Question

It is commonly believed that the mean body temperature of a healthy adult is 98.6∘F98.6∘F. You are not entirely convinced. You believe that it is not 98.6∘F98.6∘F. You collected data using 51 healthy people and found that they had a mean body temperature of 98.2∘F98.2∘F with a standard deviation of 1.18∘F1.18∘F. Use a 0.05 significance level to test the claim that the mean body temperature of a healthy adult is not 98.6∘F98.6∘F.

a) Identify the null and alternative hypotheses?

b) What type of hypothesis test should you conduct (left-, right-, or two-tailed)?

• left-tailed
• right-tailed
• two-tailed

c) Identify the appropriate significance level.

d) Calculate your test statistic. Write the result below, and be sure to round your final answer to two decimal places.

e) Calculate your p-value. Write the result below, and be sure to round your final answer to four decimal places.

f) Do you reject the null hypothesis?

• We reject the null hypothesis, since the p-value is less than the significance level.
• We reject the null hypothesis, since the p-value is not less than the significance level.
• We fail to reject the null hypothesis, since the p-value is less than the significance level.
• We fail to reject the null hypothesis, since the p-value is not less than the significance level.

g) Select the statement below that best represents the conclusion that can be made.

• There is sufficient evidence to warrant rejection of the claim that the mean body temperature of a healthy adult is not 98.6∘F98.6∘F.
• There is not sufficient evidence to warrant rejection of the claim that the mean body temperature of a healthy adult is not 98.6∘F98.6∘F.
• The sample data support the claim that the mean body temperature of a healthy adult is not 98.6∘F98.6∘F.
• There is not sufficient sample evidence to support the claim that the mean body temperature of a healthy adult is not 98.6∘F98.6∘F.

Answer 1

Given :

claim : the mean body temperature of a healthy adult is not 98.6∘F

(a) null and alternative hypothesis :

(b)

If the alternative hypothesis (H1) is of less than (<) type then it is left tailed test .

If the alternative hypothesis (H1) is of greater than (>) type then it is right tailed test .

If the alternative hypothesis (H1) is of not equal to ( ≠ ) type then it is two tailed test .

Therefore this is two-tailed

(c)

Significance level is () = 0.05

(d)

Test Statistic :

As population standard deviation is unknown , we have to use t-test .

so t-test statistic is

Therefore the test statistic is -2.42

(e) p-value :

Using excel function = TDIST( t , df , tails)

df = n-1 = 51-1 = 50

tails = 2 ( as this is two tailed)

=TDIST( 2.42 , 50 , 2 )

=0.0192

p-value = 0.0192

(f) Decision rule :

If p-value is less than the significance level , we reject the null hypothesis .

since p-value (0.0192) is less than significance level (0.05) , so we reject the null hypothesis .

We reject the null hypothesis, since the p-value is less than the significance level.

(g) conclusion :

There is sufficient evidence to support the claim .

There is not sufficient evidence to warrant rejection of the claim that the mean body temperature of a healthy adult is not 98.6∘F