7 A random sample of 106 temperatures with a mean of 982 deg

7. A random sample of 106 temperatures with a mean of 98.2 degrees Fahrenheit and a standard

deviation of 0.62 degrees Fahrenheit. Assume that temperatures have a normally distributed

population. Use a 0.05 significance level to test the claim that the mean body temperature of the

population is equal to 98.6 degrees Fahrenheit, as is commonly believed. If there sufficient evidence to

conclude that the common belief is wrong?

a. (2 pts) Give the appropriate hypotheses for this test and define any parameters used.

b. (2 pts) List and Verify conditions for the appropriate hypothesis test

c. (2 pts) Give the appropriate test statistic. Show formula, work, and value

d. (3pts) Find the appropriate rejection region. Draw an appropriate picture.

e. (2 pts) What is your decision regarding the null hypothesis?

f. (3 pts) What are your conclusions about this particular test?

g. (2 pts) Perform this test using Minitab. Provide the Minitab output here. Verify that your test

statistic from your previous steps match the Minitab output. Also verify that using the p-value

from the Minitab output will result in the same decision from part (e).

Solution

Set Up Hypothesis
Null, H0: U=98.6
Alternate, H1: U!=98.6
Test Statistic
Population Mean(U)=98.6
Sample X(Mean)=98.2
Standard Deviation(S.D)=0.62
Number (n)=106
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =98.2-98.6/(0.62/Sqrt(105))
to =-6.642
| to | =6.642
Critical Value
The Value of |t | with n-1 = 105 d.f is 1.983
We got |to| =6.642 & | t | =1.983
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Two Tailed ( double the one tail ) -Ha : ( P != -6.6423 ) = 0
Hence Value of P0.05 > 0,Here we Reject Ho