Question

Hw 21

A researcher wants to know if recreational screen time (that is, screen time for entertainment purposes, rather than for school, work, or communication) has increased or decreased since 2016. In 2016, the mean recreational screen time was 12.9 hours per week. She collects data from 125 individuals, and finds the sample mean recreational screen time to be 14.1 hours per week. The sample standard deviation was 5.25 hours per week. Test her claim that the mean amount of recreational screen time is different from 12.9 hours per week.

* What is the null hypothesis?                            [ Select ]                       ["H0: mu<12.9", "H0: mu<14.7", "H0: mu=12.9", "HA: mu>12.9", "H0: mu=14.7"]      

* What is the alternative hypothesis?                            [ Select ]                       ["HA: mu is not equal to 12.9", "HA: mu=12.9", "HA: mu < 12.9", "H0: mu is not equal to 12.9"]      

* This test is                            [ Select ]                       ["left tailed", "right tailed", "two tailed"]      

* Which distribution and what degrees of freedom do you need?                            [ Select ]                       ["The student t-distribution with 125 degrees of freedom.", "The normal distribution with 125 degrees of freedom.", "The student t-distribution with 124 degrees of freedom.", "The normal distribution with 124 degrees of freedom."]      

*The test statistic is                            [ Select ]                       ["-0.0118", "0.46957", "2.556", "0.0118", "1.96"]      

*The P-value is                            [ Select ]                       ["0.048", "0.46957", "2.556", "0.0026", "0.0118"]      

* What is the conclusion?                             [ Select ]                       ["Fail to reject the null hypothesis. Evidence supports the claim that the mean recreational screen time is different from what it was in 2016.", "Reject the null hypothesis. Evidence supports the claim that the mean recreational screen time is different from what it was in 2016.", "Reject the null hypothesis. There is insufficient evidence to conclude that the mean recreational screen time is different from what it was in 2016.", "Fail to reject the null hypothesis. There is insufficient evidence to conclude that the mean recreational screen time is different from what it was in 2016."]      

Answer 1

1.

Null hypothesis:

H0: mu=12.9

2.

Alternative hypothesis:

HA: mu is not equal to 12.9

3.

This test is two tailed.

4.

The student t-distribution with 124 degrees of freedom

5.

The test statistic is

6.

The P-value is 0.0118

It is obtained using excel with function =TDIST(2.556,124,2)

7.

Conclusion:

Reject the null hypothesis. Evidence supports the claim that the mean recreational screen time is different from what it was in 2016.

(I assumed Level of significance = 0.05)