of P-value indicates statistically significant results?

a.A large P-value.

b.A small P-value.

c.The magnitude of a P-value has no impact on statistical significance.




37.

We conduct a study to determine whether the majority of community college students plan to vote in the next presidential election. We choose a significance level of 0.05. We survey 650 randomly selected community college students and find that 54% of them plan to vote. The P-value is 0.02.

H0: 50% of community college students plan to vote in the next presidential election.

Ha: More than 50% of community college students plan to vote in the next presidential election.

What can we conclude?

a.The evidence suggests that the majority of community colleges students plan to vote in the next presidential election because the P-value is less than the significance level.

b.The evidence does not suggest that the majority of community colleges students plan to vote in the next presidential election because the difference between 50% and 54% is not statistically significant. A 4% difference could be due to random chance.

c.The evidence suggests that the majority of community colleges students plan to vote in the next presidential election because 54% is greater than 50%.

d.Nothing. The sample size is too small to represent all community college students.



38.

As a result of dog breeding for certain physical traits, many dog breeds have changed in the last 100 years. One example is basset hounds, whose height has decreased as a result of breeding. Suppose that researchers compare measurements from a random sample of 36 male basset hounds taken in 1915 and a random sample of 36 male basset hounds taken in 2015. Suppose the difference in mean heights (2015 basset hounds minus 1915 basset hounds) is -2.8 cm and the 90% confidence margin of error is 1.3 cm. The 90% confidence interval is -4.1cm to -1.5cm.

What is best conclusion about the change in height of basset hounds?

Reference: Elegans, C. 100 Years of Breed Improvement. 2012. Dog Behavior Science. Retrieved from: https://dogbehaviorscience.wordpress.com/2012/09/29/100-years-of-breed-improvement

Which of the following is a valid conclusion about the change in height in basset hounds?

a.We are 90% confident that the 2015 basset hounds are between 4.1 cm to 1.5 cm shorter on average than the 1915 basset hounds.

b.We are 90% confident that our sample of basset hounds from 1915 and 2015 will have a difference in sample means between -1.5 cm to -4.1cm.

c.We are 90% confident that there is no difference in mean heights between 1915 and 2015. The negative values suggest that the -2.8 sample difference is not statistically significant.

d.We are 90% confident that basset hounds in 1915 were 1.5cm shorter on average and in 2015 are 4.1cm shorter on average.



39.

A teacher is experimenting with computer-based instruction. In which situation could the teacher use a hypothesis test for a difference in two population means?

a.She gives each student a pretest. Then she teaches a lesson using a computer program. Afterwards, she gives each student a posttest. The teacher wants to see if the difference in scores will show an improvement.

b.The teacher uses a combination of traditional methods and computer-based instruction. She asks students if they liked computer-based instruction better. She wants to determine if the majority prefer the computer-based instruction.

c.She randomly divides the class into two groups. One group receives computer-based instruction. The other group receives traditional instruction without computers. After instruction, each student has to solve a single problem. The teachers wants to compare the proportion of each group who can solve the problem.

d.She gives each student a pretest. She then randomly divides the class into two groups. One group receives computer-based instruction. The other group receives traditional instruction without computers. After instruction, each student takes a post-test. The teacher compares the improvement in scores (post-test minus pretest) in the two groups.



40.

For this data set, the least squares regression line is Y = 31.72 + 0.62X, where X represents the final exam score as a percent and Y represents the predicted course grade as a percent.

Screen Shot 2018-05-12 at 7.45.27 PM.png


Notice that the regression line for this data set has slope 0.62. What is the most precise and accurate interpretation of the slope?

a.For every 1% increase in a student's final exam score, we expect to see a 0.62% decrease in the course grade.

b.For every 1%t increase in a student's final exam score, we expect to see a 62% increase in the course grade.

c.For every 1% increase in a student's final exam score, we expect to see a 0.62% increase in the course grade.

d.Students with higher final exam scores tend to have higher course grades.

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