91Ó°ÊÓ

In general, how does doubling the sample size change the confidence interval size? (A) Doubles the interval size (B) Halves the interval size (C) Multiplies the interval size by \(\sqrt{y}\) (D) Divides the interval size by \(\sqrt{y}\) (E) This question cannot be answered without knowing the sample size.

For a class project, an AP Statistics student wishes to determine a \(95 \%\) confidence interval for the proportion of students in the school building who have social media profile pages. The total number of students in the building is 3520 . Which of the following combinations of \(n\) and \(\hat{p}\) will satisfy the conditions for inference? (A) \(n=15\) and \(\hat{p}=0.67\) (B) \(n=25\) and \(\hat{p}=0.35\) (C) \(n=50\) and \(\hat{p}=0.17\) (D) \(n=75\) and \(\hat{p}=0.15\) (E) \(n=100\) and \(\hat{p}=0.91\)

A concerned-scientists action group wishes to learn the proportion of high school students who believe that humans are the principal cause of observed global warming. What sample size \(n\) should be obtained to determine with \(98 \%\) confidence the proportion to within \(\pm 2.5 \%\) ? (A) \(n \leq \sqrt{\frac{0.025}{2.326 \times 0.5}}\) (B) \(n \leq \sqrt{\frac{0.025}{2.326 \times 0.5}}\) (C) \(n \leq\left(\frac{2.326 \times 0.5}{0.025}\right)^{2}\) (D) \(n \leq \sqrt{\frac{0.025}{2.326 \times 0.5}}\) (E) \(n \leq\left(\frac{2.326 \times 0.5}{0.025}\right)^{2}\)

Which of the following is a true statement? (A) A well-planned hypothesis test should result in a statement either that the null hypothesis is true or that it is false. (B) The alternative hypothesis is stated in terms of a sample statistic. (C) If a sample is large enough, the necessity for it to be a simple random sample is diminished. (D) When the null hypothesis is rejected, it is because the null hypothesis is not true. (E) Hypothesis tests are designed to measure the strength of evidence against the null hypothesis.

You plan to perform a hypothesis test with a level of significance of \(\alpha=0.05 .\) What is the effect on the probability of committing a Type I error if the sample size is increased with everything else unchanged? (A) The probability of committing a Type I error decreases. (B) The probability of committing a Type I error is unchanged. (C) The probability of committing a Type I error increases. (D) The effect cannot be determined without knowing the relevant standard deviation. (E) The effect cannot be determined without knowing if a Type II error is committed.