Question

1. An SRS of 16 households is selected in Houston and the number of remote controls is counted. We are interested in a hypothesis test that tests if population mean number of remote controls is greater than 5. In the sample, the mean number of remote controls is 7. The degrees of freedom associated with the test is: [2]
   1. 16
   2. 15
   3. 7
   4. 5
   5. Not enough information

2. Question 1 above yields a test statistic of 2. Circle all levels of significance that would result in a conclusion that rejects the null hypothesis. [2]
   1. 10%
   2. 5%
   3. 1%
   4. 0.5%
   5. Not enough information

3. Based on the information provided in question 1, if we reject the null hypothesis then 7 will be in corresponding confidence interval. [2]
   1. True
   2. False
4. Assume that we rejected the null hypothesis in the test referenced in questions 1-3. If we find out that the null hypothesis was actually true, what error did we make? [2]

Answer 1

Solution:

Given:

Sample size = n = 16

Sample mean =

Part i) The degrees of freedom associated with the test is

df = n - 1

df = 16- 1

df = 15

Part ii) Question 1 above yields a test statistic of 2. Circle all levels of significance that would result in a conclusion that rejects the null hypothesis.

t critical value at 0.10 level of significance = 1.341

t critical value at 0.05 level of significance = 1.753

Since t test statistic = 2 > both critical values , so we would reject H0 at 10% and at 5% significance level.

thus required answer is:

10%

5%

Part iii) Based on the information provided in question 1, if we reject the null hypothesis then 7 will be in corresponding confidence interval.

True

Since 7 is the sample mean and it is the center of the confidence interval.

Part iv) Assume that we rejected the null hypothesis in the test referenced in questions 1-3. If we find out that the null hypothesis was actually true, what error did we make?

We make Type I Error

Since Type I Error = Reject null hypothesis H0, in fact H0 is true.