Question

he 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 10% level of significance. Give answer to at least 4 decimal places.

Hours

47

50

60

54

47

67

53

45

47

49

55

50

What are the correct hypotheses?  

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

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

Based on the hypotheses, find the following:

Test Statistic=

p-value=

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

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.

Answer 1

we have to test whether mean is more than 40 or not. So, it is a right tailed hypothesis test

Using TI 84 calculator

enter the given data set in list L1

press stat then tests then Ttest

select L1

press calculate

we get

test statiistic = 2.7262

p value = 0.0099

p value is less than 0.10 significance level, rejecting null hypothesis

Conclusion:- There is enough evidence to support the claim