AP Stats Testing Claims About Proportions

Identify the correct null hypothesis:

Is the proportion of babies born male different from 50%? In a sample of 200 babies, 96 were male. Test the claim using a level of significance of 1%.

• H₀: p = 0.50

• H₀: µ = 100

• H₀: p = 0.48

• H₀: µ = 96

When performing a test about the population proportion, what distribution would you need to use? 

• z

• t

• chi-square

What is the critical value (in a test about proportions) for a left-tailed test with α = 0.05 and n ≥ 30. 

• z₀ = -1.645

• z₀ = -2.33

• z₀ = -1.96

• z₀ = 2.58

A mayor is concerned about the percentage of city residents who express disapproval of his job performance. His political committee pays for a newspaper ad, hoping to keep his disapproval rating below 21%. They will use a follow up poll to access effectiveness. What are the correct null and alternative hypotheses?

• Ho: μ > 21

  Ha: μ < 21

• Ho: p > .20

  Ha: p < .20

• Ho: p < .21

  Ha: p > .21

• Ho: p > .21

  Ha: p < .21

The table shows the number or babies born on each day of the week.  Is there evidence that births are more likely on specific days of the week?

• yes, the p value is greater than .05

• no evidence, the p value is less than .05

• yes, the p value is less than .05

• no evidence, the p value is greater than .05

Answer explanation

The correct answer is yes, the p value is less than .05, indicating that there is evidence that births are more likely on specific days of the week.

What is the χ² _calculated value for the following situation.

• 6.65

• 6.66

• 0.00991

• 1

Answer explanation

The correct χ² calculated value is 6.65, which matches the provided answer choice.

• B
• C
• D
• E

In a survey of 104 students, it was found that 79 went to the homecoming game this year. A 99% confidence interval for p is (0.652, 0.868). Interpret this interval.

• 99% of the time the true proportion of people who went to the homecoming game this year is between 65.2% and 86.6%.

• The probability that the population proportion of people who went to the homecoming game this year is between 65.2% and 86.6% is 95%.

• Based on this sample, I am 99% confident that the true proportion of people who went to the homecoming game this year is between 65.2% and 86.6%.

• 99% of all possible intervals calculated this way will capture the true proportion of people who went to the homecoming game this year

The symbol for the sample proportion is __________.

• z*

• p̂

• E

• p

A research company wants to estimate the proportion of people who like oatmeal.  They want the confidence level to be 95%.  The company gets 325 people to sign up for the survey, but on the day that the survey is issued, only 250 people show up and take the survey.  What happens to the confidence interval?

• It gets larger

• It gets smaller

• It stays the same

• Too little information given