Question

Someone claims that the mean number of sick days that employees in New Jersey take per year is 5.3. To look into that claim, you take a representative sample of 78 employees in New Jersey and find that the mean number of sick days is 5.5 in the sample. The population standard deviation is 1.6.

Part (a)   

Given that the sample mean is different from the claimed population mean, does that show that the claim in H₀ is false? Explain your answer.

Part (b)

Carry out a hypothesis test for the claim above (with α = 0.05) using the 6-step procedure.

Part (c)   

Carry out a hypothesis test for the claim above (with α = 0.05) using the p-value method.

Answer 1

H₀: = 5.3

H₁: 5.3

a) No, it does not show that H0 is false, because without doing any hypothesis test, we cannot show that H0 is false.

The test statistic t = ()/(s/)

                            = (5.5 - 5.3)/(1.6/)

                            = 1.1

At alpha = 0.05, the critical values are t_{0.025, 77} = +/- 1.991

Since the test statistic value is not greater than the critical value (1.1 < 1.991), we should not reject the null hypothesis.

So there is sufficient evidence to support the claim that the mean number of sick days that employees in New Jersey take per year is 5.3

C) P-value = 2 * P(Z > 1.1)

                  = 2 * (1 - P(Z < 1.1))

                  = 2 * (1 - 0.8643)

                  = 2 * 0.1357 = 0.2714

Since the P-value is greater than alpha (0.2714 > 0.05), we should not reject H₀.