Homework SourseTravel Magazine reported that among the US states Hawaii is
Travel Magazine reported that among the US states, Hawaii is the one with the longest life span of residents, where the population mean life span is 77 years. A random sample of 20 obituary notices in the Honolulu Journal gave the following information about life span (in years) of Honolulu residents:
72 68 81 93 56 19 78 94 83 84
77 69 85 97 75 71 86 47 66 88
Assuming that life span in Honolulu is normally distributed; does this information indicate that the mean life span for all Honolulu residents is less than 77 years? Do you have enough evidence to say that Travel magazine’s report is not accurate? Use a 5% level of significance.
1) What type of hypothesis test is needed? What distribution should be used? Why?
2) State the two hypotheses here.
Ho : H1 :
3) Find the critical value and the test statistics. State them here.
4) Is this a right, left or two-tailed test? Sketch a normal curve, mark the critical value and test statistics and shade the rejection region on the curve.
5) Use your calculator to find the P value. State it here.
6. Do we reject or not reject the null hypothesis? Does this information indicate that the mean life span for all Honolulu residents is less than 77 years? Include the test statistics or P value in your discussion.
Solution
Set Up Hypothesis
Null, H0: U=77
Alternate, H1: U<77
Test Statistic
Population Mean(U)=77
Sample X(Mean)=74.45
Standard Deviation(S.D)=18.092
Number (n)=20
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =74.45-77/(18.092/Sqrt(19))
to =-0.63
| to | =0.63
Critical Value
The Value of |t | with n-1 = 19 d.f is 1.729
We got |to| =0.63 & | t | =1.729
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value :Left Tail -Ha : ( P < -0.6303 ) = 0.26799
Hence Value of P0.05 < 0.26799,Here We Do not Reject Ho
We don\'t have evidence to indicate that the mean life span for all Honolulu residents is less than 77 years
