# MATHEMATICS

15.Suppose on a highway with a speed limit of 65 mph, the speed of cars are independent and normally distributed with an average speed = 65 mph and standard deviation = 5 mph. What is the standard deviation for the sample mean speed in a random sample of n = 100 cars?

A) 0.5

B) 13

C) 3.25

16.The z* multiplier for a 90% confidence interval is

A) 1.65

B) 2.58

C) 2.33

D) 1.96

17.A random sample of 600 adults is taken from a population of over one million, in order to compute a confidence interval for a proportion. If the researchers wanted to decrease the width of the confidence interval, they could

A) decrease the size of the population.

B) increase the size of the population.

C) increase the size of the sample.

D) decrease the size of the sample.

18.Which statement is not true about confidence intervals?

A) A confidence interval between 20% and 40% means that the population proportion lies between 20% and 40%.

B) A 99% confidence interval procedure has a higher probability of producing intervals that will include the population parameter than a 95% confidence interval procedure.

C) An approximate formula for a 95% confidence interval is sample estimate ± margin of error.

D) A confidence interval is an interval of values computed from sample data that is likely to include the true population value.

19.In a survey of n = 950 randomly selected individuals, 17% answered yes to the question “Do you think the use of marijuana should be made legal or not?” A 90% confidence interval for the proportion of all Americans in favor of legalizing marijuana is

A) 0.139 to 0.201

B) 0.150 to 0.190

C) 0.142 to 0.198

D) 0.146 to 0.194

20.Suppose that a confidence interval for a population proportion p is to be calculated. For a sample size n = 1000 and sample proportion p-hat = 0.35 what is the approximate margin of error for a 95% confidence interval?

A) 0.025

B) 0.011

C) 0.0003

D) 0.030

21.In a past General Social Survey, a random sample of men and women answered the question “Are you a member of any sports groups?” Based on the sample data, 95% confidence intervals for the population proportion who would answer yes are 0.13 to 0.19 for women and 0.25 to 0.33 for men. Based on these results, you can reasonably conclude that

A) there is no conclusive evidence of a gender difference in the proportions of men and women who belong to sports clubs.

B) at least 25% of American men and American women belong to sports clubs.

C) there is conclusive evidence of a gender difference in proportions of American men and American women who belong to sports clubs.

22.Which of the following statements is most correct about a confidence interval for a mean?

A) It provides a good guess for the range of values the population mean is likely to have in repeated samples.

B) It provides a range of values, any of which is a good guess at the possible value of the population mean.

C) It provides a good guess for the range of values the sample mean is likely to have in repeated samples.

D) It provides a range of values, any of which is a good guess at the possible value of the sample mean.

23.A randomly selected sample of n =51 men in Brazil had an average lifespan of 59 years. The standard deviation was 10 years and the standard error was 1.400. Calculate a 98% confidence interval for the average lifespan for all men in Brazil.

A) (35.0, 83.0)

B) (55.6, 62.4)

C) (56.2, 61.8)

24.Suppose that 200 different polling organizations and academic researchers all do surveys in which the same question is asked. All 200 research groups construct a 90% confidence interval for the proportion who would say “yes” to this question. About how many of the 200 different 90% confidence intervals will capture the value of the population proportion?

A) 95

B) 90

C) 180

D) 190