Midterm Practice Questions 2

1 Practice questions for the Midterm 1. The weekly salary paid to employees of a company that supplies part-time laborers averages $700 with a standard deviation of $200. If the weekly salaries are Normally distributed, find the fraction of employees that make less than $300 per week. A) 2.5% B) 16% C) 50% D) 84% E) 97.5% 2. Consider the problem above. What is the dollar amount x , such that 84% of employees make more than x ? A) $200 B) $300 C) $500 D) $900 E) $1100 3. Consider a Normal density curve centered at x = 0.5. The area under the curve between x = -1 and x = 0 is __________ the area under the same density curve between x = 0 and x = 1. A) smaller than B) greater than C) equal to D) A, B or C depending on the value of the standard deviation 4. Historically, at the Newport Department Store, the proportion of delinquent accounts has been 14%. Newport conducted a customer communication campaign to try to reduce this percentage. After the campaign, Newport randomly selected 250 customer accounts and found that 30 were delinquent. Which of the following test statistics would be used to find the p- value to use when testing the hypothesis “the campaign had an effect” vs. “the campaign did not have an effect”? A) 250 / ) 86 . 0 ( 14 . 0 14 . 0 30 . 0 − B) 250 / ) 86 . 0 ( 14 . 0 12 . 0 14 . 0 − C) 250 / ) 88 . 0 ( 12 . 0 14 . 0 12 . 0 − D) 250 / ) 86 . 0 ( 14 . 0 14 . 0 12 . 0 − E) 250 / ) 7 . 0 ( 3 . 0 30 . 0 14 . 0 − 700 300 400 EMPIRICAL RULE 25 400 25 795 441 EMPIRICAL i 100 95 51 32 2.510 2784 1 i 16 f Lx I I StDEv 700 200 500 EMMMIN RULE AREA UNDER CURVE 50 0.12 0 12 0 1 formula cheek proportion

2 5. Which of the following is true of the sample proportion? A) Its expected value equals the population proportion B) It has a uniform distribution. C) All of the above D) None of the above 6. Using the above side-by-side boxplots, all of the following can be established, except: A) D has no outliers. B) Mean of B is greater than the mean of D. C) C is left-skewed. D) IQR of B is larger than the IQR of A. E) Range of A is greater than the range of D. 7. The following probability distribution has been assessed for the number of car accidents that occur in a Midwestern city each day: Accidents Probability 0 0.25 1 0.20 2 0.30 3 0.15 4 0.10 This distribution is an example of a A) Uniform distribution B) Normal distribution. C) continuous distribution. D) discrete distribution. E) sampling distribution. Data D C B A 350 300 250 200 150 100 50 0 Boxplot of A, B, C, D SAMPLE PROPORTION Bonnot

4 A) Only for large sample sizes B) For each given sample size C) Only for small sample sizes D) None of the above 14. A drug company produces capsules that are designed to contain a specified amount of the active ingredient. The mean amount of the ingredient in one capsule is 150 mg, the SD is 5 mg and the distribution of the amount is Normal. A sample of 25 capsules is selected at random, and the production process is stopped if the average amount of the active ingredient in this sample is outside of the range [148mg to 152mg]. What is the probability (approximately) that the production is stopped? A) 2.5% B) 5% C) 16% D) 32% E) 95% 15. Which of the following sample statistics is a measure of spread? A) Range B) SD C) IQR D) All of the above E) None of the above 16. You have computed the following 95% confidence interval for a population mean P : [7.2 , 9.2]. For the test of H 0 : P = 9.57 vs. H A : P z ±²³´ , which of the following will be your decision at the 1% significance level? A) Reject the null hypothesis. B) Do not reject the null hypothesis. C) More information is needed to make the decision. 17. It has been claimed that at least 65% of homeowners would prefer to heat with electricity instead of gas. You think that this percentage might actually be lower and want to see how much evidence the data provides in support of your suspicion. You collect a random sample of 200 homeowners and discover that 120 of them prefer electric heating to gas. How should you formulate the null hypothesis for your test? A) π≤0.6 B) π ≥0.6 C) π ≥0.65 D) π ≤0.65 E) π =0.65 18. The value of the test statistic for the above problem is: A) -1.44 B) 1.44 C) -1.48 D) 1.48 6 3 I 1550 s f 25 away i 2 JP Y 0.05 NEW Alpha O 101

5 19. Which of the following is true about t -distributions? A) they are left-skewed B) they are specified by one parameter: the mean C) as the degrees of freedom increase, they approach the chi-square distribution D) they have less probability in the tails than the standard normal distribution E) None of the above 20. Confidence interval for the population mean will be: A) Wider for a sample size of 50 than for a sample size of 40. B) Wider for 99% confidence level than for 95% confidence level. C) Wider for a standard deviation of 3.2 than for a standard deviation of 5.8 D) All of the above E) None of the above 21. When carrying out a significance test of H 0 : π = 0.65 vs. H a : π ≠ 0.65, we rejec t H 0 at the significance level α if and only if the p-value is: A) less than α/2 B) greater than α C) greater than z α/2 D) less than α E) greater than z α 22. Insurance companies track life expectancy information to assist in determining the cost of life insurance policies. Last year the average life expectancy of all policyholders was 77 years. ABI Insurance wants to determine if their clients now have a longer life expectancy, on average, so they randomly sample some of their recently paid policies. The insurance company will only change their premium structure if there is strong evidence that people who buy their policies are living longer than before. The sample of 20 people has a mean of 78.6 years and a standard deviation of 4.48 years. The correct null and alternative hypotheses are A) H 0 : µ ≤ 77 and H A : µ > 77 B) H 0 : µ ≤ 78.6 and H A : µ > 78.6 C) H 0 : µ ≥ 77 and H A : µ < 77 D) H 0 : µ ≥ 78.6 and H A : µ < 78.6 E) H 0 : µ = 78.6 and H A : µ ≠ 78.6 23. A mail-order business prides itself in its ability to fill customers' orders in no more than six calendar days, on average. Periodically, the operations manager selects a random sample of customer orders and tests the claim of the company. On one occasion when a sample of 39 orders was selected, the average number of days was 6.65 with a sample standard deviation of 1.5 days. What are the name and the value of the appropriate test statistic? A) t-statistic = 2.71 B) t-statistic = 0.43 C) z-statistic = 2.71 D) z-statistic = 0.43 L t a 2 x a n t somatic

7 28. Which of the following is true? a. Confidence intervals are wider for 88% confidence level than for 83% confidence level. b. All chi-square distributions have the mean of zero. c. All t distributions are skewed to the right. d. All of the above e. None of the above 29. Which of the following is true? E) If IQR=0, all the values in the sample are exactly the same. F) The mean of every normal distribution is zero. G) Standard deviation is robust. H) Standard deviation is a measure of the center of the distribution. I) None of the above. 30. Stanford-Binet IQ Test scores are normally distributed with a mean score of 100 and a standard deviation of 16. Find the value x for which: Probability that (a randomly selected person has an IQ test score less than x) is approximately 84%. a. 68 b. 84 c. 100 d. 116 e. 132 31. Consider the previous question. What is the probability that the average score of 4 randomly selected individuals is greater than 116? A) About 2.5% B) About 5% C) About 16% D) About 68% E) About 84% 32. You are doing a two-sided hypothesis test for the population proportion using a sample of 50, and you get a test statistic of 2.0. This means: (Use the following z or t values: ࠵? 0.1 =1.282, ࠵? 0.05 =1.645, ࠵? 0.025 =1.96; ࠵? 0.1 =1.299, ࠵? 0.05 =1.677, ࠵? 0.025 =2.01) a. you cannot reject the null hypothesis at the 10% significance level; b. you can reject the null hypothesis at the 10% significance level, but not at the 5% level; c. you can reject the null hypothesis at the 5% significance level. x x x x mum mom S 8 mean neo UE 27 1 96 Zo 025

8 33. Consider a normal density curve centered at x = 2. The area under the curve between x = 2 and x = 3 is __________ the area under the same density curve between x = 0 and x = 1. A) Less than B) Greater than C) Equal to D) Twice as large as E) More information is needed to answer this question Consider the following information for problems 10 – 12. Below is a histogram and the five number summary of salaries (in $) for a sample of U.S. marketing managers. Min Q1 Median Q3 Max 46360 69693 77020 91750 129420 34. The shape of this distribution is A) symmetric. B) bimodal. C) right skewed. D) left skewed. E) normal. 35. The IQR for these data is A) $83,060.

10 40. Hoping to lure more shoppers downtown, a city builds a new public parking garage in the central business district. The city plans to pay for the parking structure through parking fees. For a 21 day period, daily fees are collected with a sample mean of $1251 and a sample standard deviation of $160. Find the margin of error of a 95% confidence interval for the mean daily revenue of this parking garage. Here are some useful z and t values: ࠵? 0.05 =1.645, ࠵? 0.025 =1.96; for df=21: ࠵? 0.05 =1.721, ࠵? 0.025 =2.08; for df=20: ࠵? 0.05 =1.725, ࠵? 0.025 =2.086. A) 34.9 B) 60.2 C) 68.4 D) 72.6 E) 72.8 41. Among the various services a luxury spa offers to its customers are Swedish massage and aroma therapy. The spa found that 75% of all customers ask to get a Swedish massage and that 80% of all customers ask for aroma therapy. They also found that 65% of customers ask for both a Swedish massage and aroma therapy. What is the probability that someone who asks for aroma therapy also asks for a Swedish massage? A) .65 B) .75 C) .80 D) .8125 E) None of the above 42. For the luxury spa problem above, if we were to change the percentage of customers who request BOTH a Swedish massage AND aroma therapy, what value for this percentage would enable us to say the two events “customer asks for a Swedish massage” and “customer asks for aroma therapy” are independent? (Assume other numbers remain the same.) Pls A Pty 0 812

11 A) .60 B) .70 C) .75 D) .80 E) There is no value for this probability that will enable us to say the two events are independent pls Pla D