Question 1(Multiple Choice Worth 4 points)

(05.04)

Faculty members at Splitty Town High School want to determine whether there are enough students to have a Spring Formal. Seventy-two of the 225 students said they would attend the Spring Formal. Construct and interpret a 95% confidence interval for p.

A) The 95% confidence interval is (0.2590, 0.3810). There is a 95% chance that a randomly selected student who will attend the Spring Formal lies between 25.91% and 38.10%.

B) The 95% confidence interval is (0.2590, 0.3810). Ninety-five percent of all samples of this size will yield a confidence interval of (0.2590, 0.3810).

C) The 95% confidence interval is (0.2590, 0.3810). We are 95% confident that the true proportion of students attending the Spring Formal is between 25.91% and 38.10%.

D) The 95% confidence interval is (0.6190, 0.7410). Ninety-five percent of all samples of this size will yield a confidence interval of (0.6190, 0.7410).

E) The 95% confidence interval is (0.6190, 0.7410). We are 95% confident that the true proportion of students attending the Spring Formal is between 61.90% and 74.10%.

Question 2(Multiple Choice Worth 4 points)

(05.04)

Sebastian wants to estimate the proportion of the sophomores at his high school who like to waterski. He interviews a simple random sample of 60 of the 150 sophomores on campus. He finds that 19 like to waterski. Is the independent condition for finding confidence intervals met? Explain.

A) Yes, the independent condition for finding confidence intervals is met because np = 19 and n(1 p) = 41, both of which are at least 10.

B) Yes, the independent condition for finding confidence intervals is met because the sample size is greater than 30.

C) No, the independent condition for finding confidence intervals is not met because np = 19 and n(1 p) = 41, both of which are less than 100.

D) No, the independent condition for finding confidence intervals is not met, because 60 is more than 10% of 150.

E) Yes, the independent condition for finding confidence intervals is met because the sample is a simple random sample.

Question 3(Multiple Choice Worth 4 points)

(05.04)

Cilantro tastes like soap to some people. This soap taste is inherited through the olfactory receptor geneOR6A2. About 14% of the population has this gene. You want to estimate the proportion of Americans who have this gene. How large a sample must you test, with a 3% margin of error and 95% confidence, to estimate the proportion of people who carry theOR6A2gene?

A) 514 people

B) 134 people

C) 17,689 people

D) 35 people

E) 1,028 people

Question 4(Multiple Choice Worth 4 points)

(05.04)

You collect a random sample of size n from a population and calculate a 95% confidence interval. Which of the following strategies produces a new confidence interval with an increased margin of error?

A) Use a 98% confidence level.

B) Use a 90% confidence level.

C) Increase the sample size.

D) Use the same confidence level, but compute the interval n times. Approximately 5% of these intervals will be larger.

E) Nothing can guarantee that you will obtain a larger margin of error. You can only say that the chance of obtaining a larger interval is 0.05

Question 5(Multiple Choice Worth 4 points)

(05.04)

In a recent text message survey, 4,000 randomly selected teenagers were asked to cite their favorite Florida college football team. Twenty-two of 40 teenagers said the Florida Gators are their favorite team. A 99% confidence interval to estimate the true proportion of teenagers who like the Florida Gators is found to be (0.3474, 0.7526). Which of the following is a correct interpretation of the confidence level?

A) Ninety-nine percent of all samples of this size would yield a confidence interval of (0.3474, 0.7526).

B) There is a 99% chance that the true proportion of teenagers who like the Florida Gators is (0.3474, 0.7526).

C) Ninety-nine percent of all the samples of size 4,000 lie in the confidence interval (0.3474, 0.7526).

D) Ninety-nine percent of the time, the procedure used to generate this interval will capture the true proportion of teenagers who like the Florida Gators.

E) There is a 99% chance that randomly selected teenagers will be part of the 55% who like the Florida Gators.