Q: Which of the following is a correct set of null and alternative hypotheses for testing whether a coin is fair?

$$Ho: p = 0.5 \,\, Ha: p \neq 0.5$$

Q: For a two-tailed test with $$z = 1.79$$, what is the p-value if $$P(Z \u003c -1.79) = 0.03673$$?

p-value $$= 0.03673 \times 2 = 0.07346$$

Question 1

Which of the following best describes the significance level ($$\alpha) in $$hypothesis testing?

Accepted Answer

It is the probability of rejecting the null hypothesis when the null hypothesis is true.

Question 2

A p-value is calculated in a hypothesis test. Which interpretation is correct?

Accepted Answer

The p-value is the probability of obtaining a test statistic as extreme as or more extreme than the observed value, assuming the null hypothesis is true.

Question 3

Which of the following is a correct set of null and alternative hypotheses for testing whether a coin is fair?

Accepted Answer

$$Ho: p = 0.5 \,\, Ha: p 
eq 0.5$$

Question 4

A company claims its chewing gum helps more people quit smoking than the usual success rate of 34%. Which is the correct alternative hypothesis?

Accepted Answer

$$Ha: p \u003e 0.34$$

Question 5

In a hypothesis test, which rule determines whether to reject the null hypothesis?

Accepted Answer

Reject $$H_0 if p-$$value $$\u003c$$ $$\alpha$$

Question 6

A drug manufacturer claims fewer than 10% of patients experience nausea. In a sample of 250 patients, 23 experienced nausea. What is the sample proportion $$p$$?

Accepted Answer

$$p = \frac{23}{250} = 0.092$$

Question 7

Given $$p_0 = 0.1$, n = 250$, what is the standard error (SE) for the sample proportion?

Accepted Answer

$$SE = \sqrt{\frac{0.1(1-0.1)}{250}} = 0.0189$$

Question 8

A sleep expert claims more than 5.8% of men suffer from sleep apnea. In a sample of 100 men, 10 have sleep apnea. What is the z-score for this test? ($$p_0 = 0.058$, p = 0.10$, n = 100$)

Accepted Answer

$$z = \frac{0.10 - 0.058}{0.0234} = 1.79$$

Question 9

If the p-value for a test is 0.03673 and the significance level is 0.05, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis

Question 10

A mathematics chairperson wants to test if the percentage of US authors is no longer 40%. In a sample of 130 articles, 62 have US authors. What is the sample proportion?

Accepted Answer

$$p = \frac{62}{130} = 0.477$$

Question 11

For a two-tailed test with $$z = 1.79$$, what is the p-value if $$P(Z \u003c -1.79) = 0.03673$$?

Accepted Answer

p-value $$= 0.03673 	imes 2 = 0.07346$$

Question 12

A drug counselor believes the HIV rate among IV drug users is less than 2%. In a sample of 415 users, 8 are HIV positive. What is the z-score for this test? ($$p_0 = 0.02$, p = 0.019$, n = 415$, SE = 0.00687$)

Accepted Answer

$$z = \frac{0.019 - 0.02}{0.00687} = -0.15$$

Question 13

Which condition must be met to use the Central Limit Theorem for proportions?

Accepted Answer

$$np \geq 10$$ and $$n(1-p) \geq 10$$

Question 14

In hypothesis testing, what is the correct formula for the standard error of a sample proportion?

Accepted Answer

$$SE = \sqrt{\frac{p_0$(1-p_0$)}{n}}$$

Question 15

A researcher tests if the proportion of children with internet access has increased from 84%. In a sample of 750 children, 87% have access. What is the z-score if $$SE = 0.0134$$?

Accepted Answer

$$z = \frac{0.87 - 0.84}{0.0134} = 2.23$$

Question 16

If a p-value is 0.0153 and the significance level is 0.01, what is the correct decision?

Accepted Answer

Fail to reject the null hypothesis

Question 17

Which of the following best describes the p-value in the context of a medical study?

Accepted Answer

The probability of observing the sample result, or something more extreme, if the drug has no effect.

Question 18

A researcher finds $$z = -2.41$$ for a left-tailed test. What is the p-value?

Accepted Answer

$$P(Z \u003c -2.41) = 0.008$$

Question 19

Which step in hypothesis testing involves checking if the sample is random and independent, and if the sample size is large enough?

Accepted Answer

Prepare

Step-by-Step Guidance for Hypothesis Testing with Proportions

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