Question

In a report from October 14, 2016, USA TODAY reported that Americans spend 4.1 hours per weekday checking work email. This was an estimate based on a survey of 1004 white-collar workers in the United States. Conduct a hypothesis test to decide if there is evidence that the mean time spent checking work email is more than half of the 8-hour work day. The sample has standard deviation of 1.3 hours.

a. State the hypothesis (null and alternative) and if z or t test will be used?

b. Are assumptions and conditions for inference satisfied?

c. State the test statistic

d. State the p-value

e. Do these data provide strong evidence that the mean time checking email was more than half the work day? Use complete sentences

Answer 1

(A) We have to test whether the mean time spent checking work email is more than half of the 8-hour work day

So,

we will use z test because the sample size is large enough

(B) assumption and conditions for inference are satisfied because data is independent and also normally distributed.

(C) we have xbar = 4.1, mu= 4, s = 1.3 and n = 1004

test statistic =

(D) Using z table, check 2.4 in the left most column and 0.04 in the top row, then select the intersecting cell,we get

p value = 0.0073

(E) At 0.05 significance level, p value is less than 0.05 significance level, which means that the result is significant and we can reject the null hypothesis

therefore, we can conclude that the mean time spent checking work email is more than half of the 8-hour work day