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 5% level of significance. Give answer to at least 4 decimal places.

Hours
46
45
55
54
48
68
51
60
46
46
52
52

What are the correct hypotheses?

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

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

Based on the hypotheses, find the following:

Test Statistic=

p-value=

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

The correct summary would be: Select an answer There is enough evidence to reject the claim There is not enough evidence to support the claim There is not enough evidence to reject the claim There is enough 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.

Answer 1

: Mean work week;

Claim : employees at start-up companies work more on average then most working adults in the US

H0: = 47 hours
H1: > 47 hours

Right tailed test:

Hypothesized mean : = 47

xi : lengths in hours of work week for ith engineering friend

Sample size : n= 12

Sample mean :Sample mean hours of work

Sample standard deviation :s

xi:Hours
46	-5.9167	35.0069
45	-6.9167	47.8403
55	3.0833	9.5069
54	2.0833	4.3403
48	-3.9167	15.3403
68	16.0833	258.6736
51	-0.9167	0.8403
60	8.0833	65.3403
46	-5.9167	35.0069
46	-5.9167	35.0069
52	0.0833	0.0069
52	0.0833	0.0069
=623		=506.9167
=623/12=51.9167

Based on the hypotheses, find the following:

Test Statistic= 2.5089

For right ailed test:

Degrees of freedom = n-1 =12-1 =11

For 11 degrees of freedom,

P(t>2.5089) =0.0145

p-value = 0.0145

As P-Value i.e. is less than Level of significance i.e (P-value:0.0145 < 0.05:Level of significance); Reject Null Hypothesis
The correct decision is to : Reject the null hypothesis

The correct summary would be:

There is enough 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.