The Myers Summer Casual Furniture Store tells customers that

The Myers Summer Casual Furniture Store tells customers that a special order will take six weeks (42 days). During the recent months the owner has received several complaints that the special orders take longer than 46 days. A sample of 15 special orders delivered in the last month showed that the sample mean waiting time was 56 days with a sample standard deviation of 8 days. At the .05 (5%) level of significance are the customers waiting an average of more than 42 days

show all 5 steps in your hypotheses test

Solution

Given n=15, xbar=56, s=8, mean=42

The test hypothesis is
Ho:<=42
Ha:>42

The test statistic is

t=(xbar-)/(s/n)

=(56-42)/(8/sqrt(15))

=6.78

Given a=0.05, the critical value is |t(0.05, df=n-1=14)|=1.76 (check student t table)

Since t=6.78 is larger than 1.76, we reject Ho.

So we can conclude that he customers are waiting an average of more than 42 days