Question

True or False section.

1. When we reject the null hypothesis, we have proven the alternative hypothesis to be true.

2. There are only two possible conclusions in a hypothesis test: reject or fail to reject the

   alternative hypothesis.

3. A Type I error is made when a true null hypothesis is rejected.

4. A Type II error is made when we fail to reject a true null hypothesis.

5. The level of significance is the probability of making a Type II error.

6. The probability of making a Type I error is inversely related to the probability of making

   a Type II error.

7. A coach is testing his claim that the average height of this year’s MLS defenders is

   heavier than the past years. Suppose that over the past five years, the mean height of MLS defenders was 6’3.5. The null hypothesis is: p ≤ 6’3.5 and the alternative hypothesis is: p > 6’3.5.

8. The city planner in charge of Detroit is thinking of adding a second Q-line that would circle the entire city limit of Detroit. The city planner wants to know if the majority of the residents are in favor of the second Q-line before pushing the issue further. The null hypothesis is: p > 0.5 and the alternative hypothesis is: p ≤ 0.5.

9. Austin’s company golf balls. The golf balls need to be exactly 40 mm in diameter otherwise he must recalibrate his machine. Austin measured 150 golf balls off the production line in order to perform a hypothesis test. The null hypothesis is: p = 40mm and the alternative hypothesis is p ≠ 40mm.

10. Guidelines for cereal manufacturers say that to claim a cereal is “mostly fruit”, at least 51% of the cereal must be fruit. A local consumer watched a group test 17 randomly selected boxes of a cereal claiming to be mostly fruit to see if it meets the guidelines. The alternative hypothesis is: p < .51 and the null hypothesis is: p ≥ .51.

Answer 1

When we reject the null hypothesis, we have proven the alternative hypothesis to be true.True

This is because The null hypothesis is rejected means we are able to accept the alternative hypothesis.

There are only two possible conclusions in a hypothesis test: reject or fail to reject the

alternative hypothesis.False.

We reject null hypothesis or fail to reject the null hypothesis

A Type I error is made when a true null hypothesis is rejected.True.

A Type II error is made when we fail to reject a true null hypothesis.False. This is because accept null hypothesis when it is true is type 2 error.

The level of significance is the probability of making a Type II error.False. Level of significance is probability of making type 1 error.

The probability of making a Type I error is inversely related to the probability of making

a Type II error.True. As type 1 error increases, type 2 error decreases.

A coach is testing his claim that the average height of this year’s MLS defenders is heavier than the past years. Suppose that over the past five years, the mean height of MLS defenders was 6’3.5. The null hypothesis is: p ≤ 6’3.5 and the alternative hypothesis is: p > 6’3.5.False.

This is because we denote the true population mean by and not by p.p is true population proportion.

The city planner in charge of Detroit is thinking of adding a second Q-line that would circle the entire city limit of Detroit. The city planner wants to know if the majority of the residents are in favor of the second Q-line before pushing the issue further. The null hypothesis is: p > 0.5 and the alternative hypothesis is: p ≤ 0.5.False This is because the actual null and alternate hypotheses are :

H0:p0.5 vs H1:p>0.5

Austin’s company golf balls. The golf balls need to be exactly 40 mm in diameter otherwise he must recalibrate his machine. Austin measured 150 golf balls off the production line in order to perform a hypothesis test. The null hypothesis is: p = 40mm and the alternative hypothesis is p ≠ 40mm.True.

Guidelines for cereal manufacturers say that to claim a cereal is “mostly fruit”, at least 51% of the cereal must be fruit. A local consumer watched a group test 17 randomly selected boxes of a cereal claiming to be mostly fruit to see if it meets the guidelines. The alternative hypothesis is: p < .51 and the null hypothesis is: p ≥ .51.True.

If there is any understanding problem regarding this please feel free to ask any doubt in comment box. Thank you.