Question

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

49

42

57

51

50

67

48

58

48

48

53

54

(a) Determine the null and alternative hypotheses?

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

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

(b) Determine the test statistic ? t= z=  

(c) Determine the p-value. p-value =

(d) Make a decision.

• Do not reject the null hypothesis
• Accept the alternative hypotheis
• Accept the null hypothesis
• Reject the null hypothesis

(e) The correct conclusion would be:

• There is not sufficient evidence to support the claim that the mean number of hours of all employees at start-up companies work the US mean of 47 hours
• There is sufficient evidence to support the claim that the mean number of hours of all employees at start-up companies work the US mean of 47 hours
• There is sufficient evidence to support the claim that the mean number of hours of all employees at start-up companies work more than the US mean of 47 hours
• There is not sufficient evidence to support the claim the mean number of hours of all employees at start-up companies work more than the US mean of 47 hours

Answer 1