Question

For this problem, solve the problems by answering a) state the claim using a sentence, b) Ho H1 and place the claim with either one of the two, c) Test statistic, show and label the formula you use, d) find critical value(s), and reject Ho or fail to reject Ho. You may use p-value. e) Write a formal conclusion and final statement (Please show all work and label answer a,b,c,d,e)

A sample of 106 body temperatures with a mean of 98.2 F and a standard deviation of 6.62 F is given. At a 0.05 significance level, test the claim that the mean body temperature is equal to 98.6 F. Assume normality.

a)

b)

c)

d)

e)

Answer 1

Answer)

As the population standard deviation is unknown here and we are using sample s.d as the best estimate

We will use t distribution to conduct the test

A)

Null hypothesis Ho : u = 98.6

Alternate hypothesis Ha : u not equal to 98.6

B)

Ho : u = 98.6 (claim)

H1 : u not equal to 98.6

C)

Test statistics t = (sample mean - claimed mean)/(s.d/√n)

t = (98.2 - 98.6)/(6.62/√106) = -0.622

D)

Degrees of freedom is = n-1 = 105

For 105 dof and 0.05 significance level

Critical values t are = -1.983 and 1.983

Rejection region is reject Ho

If test statistics is greater than 1.983 or less than -1.983

Since, -0.622 is not less than -1.983

We fail to reject Ho

E)

We have enough evidence to support the claim that u is = 98.6