Q: If the sample proportion is $$0.05$$, the null proportion is $$0.06$$, and $$n = 300$$, what is the value of the test statistic?

$$z_p = \frac{0.05 - 0.06}{\sqrt{\frac{0.06 \times 0.94}{300}}} \approx -0.75$$

Question 1

A factory claims its new process reduces the defect rate from 6% to a lower value. In a random sample of 300 items, 15 are defective. What is the sample proportion of defective items?

Accepted Answer

$$\frac{15}{300} = 0.05$$

Question 2

Which of the following best describes the null hypothesis ($$H_0) in a $$one-proportion z-test for the factory defect rate scenario?

Accepted Answer

$$H_0$$: p = 0.06$$

Question 3

What is the alternative hypothesis ($$H_A) if $$the quality control department wants to show the new process reduces the defect rate?

Accepted Answer

$$H_A: p \u003c 0.06$$

Question 4

Which formula is used to calculate the test statistic for a one-proportion z-test?

Accepted Answer

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

Question 5

If the sample proportion is $$0.05$$, the null proportion is $$0.06$$, and $$n = 300$$, what is the value of the test statistic?

Accepted Answer

$$z_p = \frac{0.05 - 0.06}{\sqrt{\frac{0.06 	imes 0.94}{300}}} \approx -0.75$$

Question 6

What does a small P-value indicate in the context of hypothesis testing?

Accepted Answer

The observed data are unlikely under the null hypothesis, suggesting evidence against $$H_0$$

Question 7

Which of the following is NOT a correct interpretation of the P-value?

Accepted Answer

The probability that the null hypothesis is true

Question 8

If the significance level $$\alpha is $$set at 0.10 and the P-value is 0.08, what is the correct decision?

Accepted Answer

Reject the null hypothesis; the test is significant at $$\alpha = 0.10$$

Question 9

Which statement about drawing conclusions in hypothesis testing is correct?

Accepted Answer

We never prove $$H_0 or$$ $$H_A to be $$true or false; we only gather evidence from the sample data.

Question 10

What is a Type I error in hypothesis testing?

Accepted Answer

Rejecting $$H_0$$ when $$H_0 is $$true

Question 11

What is a Type II error in hypothesis testing?

Accepted Answer

Failing to reject $$H_0$$ when $$H_0 is $$false

Question 12

Which of the following conditions must be checked for the normal approximation to be valid in a one-proportion z-test?

Accepted Answer

$$np_0$$ \geq 10$$ and n(1$$-$$p_0$$) \geq 10$$

Question 13

In the context of the factory defect rate, what is the parameter of interest for the hypothesis test?

Accepted Answer

The population proportion of defective items produced by the new process

Question 14

Which of the following is the correct general procedure for hypothesis testing?

Accepted Answer

Identify the parameter, set up hypotheses, compute test statistic, compute P-value, draw conclusion

Question 15

A medical researcher tests whether a new drug reduces the proportion of patients experiencing side effects from 20%. In a sample of 100 patients, 15 experience side effects. What is the null hypothesis?

Accepted Answer

$$H_0$$: p = 0.20$$

Question 16

If a hypothesis test for a population proportion yields a P-value of 0.12 and the significance level is $$\alpha = 0.05$$, what is the correct conclusion?

Accepted Answer

Do not reject the null hypothesis; the test is insignificant at $$\alpha = 0.05$$

Question 17

Which scenario describes a two-sided alternative hypothesis for a population proportion?

Accepted Answer

$$H_A: p 
eq p_0$

Question 18

In a hypothesis test, what does the shaded area under the null model curve represent?

Accepted Answer

The P-value, or the probability of observing a test statistic as extreme or more extreme than the observed value

Testing Hypotheses About Proportions: One-Proportion z-Test

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