STAT177 Homework sheet #4 Solutions

1) Ho: m ³ 20000

Ha: m < 20000

2) The appropriate test is the Z test. Here are the output results:

Z test for one mean

Ho: population mean is not less than 20000

Ha: population mean is less than 20000

Reject Ho if test statistic < -1.645

Test statistic = -1.405

P-value = 0.08

Do not reject Ho

Conclude population mean is not less than 20000

95% confidence interval: 15710.914 to 20707.086

Since the p-value is greater than the level of significance, we do not reject the null hypothesis. We conclude that average daily sales are not significantly less than $20,000.

3) Since we did not reject the null hypothesis, we could have committed a Type II error.

4) We would have rejected the null hypothesis if the level of significance were between 8% and 10%, since the p-value would then be less than the level of significance.

5) Ho: m £ 780000

Ha: m > 780000

6) Since the scale of the data is interval/ratio, the data is normally distributed, the population standard deviation is unknown, the appropriate test is the t test.

7) It is fine to leave the level of significance in the dialogue box at 5%; we’ll be using the general rule of thumb. Here is the output:

t test for one mean

Ho: population mean is not greater than 780000

Ha: population mean is greater than 780000

Reject Ho if test statistic > 1.895

Test statistic = 0.132

P-value = 0.449

Do not reject Ho

Conclude population mean is not greater than 780000

95% confidence interval: 648070.69 to 927550.56

Since the p-value is greater than 10%, under the general rule of thumb, we do not reject the null hypothesis. We conclude the training was not successful.

8) The answer is no since the p-value is greater than 10% under the general rule of thumb.

9) Ho: m £ 120

Ha: m > 120

10) Since the scale of the data is interval/ratio, the data is normally distributed, the population standard deviation is unknown, the appropriate test is the t test.

11) Here is the output:

t test for one mean

Ho: population mean is not greater than 120

Ha: population mean is greater than 120

Reject Ho if test statistic > 1.796

Test statistic = 6.125

P-value = 0

Reject Ho

Conclude population mean is greater than 120

95% confidence interval: 143.385 to 169.615

Since the p-value is zero, we would reject the null hypothesis regardless of the level of significance. We conclude the store should locate in Smallville.

12) The p-value is less than 1%. We would still reject the null hypothesis and reach the same conclusion.

13) Since the scale of the data is ordinal, the appropriate test is the Wilcoxon test.

14) Here is the output:

Wilcoxon test for one median

Ho: population median is not greater than 7

Ha: population median is greater than 7

Reject Ho if test statistic less than or equal to 6

Sample size = 8

Test statistic = 8.5

Do not reject Ho

Conclude population median is not greater than 7

Since the test statistic is greater than 6, we do not reject the null hypothesis. We conclude they should not proceed with this peanut butter.

15) The first thing to do is copy the values in A1 through A10 to A11 through A20. Here is the output:

Wilcoxon test for one median

Ho: population median is not greater than 7

Ha: population median is greater than 7

Reject Ho if test statistic less than or equal to 36

Sample size = 16

Test statistic = 32

Reject Ho

Conclude population median is greater than 7

This time, since the test statistic is less than 36, we reject the null hypothesis and conclude they should proceed with this peanut butter.