AP Stats Unit 6 Review

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

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CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

CCSS.HSS.ID.A.4

 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.

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CCSS.HSS.IC.B.4

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?

• 
• 
• 
• 

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CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

CCSS.HSS.ID.A.4

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.

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CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

Which of the following are true statements?

I. A P-value is a conditional probability.

II. The P-value is the probability that the null hypothesis is true.

III. The P-value can be negative or positive depending upon whether the sample statistic is less than or greater than the claimed value of the population parameter in the null hypothesis.

• I only

• II only

• III only

• None of them

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CCSS.HSS.IC.B.5

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.

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CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

A newspaper article indicates that an estimate of the unemployment rate involves a sample of 47,000 people. If the reported rate must be within 0.2% and the rate is known to be 8%, find the corresponding level of confidence.

• 96%

• 93%

• 89%

• 75%

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CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

CCSS.HSS.ID.A.4

The level of significance of a hypothesis test is also commonly referred to as the:

• p-value

• Type 2 error

• a standardized value

The observed significance level of a hypothesis test is also commonly referred to as the

• p-value for that test

• Type 1 error

• the z-score

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CCSS.HSS.ID.A.4

In a two-tailed large sample z test with calculated test statistics of 1.93, the

P-value is

• 0.708

• 0.054

• 0.027

• 0.354

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CCSS.HSS.ID.A.4