2023
Practice STA Questions
Chapter 7 - Chapter 9 Sec. 2
Memorize these Formulas:
General Format for Confidence Interval estimator +/- (t or z) est. standard error
General Format of Test Statistic -- (t or
z)
estimator # from H o
estimate of stderr
Make sure you know how to use the sample size for a one sample proportion and a one
sample mean problem.
Practice Problems on next page.
1. You take a random sample from some population and form a 96% confidence interval for the
population mean, Which quantity is guaranteed to be in the interval you form?
a) 0
b)
c) x
d) .96
2. Suppose you conduct hypothesis test for the population proportionand your p-value is .184.
Given a 0.10 level of significance, which of the following should be your conclusion?
a) accept HO
b) accept HA
c) Fail to reject HA
d) Fail to reject HO
e) Reject Ho
3. Decreasing the sample size, while holding the confidence level the same, will do what to the
length of your confidence interval?
a) make it bigger
b) make it smaller
c) it will stay the same
d) cannot be determined from the given information
4. Decreasing the confidence level, while holding the sample size the same, will do what to the
length of your confidence interval?
a) make it bigger
b) make it smaller
c) it will stay the same
d) cannot be determined from the given information
5. If you increase the sample size and confidence level at the same time, what will happen to the
length of your confidence interval?
a) make it bigger
b) make it smaller
c) it will stay the same
d) cannot be determined from the given information
6. Which of the following is a property of the Sampling Distribution of x ?
a) if you increase your sample size, x will always get closer to the population mean.
b) the standard deviation of the sample mean is the same as the standard deviation from the
original population
c) the mean of the sampling distribution of x is the population mean.
d) x always has a Normal distribution.
7. Which of the following is true about p-values?
a) a p-value must be between 0 and 1.
b) if a p-value is greater than .01 you will never reject HO.
c) p-values have a N(0,1) distribution
d) None of the above are true.
8. Suppose that we wanted to estimate the true average number of eggs a queen bee lays with
95% confidence. The margin of error we are willing to accept is 0.5. Suppose we also know that
sis aboutWhat sample size should we use?
a) 1536
b) 1537
c) 2653
d) 2650
9. What should be the value of z used in a 93% confidence interval?
a) 2.70
b) 1.40
c) 1.81
d) 1.89
10. What are the possible values of x-bar for all samples of a given n from this population?
To answer this question, we would need to look at the:
a. test statistic
b. z-scores of several statistics
c. standard normal distribution
d. sampling distribution
e. probability distribution of x
11. Why do we use inferential statistics?
a. to help explain the outcomes of random phenomena
b. to make informed predictions about parameters we dont know
c. to describe samples that are normal and large enough (n>30)
d. to generate samples of random data for a more reliable analysis
12. A 95% confidence interval for the mean number of televisions per American household is
(1.15, 4.20). For each of the following statements about the above confidence interval, choose
true or false.
a. The probability that is between 1.15 and 4.20 is .95.
b. We are 95% confident that the true mean number of televisions per American household
is between 1.15 and 4.20.
c. 95% of all samples should have x-bars between 1.15 and 4.20.
d. 95% of all American households have between 1.15 and 4.20 televisions.
e. Of 100 intervals calculated the same way (95%), we expect 95 of them to capture the
population mean.
f. Of 100 intervals calculated the same way (95%), we expect 100 of them to capture the
sample mean.
13. When doing a significance test, a student gets a p-value of 0.003. This means that:
I. Assuming Ho were true, this samples results were an unlikely event.
II. 99.97% of samples should give results which fall in this interval.
III. We reject Ho at any reasonable alpha level.
a.
b.
c.
d.
II only
III only
I and III
I, II, and III
14. Parameters and statistics
a. Are both used to make inferences about x
b. Describe the population and the sample, respectively.
c. Describe different groups of individuals.
d. Describe the same group of individuals.
15. A waiter believes that his tips from various customers have a slightly right skewed
distribution with a mean of 10 dollars and a standard deviation of 2.50 dollars. What is the
probability that the average of 35 customers will be more than 13 dollars?
a.) almost 1
b.) almost zero
c.) 0.1151
d.) 0.8849
Questions 16-19 A certain brand of jelly beans are made so that each package of these jelly
beans contains about the same number of beans. The filling procedure is not perfect, however.
The packages are filled with an average of 375 jelly beans, but the number going into each bag is
normally distributed with a standard deviation of 8. Yesterday, Jane went to the store and
purchased four of these packages in preparation for a Spring party. Jane was curious, and she
counted the number of jelly beans in these packages. She determined that her four bags
contained an average of 382 jelly beans.
16. In the above scenario, which of the following is a parameter?
a) The average number of jelly beans in Janes packages, which is 382.
b) The average number of jelly beans in Janes packages, which is unknown.
c) The average number of jelly beans in all packages made, which is 375.
d) The average number of jelly beans in all packages made, which is unknown.
17. If you went to the store and purchased six bags of this brand of jelly beans, what is the
probability that the average number of jelly beans in your bags is less than 373?
a) .2709
b) .3085
c) .4013
d) .7291
18. Why can we use the Z table to compute the probability in the previous question?
a) because np>15 and n(1-p) > 15
b) because n is large in this problem
c) because the distribution of jelly beans is Normal
d) because the average is large
19. According to the central limit theorem, what is the standard deviation of the sampling
distribution of the sample mean?
a) The standard deviation of the population
b) The standard deviation of the sample
c) The standard deviation of the population divided by the square root of the sample size
d) The standard deviation of the sample divided by the square root of the sample size
Questions 20-23 Researchers are concerned about the impact of students working while they
are enrolled in classes, and theyd like to know if students work too much and therefore are
spending less time on their classes than they should be. First, the researchers need to find out, on
average, how many hours a week students are working. They know from previous studies that
the standard deviation of this variable is about 5 hours.
20. A survey of 200 students provides a sample mean of 7.10 hours worked. What is a 95%
confidence interval based on this sample?
a) (6.10, 8.10)
b) (6.41, 7.79)
c) (6.57, 7.63)
d) (7.10, 8.48)
21. Suppose that this confidence interval was (6.82, 7.38). Which of these is a valid
interpretation of this confidence interval?
a) There is a 95% probability that the true average number of hours worked by all UF
students is between 6.82 and 7.38 hours.
b) There is a 95% probability that a randomly selected student worked between 6.82 and
7.38 hours.
c) We are 95% confident that the average number of hours worked by students in our
sample is between 6.82 and 7.38 hours.
d) We are 95% confident that the average number of hours worked by all UF students is
between 6.82 and 7.38 hours.
22. We have 95% confidence in our interval, instead of 100%, because we need to account for
the fact that:
a) the sample may not be truly random.
b) we have a sample, and not the whole population.
c) the distribution of hours worked may be skewed
d) all of the above
23. The researchers are not satisfied with their confidence interval and want to do another
study to find a shorter confidence interval. What should they change to ensure they
find a shorter confidence interval?
a) They should increase their confidence level and increase their sample size.
b) They should increase their confidence level but decrease their sample size.
c) They should decrease their confidence level but increase their sample size.
d) They should decrease their confidence level and decrease their sample size.
24. Suppose our p-value is .044. What will our conclusion be at alpha levels of .10, .05,
and .01?
a) We will reject Ho at alpha=.10, but not at alpha=.05
b) We will reject Ho at alpha=.10 or .05, but not at alpha=.01
c) We will reject Ho at alpha=.10, .05, or .01
d) We will not reject Ho at alpha=.10, .05, or .01
25. For each of the following situations, can we use the Z table to compute probabilities (T/F):
_____ a. Weights of adults are approximately Normally distributed with mean 150 lbs and
stdev 25 lbs. We want to know the probability that a randomly selected person weights
more than 200 pounds.
_____ b. Weights of adults are approximately Normally distributed with mean 150 lbs and
stdev 25 lbs. We want to know the probability that the average weight of 10 randomly
selected people is more than 200 pounds.
_____ c. Weights of adults are approximately Normally distributed with mean 150 lbs and
stdev 25 lbs. We want to know the probability that the average weight of 50 randomly
selected people is more than 200 pounds.
_____ d. Salaries at a large corporation have mean of $40,000 and stdev of $20,000. We want
to know the probability that a randomly selected employee makes more than $50,000.
_____ e. Salaries at a large corporation have mean of $40,000 and stdev of $20,000. We want
to know the probability that the average of ten randomly selected employees is more than
$50,000.
_____ f. Salaries at a large corporation have mean of $40,000 and stdev of $20,000. We want
to know the probability that the average of fifty randomly selected employees is more
than $50,000.
_____ g. A club has 50 members, 10 of which think the president should be deposed. What is
the probability that, if we select 20 members at random, 18% or more in our sample think
the president should be deposed?
_____ h. A club has 5000 members, 1000 of which think the president should be deposed.
What is the probability that, if we select 91 members at random,20% or more in our
sample think the president should be deposed?
Questions 26-27 Recent studies have shown that 20% of Americans are fit the medical definition
of obese. A nutrition professor would like to study the percentage of students on campus that are
obese. Suppose that the percentage of students that are obese at UF is the same as the percentage
of Americans. Let X equal the number of students that are obese.
26. For the sample of 100 teenagers, what is the sampling distribution of the sample proportion?
a.) p ~ N(10, 0.2)
b.) p ~N(2, 1.27)
c.) p ~N(0.2, 0.04)
d.) Can not be determined
27. Suppose that she took a sample of 100 teenagers. What is the probability that the sample
proportion is greater than 0.24?
a.) 0.1841
b.) 0.1587
c.) 0.8413
d.) 1.0
28. An auto insurance company has 32000 clients. They take a sample of 3,200 clients, they
believe that 5% of them will have submitted a claim in the past year. What is the sampling
distribution of p ?
a.) p ~ N(3200, 0.2)
b.) p ~N(160, 152)
c.) p ~N(0.05,0.003852)
d.) Can not be determined
Questions 29- 30 Suppose 20 donors come to a blood drive. Assume that the blood donors are
not related in any way, so that we can consider them independent. The probability that the donor
is O- blood is 0.06, which is constant from donor to donor. Let X = the number of donors that
have O- blood.
29.For the sample of 100 donors, what is the sampling distribution of the sample proportion?
a.) p ~ Binomial (100, 0.06)
b.) p ~Normal (0.06, 0.0237)
c.) p ~Normal(6, 2.37)
d.) Can not be determined
30. For the sample of 300 donors, what is the sampling distribution of the sample proportion?
a.) p ~ Binomial (200, 0.06)
b.) p ~Normal (12, 3.359)
c.) p ~Normal(0.06, 0.013711)
d.) Can not be determined
31. For the sample of 300 donors, what is the probability that the sample proportion is greater
than 0.10?
a.) 0.0019
b.) 0.181
c.) 0.819
d.) 0.991
32.The executives at Sandbachian, Inc. having recently solved their widget crises, have another
major problem with one of their products. Many cities are sending complaints that their manhole
covers are defective and people are falling into the sewers. Sandbachian, Inc. is pretty sure that
only 4% of their manhole covers are defective, but they would like to do a study to confirm this
number. They are hoping to construct a 95% confidence interval to get within 0.01 of the of true
proportion defective manhole covers. How many manhole covers need to be tested?
a. 8
b. 1476
c. 9604
d. 9605
33. The executives at Sandbachian, Inc., having recently solved their widget crisis, have another
problem with one of their products. Many cities are sending complaints that their manhole
covers are defective and people are falling into the sewers. The workers took a random sample
of 800 manhole covers and found that 40 of them were defective. What is the 95% CI for p, the
true proportion of defective manhole covers, based on this sample?
a) (37.26, 42.74)
b) (.035, .065)
c) (.047, .053)
d) (.015, .085)
Questions 34 Researchers are designing a study to determine if the age of the victim is a factor
in reported scams. The researchers are testing to determine if more than
half of all reported scams victimize the elderly. They randomly sample 350 reported
scams over the past 10 years from the Better Business Bureau archives, and note that,
for 287of them, the victim is over 65 years old.
34. Match the following symbols with the correct number on the right:
_____
_____
_____
_____
_____
p
p-hat
p0
x
n
a)
b)
c)
d)
e)
f)
g)
0.50
65
287
350
0.820
0.816
unknown
35. When are p-values negative?
a) when the test statistic is negative.
b) when the sample statistic is smaller than the hypothesized value of the parameter
c) when the confidence interval includes only negative values
d) when we fail to reject the null hypothesis
e) never
36. Let x1, x2, , x50 be independent observations from a distribution X which is not normal.
Suppose it is known that the mean of this distribution is 48 and the standard deviation is 5. What
can we say about the sample mean x-bar?
a)
b)
c)
d)
x-bar = 48
x-bar is distributed approximately normal with mean 48 and standard error 5
x-bar is distributed approximately normal with mean 48 and standard error 5/(50)
x-bar cannot be approximated with the normal distribution since the distribution of X is
not normal
37. Suppose that the probability that Joakim Noah, a former UF basketball player, makes a free
throw is p = 0.75. Now suppose that he shoots 100 free throws over the course of a basketball
season (sample of 100 independent free throws). Find the approximate probability that Joakim
makes less than 65% of his free throws during the course of the season.
a)
b)
c)
d)
0.0104
0.9896
0.409
0.591
38. Suppose the average weight for adult males (age 18 or older) in Alachua County is 190 lbs
with a standard deviation of 20. Now suppose we take a random sample of 143 adult males (age
18 or older) in Alachua County. Approximately, what is the probability that the sample mean of
our 143 subjects is bigger than 193 lbs?
a)
b)
c)
d)
0.4404
0.0367
0.5596
Cannot say from the information provided
39. Refer to question 38, but this time suppose we take a random sample of 16 males from
Alachua County. Approximately, what is the probability that the sample mean of our 16 subjects
is bigger than 193 lbs?
a)
b)
c)
d)
0.4404
0.2743
0.7257
Cannot say from the information provided
40. Suppose the probability that Barry Bonds, a famous baseball player, gets a hit in a given at
bat is p = 0.3. If Barry has 400 at bats in a single season (sample of 400 independent at bats),
what is the mean and standard error of the sampling distribution p-hat (the sample proportion of
hits per at bat)?
a)
b)
c)
d)
mean = 0.3, standard error = 0.0011
mean = 0.3, standard error = 0.0229
mean = 0.7, standard error = 0.0011
mean = 0.7, standard error = 0.0229
41. Suppose our p-value is .02. Which of the following is true?
a) We will not reject H0 at alpha = .05
b) We will reject H0 at alpha = .01
c) We will reject H0 at alpha = 0.05
d) We will reject H0 at alpha equals 0.01, 0.05, and 0.10
e) None of the above is true.
42. A random sample of married people were asked "Would you remarry your spouse if you
were given the opportunity for a second time?"; Of the 150 people surveyed, 127 of them said
that they would do so. Find a 95% confidence interval for the proportion of married people who
would remarry their spouse.
a)
b)
c)
d)
e)
0.847 0.002
0.847 0.029
0.847 0.048
0.847 0.058
0.847 0.113
43. You would like to estimate the proportion of "regular users of vitamins" in a large
population. In order to find a confidence interval for the proportion,
a) we must assume that we have a random sample from a normal population
b) we must assume that we have a random sample from some binary population where np>
15 and n(1-p)> 15
c) we must assume that the population is normal (but we do not require a random sample
because of the Central Limit Theorem).
d) we do not need to assume that the population is normal nor that the sample is random
(because of the Central Limit Theorem).
e) We do not need to assumption anything.
44. A survey was conducted to get an estimate of the proportion of smokers among the graduate
students. Report says 38% of them are smokers. Chatterjee doubts the result and thinks that the
actual proportion is much less than this. He takes a sample of 25 students to test the survey
result. Let p be the proportion of smokers among the graduate students.
Choose the correct choice of null and alternative hypothesis Chatterjee wants to test.
a) Ho: p=.38 versus Ha: p .38.
b) Ho: p=.38 versus Ha: p > .38.
c) Ho: p=.38 versus Ha: p< .38.
d) None of the above.
45. A political poll of Americans was conducted to investigate their opinions on gun control.
Each person was asked if they were in favor of gun control or not in favor of gun control - no
respondents were removed from the results. The survey found that 25% of people contacted were
not in favor of gun control laws. These results were accurate to within 3 percentage points, with
95% confidence. Which of the following is NOT CORRECT?
a) The 95% confidence interval is approximately from (22% to 28%).
b) We are 95% confidence that the true proportion of people not in favor is within 3
percentage points of 25%.
c) In approximately 95% of polls on this issue, the confidence interval will include the
sample proportion.
d) For this sample, the 95% confidence interval for the proportion of those IN FAVOR of
gun control would be (0.72 to 0.78).
46. Suppose we are interested in finding a 95% confidence interval for the proportion p of UF
undergraduate students who are from the state of Florida. We take a random sample of 20
students, and we find that 17 of them are from Florida. What should we compute as our 95%
confidence interval for p?
a) (.694, 1.000)
b) (.629, .954)
c) (.850, .930)
d) (.688, 1.000)
47. Which of the following statements about small-sample and large-sample confidence intervals
for proportions are true?
I.
The large-sample confidence interval formula for proportions is valid if np 15 and
n(1-p) 15.
II.
Large-sample confidence intervals always contain the true parameter value, whereas
small-sample confidence intervals may not.
III.
We form small-sample confidence intervals by using the large-sample formula after
adding 4 successes and 4 failures.
a) I and III only
b) II only
c) I only
d) I, II, and III
Questions 48-50: Suppose we are interested in finding a 95% confidence interval for the mean
SAT Verbal score of students at a certain high school. (Assume that these scores are normally
distributed.) Five students are sampled, and their SAT Verbal scores are 560, 500, 470, 660, and
640.
48. What is the standard error of the sample mean?
a) 16.71
b) 37.36
c) 83.55
d) 113.2
49.
a)
b)
c)
d)
What is the 95% confidence interval for the population mean?
(462.3, 669.7)
(469.9, 662.1)
(486.3, 645.7)
(492.8, 639.2)
50. The method used to calculate the confidence interval in Question 49 assumes which one of
the following?
a) The sample mean equals the population mean.
b) The sample standard deviation does not depend on the sample drawn.
c) The population has an approximately normal distribution.
d) The degrees of freedom df 30.
51. A sample of size 45 is drawn from a slightly skewed distribution. What is the approximate
shape of the sampling distribution?
a . Skewed Distribution
b . Binary Distribution
c. Normal Distribution
d. Uniform Distribution
Questions 52-53 We know that 65% of all Americans prefer chocolate over vanilla ice cream.
Suppose that 1000 people were randomly selected.
52. The standard error of the sample proportion is
a.
b.
c.
d.
0.03567
0.01508
0.01798
0.3785
53. The Sampling Distribution of the sample proportion is
a.
b.
c.
d.
Bin ( 1000, 0.65)
Normal( 0.65, 0.01508)
Normal(10000,0.65)
None Of The Above
54. What is the probability that our sample will have more than 70% of people prefer chocolate
ice cream?
a.
b.
c.
d.
0.9995
0.0005
0.70
none of the above
55. We are doing an experiment where we record the number of heads we get when we flip an
unbiased coin many times. For what sample sizes below would the sampling distribution of the
sample proportion be approximately normally distributed?
a.
b.
c.
d.
5
28
50
none of the above
56.For a test with the null hypothesis Ho: p = 0.5 vs. the alternative Ha: p > 0.5, the null
hypothesis was not rejected at level alpha=.05.Das wants to perform the same test at level
alpha=.025.What conclusion will he make after doing the test?
a) Reject H0.
b) Fail to Reject H0.
c) No conclusion can be made.
d) Reject Ha.
57.The null hypothesis Ho: p=.5 against the alternative Ha: p>.5 was rejected at level
alpha=0.01.Nate wants to know what the test will result at level alpha=0.10.what will be the
result if Nate performs the test at level alpha=0.10?
a.) Reject Ho
b.) Fail to Reject Ho
c.) No conclusion can be made
d.) Reject Ha
58. A null hypothesis was rejected at level alpha=0.10.What will be the result of the test at level
alpha=0.05?
a.) Reject Ho
b.) Fail to Reject Ho
c.) No conclusion can be made
d.) Reject Ha
Questions 59 - 61. Commercial fishermen working in certain parts of the Atlantic Ocean
sometimes find their efforts being hindered by the presence of whales. Ideally, they would like to
scare away the whales without frightening the fish. One of the strategies being experimented
with is to transmit underwater the sounds of a killer whale. On the 52 occasions that that
technique has been tried, it worked 24 times (that is, the whales left the area immediately).
Experience has shown, though, that 40% of all whales sighted near fishing boats leave on their
own accord, anyway, probably just to get away from the noise of the boat.
59. What would a reasonable hypothesis test be:
a) Ho: p=0.4 versus Ha: p = 0.46
b) Ho: p=0.46 versus Ha: p > 0.46
c) Ho: p=0.46 versus Ha: p 0.46
d) Ho: p=0.4 versus Ha: p > 0.40
60. Suppose you want to test Ho: p=0.4 versus Ha: p > 0.40 at the 0.05 level of significance.
What would your conclusion be?
a) Reject Ho.
b) Accept Ho.
c) Accept Ha.
d) Fail to reject Ho.
61. The following is a list of assumptions that you might want to check before proceeding to a
significance test for p .
I. The data is obtained from a random sample
II. The variable is categorical
III. The variable is quantitative
IV. The population size is large
V. The population is normally distributed
VI. The sample size is sufficiently large
VII. The sampling distribution of p is approximately normal
What assumptions must be satisfied in order to be able to conduct a significance test for p ?
a) I, IV, and VII
b) I, II, and VII
c) I, III, and VI
d) I, IV, V and VI
62. You suspect that the most popular color for a Nalgene water bottle is blue, but you would
like to verify that. For this purpose you decide to estimate what proportion of the Nalgene water
bottles used at UF are blue. Describe what the population is, and state how you plan to find p . In
answering this question, keep in mind that a single student may have more than one water bottle
(possibly of different colors), or none at all.
a) The population is all UF students.
(Number of students in the sample who have at least 1 blue Nalgene bottle)
p = ----------------------------------------------------------------------------------------(Total number of students in the sample)
b) The population is all Nalgene water bottles used at UF.
(Number of blue Nalgene bottles in the sample)
p = ----------------------------------------------------------------------------------------(Total number of Nalgene bottles in the sample)
c) The population is all Nalgene water bottles used at UF.
(Number of blue Nalgene bottles in the sample)
p = ----------------------------------------------------------------------------------------(Total number of Nalgene bottles in the sample that are NOT blue)
d) The population is all UF students.
(Number of students in the sample who own ONLY blue Nalgene bottles)
p = ----------------------------------------------------------------------------------------(Total number of students in the sample)