Each question below has multiple correct answers, and you must select all correc

Question

Each question below has multiple correct answers, and you must select all correct answers and no incorrect answers for full credit.

a. Suppose we are testing H0: ?1 - ?2 = 0, and we commit a Type II error. Which of the following statements are true, assuming we use ? = 0.05? Select all that apply.

We reject H0We FTR H0The p-value is greater than 0.05The p-value is less than 0.05?1 = ?2?1 ? ?2The difference in sample means is statistically significantThe difference in sample means is not statistically significant

b. Suppose we are planning to test H0: ?1 - ?2 = 0, and in truth ?1 = ?2. Which of the following statements are true, assuming we have not yet collected the data and we plan to use ? = 0.05? Select all that apply.

H0 is true

H0 is false

There is a 95% chance that the 95% CI for ?1 - ?2 will contain zero

There is a 5% chance that the 95% CI for ?1 - ?2 will contain zero

There is a 95% chance that the p-value will be less than 0.05

There is a 5% chance that the p-value will be less than 0.05

If we reject H0, we will be committing a Type I error

If we FTR H0, we will be committing a Type II error

c. Suppose we are testing H0: ?1 - ?2 = 0, and we get a test statistic of t = -1.44. Which of the following statements are true, given this result and assuming we use ? = 0.05? Select all that apply

The p-value is greater than 0.05

The p-value is less than 0.05

The difference in sample means is statistically significant

The difference in sample means is not statistically significant

We reject H0

We FTR H0

The corresponding 95% CI should contain zero

The corresponding 95% CI should not contain zero

It is possible we have committed a Type I error

It is possible we have committed a Type II error

Explanation / Answer

a)

We FTR H0

The p-value is greater than 0.05

?1 ? ?2

The difference in sample means is not statistically significant

b)

H0 is true

There is a 95% chance that the 95% CI for ?1 - ?2 will contain zero

There is a 5% chance that the p-value will be less than 0.05

If we reject H0, we will be committing a Type I error

c)

The p-value is greater than 0.05

The difference in sample means is not statistically significant

We FTR H0

The corresponding 95% CI should contain zero

It is possible we have committed a Type II error

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