Question

1. U.S Centers for Disease Control and Prevention reports that the American adults have the average of 8.6 days per month without sufficient sleep, with a standard deviation of 1.8 days. A researcher thinks the average days without sufficient sleep is not 8.6 days, and her sample of 50 households produced a mean of 9.1 days. Test her claim, using a significance level of 0.01. Show all the steps (4 steps) discussed in class.

Answer 1

STEP 1

we have to test whether the average is equal to 8.6 days or not. So, it is a two tailed hypothesis test

STEP 2

We will reject the null hypothesis if p value is less than 0.01 significance level

STEP 3

test statistic =

using z distribution table, checking 1.9 in the left most column and 0.06 in the top row, select the intersecting cell, we get

p value = 0.0500

STEP 4

it is clear that the p value is greater than the significance level of 0.01, failing to reject the null hypothesis

therefore, we can say that there is insufficient evidence to support the claim that the mean is not equal to 8.6 days