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 10% level of significance. Give answer to at least 4 decimal places. Hours 49 48 60 53 47 62 45 58 50 50 53 55 What are the correct hypotheses? H0: hours H1: hours Based on the hypotheses, find the following: Test Statistic= p-value= The correct decision is to . The correct summary would be: that the mean number of hours of all employees at start-up companies work more than the US mean of 47 hours.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis: μ = 47
Alternative Hypothesis: μ > 47

Rejection Region
This is right tailed test, for α = 0.1 and df = 11
Critical value of t is 1.363.
Hence reject H0 if t > 1.363

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (52.27 - 47)/(5.5514/sqrt(12))
t = 3.289

P-value Approach
P-value = 0.0036
As P-value < 0.1, reject the null hypothesis.

There is sufficient evidence to conclude that 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