Question

A recent national survey showed that the mean amount of time high school students spent per day using Snapchat was 65 minutes, with a standard deviation of 9 minutes. Mrs. Jones, a school principal, surveyed 100 of her students and computed a sample mean of 67.6 minutes of daily Snapchat use. She would like to determine, with a .01 significance level, whether her school is significantly different from the national results.

1. State the null and alternate hypotheses for this two-tailed test.
   H0:
   Ha:

2. Use the significance level to determine the “critical values” (cut-off points) and draw on a distribution. Clearly label the rejection areas, confidence level area, and critical values.

3. Compute the test statistic

4. Make your decision: accept or reject Ho. Explain why you made this choice.

5. Do Mrs. Jones’ students differ significantly from the national average?

Answer 1

We will set up the null hypothesis

Under the null hypothesis the test statistics is

Where   , , and .

and its corresponding p.value = 0.004

The critical Value for the Z.test at 0.01% of significance level is 2.58.

Since calculated Z = 2.89 which is greater then 2.58 the critical value, hence we will reject null hypothesis and conclude that .