Suppose that sample results representative of the times for

Suppose that sample results representative of the times for an airline to locate flight information on their internet web site are as follows Sample Mean = 2.5 minutes, Sample Size = 22. Population standard deviation is Known to be 0.8 minutes Calculate the 90% confidence interval for the population mean. Formulate the hypotheses if the purpose is to test that the mean time for all users to locate the information should be less than 3 minutes. Perform the test and describe your conclusion, using 0.05 level of significant.

Solution

Given xbar=2.5, n=22(small sample), S=0.8,

The table value of t at (22-1) at 10% is 1.72.

The 90% confidence interval for the population mean=[xbar+-(1.72*S/n)]=[2.5+-(1.72*0.8/22)]=[2.2066,2.7934].

Ho:=3 vs H1:<3(left tail test), the table value of ttab with 21 degrees of freedom at 0.05 is -1.72, then tcal=(xbar-)/((S²/n))=(2.5-3)/0.1706=-2.9308<-1.72, here tcal<ttab, so we accept null hypothesis. Therefore, Ho:=3.