Statistics 300



Advanced College Prep Statistics

Final Review

2014-2015

Name: ________________________

Choose the best answer

1) High temperatures in a certain city for the month of August follow a uniform distribution over the interval 61ºF to 91ºF. Find the high temperature which 90% of the August days exceed.

a. 71ºF b. 64ºF c. 88ºF d. 91ºF

2) Find the area under the standard normal curve to the right of z = 1.

a. 0.8413 b. 0.1587 c. 0.5398 d. 0.1397

3) For a standard normal curve, find the z-score that separates the bottom 30% from the top 70%.

a. -0.1249 b. -0.4711 c. -0.5244 d. -0.9823

4) IQ test scores are normally distributed with a mean of 101 and a standard deviation of 20. An individual’s IQ score is found to be 111. Find the z-score corresponding to this value.

a. 2.00 b. 0.50 c. -2.00 d. -0.50

5) Suppose that prices of a certain model of new homes are normally distributed with a mean of $150,000. Find the percentage of buyers who paid between $150,000 and $152,400 if the standard deviation is $1200. (Empirical Rule!)

a. 34% b. 47.5% c. 99.7% d. 68%

6) A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 450 seconds and a standard deviation of 50 seconds. Between what times do we expect most (approximately 95%) of the boys to run the mile?

a. between 355 and 545 seconds

b. between 352 and 548 seconds

c. between 0 and 532.28 seconds

d. between 367.75 and 532.28 seconds

7) The number of violent crimes committed in a day possesses a distribution with a mean of 4.1 crimes per day and a standard deviation of 6 crimes per day. A random sample of 100 days was observed, and the sample mean number of crimes for the sample was calculated. Describe the sampling distribution of the sample mean.

a. shape unknown with mean = 4.1 and standard deviation = 0.6

b. approximately normal with mean = 4.1 and standard deviation = 6

c. approximately normal with mean = 4.1 and standard deviation = 0.6

d. shape unknown with mean = 4.1 and standard deviation = 6

8) The average score of all golfers for a particular course has a mean of 79 and a standard deviation of 3.5. Suppose 49 golfers played the course today. Find the probability that the average score of the 49 golfers exceeded 80.

a. .1293 b. .4772 c. .3707 d. .0228

9) The grade point averages for 10 randomly selected students in a statistics class with 125 students are listed below. Find the best point estimate for the mean.

2.4 2.5 1.9 3.5 2.1 3.1 2.9 3.9 3.6 2.6

a. 3.17 b. 2.6 c. 2.85 d. 28.5

10) Suppose a 95% confidence interval for[pic] turns out to be (120, 310). To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. Which of the following will result in a reduced interval width?

a. Decrease the confidence level

b. Increase the sample size

c. Increase the standard deviation

d. All of the choices will result in a reduced interval width

11) Suppose a 90% confidence interval for[pic] turns out to be (110, 260). Based on the interval, do you believe the average is equal to 270?

a. Yes, and I am 100% sure of it. b. No, and I am 100% sure of it.

c. Yes, and I am 90% sure of it. d. No, and I am 90% sure of it.

12) A nurse at a local hospital is interested in estimating the birth weight of infants, which is known to be normally distributed. How large a sample must she select if she desires to be 90% confident that the true mean is within 4 ounces of the sample mean? The standard deviation of the birth weights is known to be 6 ounces.

a. 6 b. 3 c. 2 d. 7

13) Find the critical t-value that corresponds to confidence level of 99% and n = 10.

a. 2.281 b. 2.262 c. 3.250 d. 3.169

14) Construct a 95% confidence interval for the population mean[pic]. Assume the population has a normal distribution. A sample of 20 college students had mean annual earnings of $3120 with a standard deviation of $677.

a. ($1324, $ 1567) b. ($2135, $2567) c. ($2803, $3437) d. ($2657, $2891)

15) A survey of 100 fatal accidents showed that 43 were alcohol related. Find a point estimate for p, the population proportion of accidents that were alcohol related.

a. 0.43 b. 0.301 c. 0.754 d. 0.57

16) A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. Use a 98% confidence interval to estimate the true proportion of students on financial aid.

a. .59 [pic] .003 b. .59[pic] .006 c. .59[pic] .081 d. .59[pic] .564

17) A private opinion poll is conducted for a politician to determine what proportion of the population favors decriminalizing marijuana possession. How large a sample is needed in order to be 99% confident that the sample proportion will not differ from the true proportion by more than 5%?

a. 543 b. 1327 c. 666 d. 13

18) Find the critical values, [pic]and [pic], for c = 0.98 and n = 20.

a. 10.117 and 32.852 b. 7.633 and 36.191 c. 8.907 and 38.582 d. 6.844 and 36.191

19) Assume that the heights of women are normally distributed. A random sample of 20 women has a mean height of 62.5 inches and a standard deviation of 1.2 inches. Construct a 98% confidence interval for the population variance[pic].

a. (0.9, 1.9) b. (0.6, 3.0) c. (0.8, 3.6) d. (0.8, 3.8)

20) The mean age of bus drivers in Chicago is greater than 46.1 years. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?

a. There is sufficient evidence to reject the claim [pic] > 46.1.

b. There is sufficient evidence to support the claim [pic] > 46.1.

c. There is not sufficient evidence to support the claim [pic] > 46.1.

d. There is not sufficient evidence to reject the claim [pic] > 46.1.

21) Suppose you want to test the claim that [pic] [pic] 3.5. Given a sample size of n = 39 and a level of significance of[pic]= 0.05, when should you reject[pic]?

a. Reject [pic] if the test statistic is greater than 1.645 or less than -1.645

b. Reject [pic] if the test statistic is greater than 2.575 or less than –2.575

c. Reject [pic] if the test statistic is greater than 1.96 or less than -1.96

d. Reject [pic] if the test statistic is greater than 2.33 or less than -2.33

22) You wish to test the claim that [pic]22 at a level of significance of[pic]= 0.01 and are given sample statistics n = 40, [pic]= 23.8, and s= 4.3. Compute the value of the test statistic. Round your answer to two decimal places.

a. 2.65 b. 1.96 c. 2.12 d. 3.51

23) Suppose you are using[pic]= 0.01 to test the claim that [pic]26 using a P-value. You are given the sample statistics n = 40, [pic]= 27.8, and s = 4.3. Find the P-value.

a. 0.0211 b. 0.9942 c. 0.1030 d. 0.0040

24) Find the test statistic t for a sample with n = 15, [pic]= 7.3, s = 0.8, and

[pic]= 0.05 if [pic]:[pic]7. Round your answer to three decimal places.

a. 1.728 b. 1.631 c. 1.452 d. 1.312

25) A local eat-in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. The owner of the store has determined that home delivery will be successful if the average time spent on the deliveries does not exceed 36 minutes. The owner has randomly selected 21 customers and has delivered pizzas to their home in order to test if the mean delivery time usually exceeds 36 minutes. Suppose the p-value for the test was found to be .0277. State the correct conclusion.

a. At[pic]= .03, we fail to reject[pic]. b. At[pic]= .05, we fail to reject[pic].

c. At[pic]= .02, we reject[pic]. d. At[pic]= .025, we fail to reject [pic]

26) The business college computing center wants to determine the proportion of business students who have personal computers (PC’s) at home. If the proportion exceeds 25%, then the lab will scale back a proposed enlargement of its facilities. Suppose 250 business students were randomly sampled and 85 have PC’s at home. What assumptions are necessary for this test to be satisfied?

a. The population has an approximately normal distribution.

b. The sample variance equals the population variance.

c. The sample mean equals the population mean.

d. None of the above are necessary.

27) Compute the test statistic,[pic], to test the claim [pic] 9.6 if n = 20,

s[pic]= 18.6, and [pic]= 0.01.

a. 12.82 b. 36.813 c. 33.41 d. 9.322

Answer each question.

28) The analytic scores on a standardized aptitude test are known to be normally distributed with mean [pic]=610 and standard deviation [pic]=115.

a. Draw a normal curve with the parameters labeled.

b. Shade the region that represents the proportion of test takers who scored less

than 725.

c. Suppose that the area under the normal curve to the left of X = 725 is 0.8413.

Provide two interpretations of this result.

1. _________________________________________________________

2. ________________________________________________________

29) In a recent study of 96 eighth graders, the mean number of hours per week that they watched television was 21.6. Assume s = 5.3 hours.

a. Find the 95% confidence interval of the mean.

b. If the standard deviation is doubled to 10.6, what will be the effect on the

confidence interval?

30) In a survey of 10 golfers, 2 were found to be left-handed. Is it practical to construct the 90% confidence interval for the population proportion, p? Explain.

31) The mean age of bus drivers in Chicago is 56.4 years. Write the null and alternative hypotheses.

H[pic]= _____________________ H[pic]= _______________________

32) The mean age of bus drivers in Chicago is 53.5 years. Identify the Type I and Type II errors for the hypothesis test of this claim.

Type I:__________________________________________________________________

________________________________________________________________________

Type II: ________________________________________________________________

________________________________________________________________________

33) A group of 49 randomly selected students has a mean age of 22.4 years with a standard deviation of 3.8. According to a recent survey, the mean age should be [pic]= 21.9 years. Test this hypothesis that the mean is actually higher by constructing a 98% confidence interval for the population mean.

34) Fifty-five percent of registered voters in a congressional district are registered Democrats. The Republican candidate takes a poll to assess his chances in a two-candidate race. He polls 1200 potential voters and finds that 621 plan to vote for the Democratic candidate. Does the Republican candidate have a chance to win? Test the hypothesis that the proportion is less than 55%. Use [pic] = 0.05.

35) According to a prestigious historical society, in 1999 7.2% of recent high school graduates believe that the Romans invented mayonnaise. A classics scholar believes that the percentage has increased since then. He randomly selects 125 recent high school graduates and finds that 17 of them believe in the Roman invention of mayonnaise. Test this researcher’s claim at the[pic]= 0.01 level of significance.

36) A fast food outlet claims that the mean waiting time in line is less than 3.6 minutes. A random sample of 20 customers has a mean of 3.4 minutes with a standard deviation of 0.8 minute. If[pic]= 0.05, test the fast food outlet’s claim using P-values.

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