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.