Q: A researcher is testing whether the proportion of Canadians who believe global warming is a fact is different from the proportion of Americans (0.45). Which is the correct set of hypotheses?

$$H_0$$: p = 0.45$$, H_a$$: p \neq 0.45$$

Question 1

Which of the following best describes the P-value in hypothesis testing?

Accepted Answer

The probability of observing a statistic as extreme as, or more extreme than, the observed value, given that the null hypothesis is true.

Question 2

A researcher is testing whether the proportion of Canadians who believe global warming is a fact is different from the proportion of Americans (0.45). Which is the correct set of hypotheses?

Accepted Answer

$$H_0$$: p = 0.45$$, H_a$$: p 
eq 0.45$$

Question 3

In the context of hypothesis testing, what does the shaded region in the first image (right tail) represent?

Accepted Answer

The P-value for an upper-tailed test.

Question 4

Given a sample proportion $$\hat{p} = 0.58$$, $$n = 200$$, and $$p_0 = 0.54$, what is the formula for the test statistic z$ in a one-proportion z-test?

Accepted Answer

$$z = \frac{\hat{p} - p_0$}{\sqrt{p_0$(1-p_0$)/n}}$$

Question 5

If a hypothesis test yields a P-value of 0.128 and the significance level $$\alpha is 0.05$$, what is the correct conclusion?

Accepted Answer

Fail to reject the null hypothesis.

Question 6

Which of the following is a correct interpretation of a 99% confidence interval for a population proportion?

Accepted Answer

If we repeated the sampling process many times, about 99% of the calculated intervals would contain the true proportion.

Question 7

Which error is made when the null hypothesis is true, but we reject it?

Accepted Answer

Type I error

Question 8

What is the probability of making a Type I error in a hypothesis test?

Accepted Answer

$$\alpha$$

Question 9

Which of the following increases the power of a statistical test?

Accepted Answer

Increasing the significance level $$\alpha$$

Question 10

A two-tailed hypothesis test at $$\alpha = 0.05$$ corresponds to which confidence interval?

Accepted Answer

95% confidence interval

Question 11

In the context of the salinity example, which formula is used for the test statistic when the population standard deviation $$\sigma is $$known?

Accepted Answer

$$z = \frac{\bar{y} - \mu_0$}{\sigma/\sqrt{n}}$$

Question 12

Which of the following is NOT an assumption for the one-proportion z-test?

Accepted Answer

Population mean is normally distributed.

Question 13

If the P-value is less than the chosen $$\alpha$$ level, what should you conclude?

Accepted Answer

Reject the null hypothesis.

Question 14

Which of the following best describes the power of a statistical test?

Accepted Answer

The probability of correctly rejecting a false null hypothesis.

Question 15

A large sample size in hypothesis testing will generally:

Accepted Answer

Decrease the probability of a Type II error.

Question 16

Which of the following statements about statistical significance is TRUE?

Accepted Answer

Statistical significance means the observed effect is unlikely under the null hypothesis.

Question 17

In a two-tailed test, what is the rejection region for the null hypothesis at significance level $$\alpha$$?

Accepted Answer

The area in both tails, each with probability $$\alpha/2$$

Question 18

Which of the following is a correct statement about the relationship between confidence intervals and hypothesis tests?

Accepted Answer

A 95% confidence interval corresponds to a two-sided test at $$\alpha = 0.05.$$

Question 19

Which of the following is a potential consequence of using a very large sample size in hypothesis testing?

Accepted Answer

It may lead to statistical significance for a difference that is not practically important.

Question 20

Which of the following best describes a Type II error?

Accepted Answer

Failing to reject the null hypothesis when it is false.

More About Tests of Hypothesis: One-Proportion and One-Mean z-Tests

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