Question

There are major issues with people “goofing off” during working hours with the availability of the internet. Previous studies have found that the average amount of time wasted in the population per day to have a population standard deviation of 12 minutes. You have implemented employee satisfaction programs in your non-profit and you claim that at your workplace the amount of time wasted is less than 60 minutes due to these efforts. Your boss knows that you took statistics and asks you to provide some evidence that this is occurring. You take a sample of 36 individuals and find a mean of 59 minutes wasted per day. Using the technique you learned in this class test your claim at the .05 significance level. Be sure to show the claim and the null and alternative hypothesis. What do you conclude? What do you conclude about the claim?

Answer 1

Solution :

The null and alternative hypothesis are

H₀ : = 60 ........ Null hypothesis

H_a : < 60 ........ Alternative hypothesis

Here, n = 36, = 59, = 12

The test statistic z is,

z = - /(/n)

= [59 - 60]/[12 /36]

= -0.5

The value of the test​ statistic t = -0.5

Now ,

d.f. = n - 1 = 36 - 1 = 35

< sign in Ha indicates that the test is ONE TAILED.

t = -0.5

So , using calculator ,

p value = 0.3085

p value is greater than the significance level.

Decision: Fail to Reject the null hypothesis H0

Conclusion : There is not sufficient evidence to support the claim that the population mean is less than 60.