Question

When the 636 male workers in the 2008 GSS were asked how many hours they worked in the previous. week, the mean was 45.5 with a standard deviation of 15.16.

Does this suggest that population mean work week for men exceeds 40 hours? (hint: 1 tailed or 2 tailed)

1. Given your conclusion, are you at risk of making a Type1 or Type II error? Provide your answer in the context of the problem.

2. Report the 95% confidence region for µ = mean weekly work hours for men

3. Interpret the result

4. Make a decision based on the confidence region from vii.

1.   µ = 39

Since µ = 39 ______(is/is not) in the confidence region, we ______(reject Ho/do not reject Ho)

2.   µ = 45

Since µ = 45______( is/is not) in the confidence region, we (reject Ho/do not reject Ho)

Answer 1

There is sufficient evidence to conclude that population mean work week for men exceeds 40 hours.

i) Since we reject H₀ in this case, one would make a Type I error in this case, i.e. rejecting H₀ when H₀ is actually true.

ii)

Interpretation : Out of 100 samples drawn, sample mean will lie between (44.3, 46.7) for 95 samples.

a) Since µ = 39 is not in the confidence region, we reject H₀

b) Since µ = 45 is in the confidence region, we do not reject H₀