Question

16) A local school district claims that the number of school days missed by its teachers due 16 to illness is below the national average of u=5. A random sample of 20 teachers provided the data below. At a =0.05, Use the five steps or otherwise to test the district's claim. Assume population standard deviation is 3.5. (10 points) 0 3 6 3 3 5 4 1 3 5 7 3 1 2 3 3 2 4 16

Answer 1

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho:μ=5

Ha: μ<5

This corresponds to a left-tailed test, for which a z-test for one mean, with known population standard deviation will be used.

(2) Rejection Region

Based on the information provided, the significance level is \alpha = 0.05α=0.05, and the critical value for a left-tailed test is zc​=−1.64.

The rejection region for this left-tailed test is R={z:z<−1.64}

(3) Test Statistics

- х – до - о/п 3.25 – 5 3.5//20 = -2.236

(4) Decision about the null hypothesis

Since it is observed that z=−2.236<zc​=−1.64, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p=0.0127, and since p=0.0127<0.05, it is concluded that the null hypothesis is rejected.

(5) Conclusion: It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean μ is less than 5, at the 0.05 significance level.