AP Stats Unit 6

In a binomial distribution with n = 9, p = 0.52. Find the mean and standard deviation.

• mean = 1.50, sd = 4.32

• mean = 4.68, sd = 1.50

• mean = 2.16, sd = 2.25

• mean = 4.32, sd = 1.50

• mean = 4.32, sd = 2.25

Which of these variables is binomial?

• time it takes to attempt 10 independent free throws

• time it takes to make 10 independent free throws

• number of shots made in 10 independent attempts at free throws

• number of attempts to make 10 independent free throws

• none of these

A college basketball player makes 80% of her free throws. Suppose this probability is the same for each free throw she attempts, and free throw attempts are independent. The expected number of free throws required until she makes her first free throw of the season is

• 2

• 1.25

• 0.80

• 0.31

• 0.13

Suppose that 40% of the cars in a certain town are white. A person stands at an intersection waiting for a white car. Let X = the number of cars that must drive by until a white one drives by. P(X < 5) =

• 0.0518

• 0.1296

• 0.2592

• 0.8704

• 0.9482

A national polling company wants to estimate the true proportion of all people who believe that life exists elsewhere in the universe. Past data indicate that 65% of the general population believe that life exists elsewhere in the universe. If you want to estimate the true proportion of those who believe that life exists elsewhere in the universe, and you want 95% confidence within 5% of the true proportion, what is the least number of people that you need to sample?

• 265

• 320

• 402

• 350

Which of the following statements is INCORRECT?

• As confidence increases, the sample size must increase in order to maintain the same margin of error.

• As our confidence level increases, the margin of error will remain the same.

• As sample size increase, the confidence interval width will decrease.

• As confidence increases, the standard deviation must decrease in order to maintain the same margin of error.

In a random sample of 250 high school seniors, it was found that 65% of them went on to a four year university. Which of the following represents the 98% confidence interval that captures the true proportion of all high school seniors who go on to a four year university?

• 
• 
• 
• 

Your high school is considering adding an “Activity Bus” as an option for students who want a ride home 45 minutes after school ends. In order to see if there is enough demand to justify having one, your school selects a random sample of students to see if they would use the bus if it was available. If the school constructs a 98% confidence interval to estimate the proportion of students who would use the activity bus, instead of a 95% confidence interval, which one of the following statements would be TRUE?

• The 98% confidence interval would be narrower, and therefore more precise.

• The 98% confidence interval would be narrower, and therefore less precise.

• The 98% confidence interval would be wider, and therefore less precise.

• The 98% confidence interval would be wider, and therefore more precise.

A national polling company reports that 65% of the general population believe that life exists elsewhere in the universe. A national TV news station wants to investigate this story because they believe that 65% overestimates the amount of people in the population that hold that belief. They surveyed a random sample of 200 adults and found that 113 people hold this belief. What is the correct p-value and conclusion for the significance test performed at the 5% significance level?

• p-value = 0.0059; Because our p-value of 0.0059 is less than our significance level of 0.05, we fail to reject the null hypothesis that 65% of the general population believe that life exists elsewhere in the universe.

• p-value = 0.0059; Because our p-value of 0.0059 is less than our significance level of 0.05, we can reject the null hypothesis that 65% of the general population believe that life exists elsewhere in the universe.

• p-value = 0.0059; Because our p-value of 0.0059 is less than our significance level of 0.05, we can accept our alternative hypothesis that less than 65% of the general population believe that life exists elsewhere in the universe.

•  p-value = 0.565; Because our p-value of 0.0059 is greater than our significance level of 0.05, we fail to reject the null hypothesis that 65% of the general population believe that life exists elsewhere in the universe.

Evergreen High students were tardy at an alarming 9% of the time.  Administrators determined to fix the problem instituted new tardy rules.  After a few weeks with the new procedures a sample was to be taken to determine if the tardy rate was lower. Ho: p = 0.09 versus HA: p < 0.09, where p is the proportion of tardies   Of those listed below, what is the smallest sample size for which it would be appropriate to use the large sample z test to test the hypothesis?

• 90

• 100

• 110

• 120