Question : A marketing research company is estimating which of two soft drinks college students prefer : 2150494

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

74) A marketing research company is estimating which of two soft drinks college students prefer. A random sample of 168 college students produced the following confidence interval for the proportion of college students who prefer drink A: (.344, .494). Is this a large enough sample for this analysis to work?

A) Yes, since n = 168 (which is 30 or more).

B) Yes, since both nhat(p) ≥ 15 and nhat(q) ≥ 15.

C) No.

D) It is impossible to say with the given information.

Solve the problem.

83) A marketing research company is estimating which of two soft drinks college students prefer. A random sample of n college students produced the following 99% confidence interval for the proportion of college students who prefer drink A: (.232, .592). Identify the point estimate for estimating the true proportion of college students who prefer that drink.

A) .592

B) .18

C) .412

D) .232

85) What type of car is more popular among college students, American or foreign? One hundred fifty-nine college students were randomly sampled and each was asked which type of car he or she prefers. A computer package was used to generate the printout below of a 90% confidence interval for the proportion of college students who prefer American automobiles.

SAMPLE PROPORTION = .396

SAMPLE SIZE = 159

UPPER LIMIT = .460

LOWER LIMIT = .332

Which of the following is a correct practical interpretation of the interval?

A) 90% of all college students prefer American cars between .332 and .460 of the time.

B) We are 90% confident that the proportion of all college students who prefer foreign cars falls between .332 and .460.

C) We are 90% confident that the proportion of the 159 sampled students who prefer American cars falls between .332 and .460.

D) We are 90% confident that the proportion of all college students who prefer American cars falls between .332 and .460.

87) A newspaper reported on the topics that teenagers most want to discuss with their parents. The findings, the results of a poll, showed that 46% would like more discussion about the family's financial situation, 37% would like to talk about school, and 30% would like to talk about religion. These and other percentages were based on a national sampling of 532 teenagers. Estimate the proportion of all teenagers who want more family discussions about school. Use a 95% confidence level.

A) .37 ± .002

B) .63 ± .041

C) .63 ± .002

D) .37 ± .041

88) A newspaper reported on the topics that teenagers most want to discuss with their parents. The findings, the results of a poll, showed that 46% would like more discussion about the family's financial situation, 37% would like to talk about school, and 30% would like to talk about religion. These and other percentages were based on a national sampling of 549 teenagers. Using 99% reliability, can we say that more than 30% of all teenagers want to discuss school with their parents?

A) No, since the value .30 is not contained in the 99% confidence interval.

B) Yes, since the values inside the 99% confidence interval are greater than .30.

C) Yes, since the value .30 falls inside the 99% confidence interval.

D) No, since the value .30 is not contained in the 99% confidence interval.

89) A random sample of 4000 U.S. citizens yielded 2190 who are in favor of gun control legislation. Find the point estimate for estimating the proportion of all Americans who are in favor of gun control legislation.

A) 2190

B) .5475

C) .4525

D) 4000

93) A confidence interval was used to estimate the proportion of statistics students who are female. A random sample of 72 statistics students generated the following 99% confidence interval: (.438, .642). State the level of reliability used to create the confidence interval.

A) 64.2%

B) 99%

C) between 43.8% and 64.2%

D) 72%

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

99) We intend to estimate the average driving time of a group of commuters. From a previous study, we believe that the average time is 42 minutes with a standard deviation of 9 minutes. We want our 90 percent confidence interval to have a margin of error of no more than plus or minus 3 minutes. What is the smallest sample size that we should consider?

A) 3

B) 5

C) 25

D) 74

100) A local men's clothing store is being sold. The buyers are trying to estimate the percentage of items that are outdated. They will choose a random sample from the 100,000 items in the store's inventory in order to determine the proportion of merchandise that is outdated. The current owners have never determined the percentage of outdated merchandise and cannot help the buyers. How large a sample do the buyers need in order to be 90% confident that the margin of error of their estimate is about 3%?

A) 752

B) 3007

C) 1504

D) 457

101) A confidence interval was used to estimate the proportion of statistics students who are female. A random sample of 72 statistics students generated the following confidence interval: (.438, .642). Using the information above, what sample size would be necessary if we wanted to estimate the true proportion to within 2% using 95% reliability?

A) 2386

B) 2401

C) 2305

D) 2498

102) Sales of a new line of athletic footwear are crucial to the success of a company. The company wishes to estimate the average weekly sales of the new footwear to within $500 with 90% reliability. The initial sales indicate that the standard deviation of the weekly sales figures is approximately $1500. How many weeks of data must be sampled for the company to get the information it desires?

A) 5 weeks

B) 12,178 weeks

C) 15 weeks

D) 25 weeks

103) The director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a 24-hour period. The director randomly selects 64 different 24-hour periods and determines the number of admissions for each. For this sample, overbar(x) = 19.8 and s² = 36. If the director wishes to estimate the mean number of admissions per 24-hour period to within 1 admission with 95% reliability, what is the minimum sample size she should use?

A) 4979

B) 71

C) 139

D) 2541

104) A previous random sample of 4000 U.S. citizens yielded 2250 who are in favor of gun control legislation. How many citizens would need to be sampled for a 90% confidence interval to estimate the true proportion within 1%?

A) 7036

B) 6224

C) 6660

D) 6766

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

110) A local men's clothing store is being sold. The buyers are trying to estimate the percentage of items that are outdated. They will choose a random sample from the 100,000 items in the store's inventory in order to determine the proportion of merchandise that is outdated. The current owners have never determined the percentage of outdated merchandise and cannot help the buyers. How large a sample do the buyers need in order to be 99% confident that the margin of error of their estimate is within 4%?

111) Suppose you wanted to estimate a binomial proportion, p, correct to within .01 with probability 0.99. What size sample would need to be selected if p is known to be approximately 0.75?

112) The standard deviation of a population is estimated to be 275 units. To estimate the population mean to within 48 units with 90% reliability, what size sample should be selected?

113) Sales of a new line of athletic footwear are crucial to the success of a newly formed company. The company wishes to estimate the average weekly sales of the new footwear to within $250 with 95% reliability. The initial sales indicate that the standard deviation of the weekly sales figures is approximately $1700. How many weeks of data must be sampled for the company to get the information it desires?

Solve the problem.

118) For the given combination of α and degrees of freedom (df), find the value of χ and ((2) over ((1 - α/2))) that would be used to find the upper endpoint of a confidence interval for σ².

α = 0.01, df = 6

A) 0.675727

B) 18.5476

C) 0.411740

D) 0.872085

119) Given the values of overbar(x), s, and n, form a 99% confidence interval for σ².

overbar(x) = 10.9, s = 5.1, n = 17

A) (13.01, 71.6)

B) (12.14, 80.93)

C) (12.9, 85.99)

D) (2.55, 14.04)

120) Given the values of overbar(x), s, and n, form a 99% confidence interval for σ.

overbar(x) = 5.3, s = 9.7, n = 24

A) (48.98, 233.69)

B) (7, 15.29)

C) (7.21, 14.57)

D) (5.05, 24.09)

121) The daily intakes of milk (in ounces) for ten five-year old children selected at random from one school were:

10.6 23.5 25.6 31.6 14.1

16.9 16.1 13.3 31.5 14.1

Find a 99% confidence interval for the standard deviation, σ, of the daily milk intakes of all five-year olds at this school. Round to the nearest hundredth when necessary.

A) (4.77, 15.81)

B) (4.62, 15.81)

C) (0.99, 3.59)

D) (4.77, 17.60)

122) The mean systolic blood pressure for a random sample of 28 women aged 18-24 is 115.1 mm Hg and the standard deviation is 13.4 mm Hg. Construct a 90% confidence interval for the standard deviation σ, of the systolic blood pressures of all women aged 18-24. Round to the nearest hundredth when necessary.

A) (10.83, 16.92)

B) (10.99, 17.33)

C) (10.45, 18.76)

D) (11.49, 16.36)

123) The mean replacement time for a random sample of 12 CD players is 8.6 years with a standard deviation of 2.6 years. Construct the 99% confidence interval for the population variance, σ². Assume the data are normally distributed, and round to the nearest hundredth when necessary.

A) (1.07, 10.99)

B) (2.78, 28.56)

C) (1.67, 5.34)

D) (3.01, 24.35)

124) A random sample of 15 crates have a mean weight of 165.2 pounds and a standard deviation of 12.6 pounds. Construct a 95% confidence interval for the population standard deviation σ. Assume the population is normally distributed, and round to the nearest hundredth when necessary.

A) (85.1, 394.87)

B) (9.22, 19.87)

C) (9.69, 18.39)

D) (2.6, 5.6)

125) The volumes (in ounces) of juice in eight randomly selected juice bottles are as follows:

15.2 15.7 15.8 15.6

15.4 15.4 15.0 15.1

Find a 99% confidence interval for the standard deviation, σ, of the volumes of juice in all such bottles. Round to the nearest hundredth when necessary.

A) (0.19, 0.88)

B) (0.16, 0.66)

C) (0.17, 0.77)

D) (0.17, 0.66)