Question

A growing concern of employers is time spent in activities like surfing the Internet and e-mailing friends during work hours. The San Luis Obispo Tribune summarized the fundings from a survey of a large sample of workers in an article that ran under the headline "Who Goofs Off 2 Hours a Day? Most Workers, Survey Says" (August 3, 2006). Suppose that the CEO of a large company wants to determine whether the average amount of wasted time during an 8-hour work day for employees of her company is less than the reported 120 minutes. Each person in a random sample of 12 employees was contacted and asked about daily wasted time at work. The resulting data are the following:

108 112 117 128 130 111 131 116 113 113 105 128

Is the following statement "These data provide evidence that the mean wasted time for this company is less than 120 minutes with significance level alpha equals 0.05" true or false?

Answer 1

The claim is that true mean wasted time for this company is less than 120 minutes.

Null Hypothesis H0: = 120 minutes

Alternative Hypothesis Ha: < 120 minutes

From the data,

Sample mean, = 117.6667

Sample standard deviation s = 9.148605

Since we do not know the true population standard deviation we will conduct one sample t test.

Standard error of mean, SE = s / = 9.148605 / = 2.640975

Test statistic, t = ( - ) / SE =  (117.6667 - 120) / 2.640975 = -0.8834995

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

p-value = p(t < -0.8834995, df = 11) =  0.1979

Since, p-value is greater than 0.05 significance level, we fail to reject null hypothesis H0 and conclude that there is no strong evidence to support the claim that true mean wasted time for this company is less than 120 minutes.

So, we can treat the statement claim as false.