Question 1

Which of the following best describes the null hypothesis ($$H_0) in $$the context of the ingot cracking example?

Accepted Answer

The proportion of cracked ingots is equal to the historical rate of 20%.

Question 2

In the ingot example, what is the alternative hypothesis ($$H_a) if $$the goal is to show the process improvement reduced the crack rate?

Accepted Answer

$$H_a: p \u003c 0.20$$

Question 3

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

Accepted Answer

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

Question 4

A P-value is best described as:

Accepted Answer

The probability of observing a statistic as extreme as, or more extreme than, the sample value, assuming the null hypothesis is true.

Question 5

In the DMV study, 61 out of 90 teens passed the driving test. What is the sample proportion $$\hat{p}$$?

Accepted Answer

$$\hat{p} = \frac{61}{90} = 0.678$$

Question 6

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

Accepted Answer

Population must be normally distributed

Question 7

If the P-value is 0.067 in a lower-tailed test and the significance level $$\alpha is 0.05$$, what is the correct conclusion?

Accepted Answer

Fail to reject the null hypothesis.

Question 8

In a two-sided test with $$z = \pm 1.50$$, what is the P-value if the area in one tail is 0.067?

Accepted Answer

$$0.134$$

Question 9

Why is it incorrect to say we 'accept' the null hypothesis if we fail to reject it?

Accepted Answer

Because failing to reject only means there is not enough evidence against the null hypothesis, not that it is true.

Question 10

Which of the following scenarios would require the smallest P-value to reject the null hypothesis?

Accepted Answer

Testing if a psychic can predict coin flips.

Question 11

In the home field advantage example, the test statistic was $$z = 3.75. $$What does a P-value of 0.0001 indicate?

Accepted Answer

There is strong evidence to reject the null hypothesis.

Question 12

Which of the following is the correct formula for the standard deviation of the sampling distribution of $$\hat{p}$$ under the null hypothesis?

Accepted Answer

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

Question 13

Which of the following best describes a two-sided alternative hypothesis?

Accepted Answer

$$H_a: p 
eq p_0$

Question 14

What is the main purpose of checking the Success/Failure condition before performing a one-proportion z-test?

Accepted Answer

To justify the use of the Normal model for the sampling distribution.

Question 15

If a hypothesis test yields a P-value of 0.002, what does this mean in context?

Accepted Answer

The observed result is very unlikely under the null hypothesis.

Question 16

Which of the following is a correct interpretation of a 95% confidence level in the context of hypothesis testing?

Accepted Answer

If we repeated the test many times, about 95% of the intervals would contain the true parameter.

Testing Hypotheses About Proportions

스터디 가이드 - 연습 문제