Final I - PrintTest PRINTABLEVERSION Final Youscored70outof70 Question1 YouranswerisCORRECT ,84%.Supposeyouare .

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Unformatted text preview: 12/20/2015 Print Test PRINTABLE VERSION Final You scored 70 out of 70 Question 1 Your answer is CORRECT. Suppose that in a large metropolitan area, 84% of all households have cable tv. Suppose you are interested in selecting a group of six households from this area. Let X be the number of households in a group of six households from this area that have cable tv. For what proportion of groups will at most three of the households have cable tv? a) 0.247 b) 0.944 c) 0.753 d) 0.056 e) 0.191 Question 2 Your answer is CORRECT. A potato chip company calculated that there is a mean of 75.4 broken potato chips in each production run with a standard deviation of 5.2. If the distribution is approximately normal, find the probability that there will be fewer than 66 broken chips in a run. a) 0.035 b) 0.335 c) 0.018 d) 0.285 e) 0.965 Question 3 Loading [MathJax]/extensions/MathZoom.js Your answer is CORRECT. 1/9 12/20/2015 Print Test A distribution of grades in an introductory statistics class (where A = 4, B = 3, etc) is: x 0 1 2 3 4 p(x) 0.1 0.15 0.21 0.31 0.23 Find the mean and variance for the grades in this class. a) mean = 2.32, variance = 1.6036 b) mean = 2.52, variance = 0.8018 c) mean = 2.42, variance = 1.6036 d) mean = 2.42, variance = 0.8018 e) mean = 2.32, variance = 1.2663 Question 4 Your answer is CORRECT. The weights of male and female students in a class are summarized in the following boxplots: Which of the following is NOT correct? a) The mean weight of the female students is about 120 because of symmetry. b) About 75% of the female students have weights more than 128 lbs. c) The median weight of the male students is about 166 lbs. d) About 50% of the male students have weights between 150 and 185 lbs. Question 5 Your answer is CORRECT. Given that P (A) = 0.27, P (B) = 0.46, and P (A ∩ B) = 0.11 , find P (A | B). 2/9 12/20/2015 Print Test a) 0.761 b) 0.124 c) 0.876 d) 0.239 e) 0.407 Question 6 Your answer is CORRECT. Identify the most appropriate test to use for the following situation: A national computer retailer believes that the average sales are greater for salespersons with a college degree. A random sample of 14 salespersons with a degree had an average weekly sale of $3542 last year, while 17 salespersons without a college degree averaged $3301 in weekly sales. The standard deviations were $468 and $642 respectively. Is there evidence to support the retailer's belief? a) Two sample z test for means b) Two sample z test for proportions c) Two sample t test for means d) One sample z test for proportions e) One sample t test for means f) Matched pairs t test for means g) One sample z test for means Question 7 Your answer is CORRECT. A random sample of 121 cans of fruit nectar is drawn from among all cans produced in a run. Prior experience has shown that the distribution of the contents has a mean of 13.25 ounces and a standard deviation of 2.17 ounce. What is the probability that the average contents of the 121 sample cans is less than 12.88 ounces? a) 0.076 b) 0.970 c) 0.030 3/9 12/20/2015 Print Test d) 0.061 e) 0.939 Question 8 Your answer is CORRECT. A random variable X has a probability distribution as follows: X 0 1 2 3 4 P(X) 3k 4k 5k 6k 5k What is P(X < 3)? a) b) c) d) e) 12 23 1 23 18 23 20 23 Cannot be determined. Question 9 Your answer is CORRECT. Find a value of c so that P (Z a) 0.553 b) −0.704 c) −1.068 d) 0.901 e) 0.808 ≤ c) = 0.71 . Question 10 Your answer is CORRECT. 4/9 12/20/2015 Print Test The following table displays the results of a sample of 100 in which the subjects indicated their favorite ice cream of three listed. The data are organized by favorite ice cream and age group. What is the probability that a person chosen at random will be under 20 years old if he or she favors chocolate? Age Chocolate Vanilla Strawberry Over 40 12 20­40 12 Under 20 13 a) b) c) d) e) 5 9 18 13 14 4 24 37 13 37 13 100 13 30 87 100 Question 11 Your answer is CORRECT. A random sample of 100 observations produced a sample proportion of 0.25. An approximate 95% confidence interval for the population proportion p is between a) 0.165 and 0.335 b) 0.165 and 0.321 c) 0.179 and 0.321 d) 0.207 and 0.293 e) 0.152 and 0.348 Question 12 Your answer is CORRECT. Data for gas mileage (in mpg) for different vehicles was entered into a software package and part of the ANOVA table is shown below: 5/9 12/20/2015 Print Test Source DF SS MS Vehicle 5 642 321.00 Error Total 66 206 3.12 71 848 Determine the value of w needed to apply Tukey's procedure for the distance allowed between means at the 5% significance level. a) 2.1 b) 3.6 c) 4.2 d) 102.8 e) 0.5 Question 13 Your answer is CORRECT. If the P­value is larger than the level of significance α, then the researcher should __________ at level α. a) Fail to reject H0 b) Reject H0 c) Accept H0 Question 14 Your answer is CORRECT. The one­sample t statistic for a test of H0: μ = 11 vs. Ha: μ < 11 based on n = 13 observations has the test statistic value of t = −1.25. What is the p­value for this test? a) 0.418 b) 0.882 c) 0.000 d) 0.118 6/9 12/20/2015 e) Print Test 0.235 Question 15 Your answer is CORRECT. This is a written question, worth 9 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full credit. Problem Code: 1561 The amount of lateral expansion (in mils) was determined for a sample of n = 9 pulsed­power gas metal arc welds used in LNG ship containment tanks. The resulting sample standard deviation was s = 2.83 mils. Assuming normality, derive a 95% confidence interval for σ, the population standard deviation. (Hint: You will first need to come up with a 95% confidence interval for the variance) a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem. Question 16 Your answer is CORRECT. This is a written question, worth 9 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) on youranswer sheet for full credit. Problem Code: 1662 Consumer Reports rated 77 cereals on a scale of 0 to 100. The number of grams of sugar contained in each serving of the corresponding cereals was also recorded. Using sugar as the explanatory variable and the Consumer Reports rating as the dependent variable, computer output of the data is as follows (the p­values are intentionally left blank): Predictor Coef StDev T P Constant 58.93 1.847 30.58 ­­­ Sugars − 2.56 0.28 − 9.98 ­­­ S = 9.204 R­Sq = 61.2% R­Sq(adj) = 59.9% Part a: What is the regression equation? Part b: Calculate the 95% confidence interval of the slope of the regression line for all cereals. Part c: Use the information provided to test whether there is a significant relationship between the sugar content and the Consumer Report rating at the 5% level. 7/9 12/20/2015 Print Test a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem. Question 17 Your answer is CORRECT. This is a written question, worth 9 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full credit. Problem Code: 1723 Suppose the random variable X has CDF given by the function 0 ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ F (x) = ⎨ x < 0 1 ⎪ 27 ⎪ ⎪ ⎪ ⎩ ⎪ 1 x 3 0 ≤ x ≤ 3 x > 3 Part a: Find P (X ≤ 1) . Part b: Find P (0.5 ≤ X ≤ 1) . Part c: Find the desity function f (x) . a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem. Question 18 Your answer is CORRECT. This is a written question, worth 9 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full credit. Problem Code: 1881 Suppose you wish to test if a number cube (die) is loaded or not. If the die is not loaded, the theoretical probabilities for each roll should be: 1 2 3 4 5 6 16 2/3 % 16 2/3 % 16 2/3 % 16 2/3 % 16 2/3 % 16 2/3 % You roll the die 84 times and come up with the following distribution: 8/9 12/20/2015 Print Test 1 2 3 4 5 6 12 11 20 13 15 13 Part a: What type of test should be used in this situation? Part b: State the hypothesis. Part c: What is the test statistic? Part d: Find the p ­value and state your conclusion. a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem. 9/9 ...
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