The work week for adults in the US that work full time is normally distributed with a mean of 47 hours. A newly hired engineer at a start-up company believes that employees at start-up companies work more on average then most working adults in the US. She asks 12 engineering friends at start-ups for the lengths in hours of their work week. Their responses are shown in the table below. Test the claim using a 1% level of significance. Give answer to at least 4 decimal places.

Hours
48
49
55
55
46
69
53
46
46
47
50
55

a. What are the correct hypotheses? 

H₀: Select an answer σ² x̄ μ s σ p̂ p s² ? ≥ > < ≤ ≠ = hours

H₁: Select an answer x̂ μ σ² s p̂ σ p s² ? > < ≥ ≤ = ≠ hours

Based on the hypotheses, find the following:

b. Test Statistic =

c. p-value =

d. The correct decision is to Select an answer Accept the null hypothesis Reject the null hypothesis Fail to reject the null hypothesis Accept the alternative hypotheis .

e. The correct summary would be: Select an answer There is enough evidence to reject the claim There is enough evidence to support the claim There is not enough evidence to support the claim There is not enough evidence to reject the claim that the mean number of hours of all employees at start-up companies work more than the US mean of 47 hours.