Question

A recent article in a computer magazine suggested that the mean time to fully learn a new software program is 40 hours. A sample of 100 first-time users of a new statistics program revealed the mean time to learn it was 39 hours with the standard deviation of 8 hours. At the 0.05 significance level, can we conclude that users learn the package in less than a mean of 40 hours?

a. State the null and alternate hypotheses.

H0:

H1:

b. State the significance level

c. Compute the value of the test statistic.

d. Write the decision rule:

e. Make the decision and state the reason

Answer 1

a)

Null hypothesis is given by

It is one tailed i.e. left tailed test.

b)

Significance level,

c)

We are given sample size,n=100

Population standard deviation is not given we approximate it with sample standard mean.

So, standard error mean is given by

Critical value of z can be found normal probability distribution table for significance level=0.05

i.e. look for area =0.45 , we get z=-1.65 (we have taken negative sign as it is left tailed test)

Let us standardize the sample mean

d)

If Z>Critical value, accept Null hypothesis

If Z<Critical value, reject Null Hypothesis

e)

We observe that -1.25>-1.65, So, we fail to reject null hypothesis that mean is 10 hours. Statistics does not support that users learn package in less than 40 hours.