Question

Can you conclude that the mean of this data set is greater than 11? Use the appropriate hypothesis test. Use an alpha of 0.05. Be sure to clearly state the null and alternative hypotheses. ** Do this "manually" by calculating the test statistic and comparing to the critical value. You may then use built in functions or the XLminer Analysis Toolpak to check your results.

16.11383372 12.21679045 12.54830756 11.77001117 9.905112875 10.5547892 10.12129959 12.2995907 14.4705887 11.08819674 6.596124654 11.40694938 10.49983291 12.59209546 15.93683421 16.71547626 13.93784335 14.11894487 14.8886567 11.43743988 6.885663846 5.838637434 11.51012868 11.76756143 7.786938153 7.317429767 10.16603397 13.36174883 16.61404432 9.413674637 11.33574022 11.10582318 10.67265639 12.85222422 12.40920101 11.1622107 8.853601712 15.14525452 11.15134392 13.58139079 8.657948387 12.66292433 9.662952894 15.05779943 12.27691305 7.371202535 6.876353718 9.073732817 11.62291349 13.56349149 12.85249293 14.86431774 14.6889657 16.51114988

Answer 1

Sol:

Ho:mu=11

Ha:mu>11

alpha=0.05

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

xbar=sample mean=sum of values/total values=633.893184499/54=11.7388

mu=population mean=11

s=sample standard deviation=sqrt(404.1995/54-1)=2.7616

n=sample size=54

t=(11.7388-11)/(2.7616/sqrt(54))

t=1.965907

df=n-1=54-1=53

p value in excel

=T.DIST.RT(1.965907,53)

p=0.0273

p<0.0.5

Reject null hypothesis

Accept alternative Hypothesis

Conclusion:

There is sufficient evidence at 5% level of significance to conclude that the mean of this data set is greater than 11