Question

It is commonly believed that the mean body temperature of a healthy adult is 98.6∘F. You are not entirely convinced. You believe that it is not 98.6∘F. You collected data using 54 healthy people and found that they had a mean body temperature of 98.26∘F with a standard deviation of 1.16∘F. Use a 0.05 significance level to test the claim that the mean body temperature of a healthy adult is not 98.6∘F.

a) Identify the null and alternative hypotheses?

H0: ?

H1: ?

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

Answer 1

a)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 98.6
Alternative Hypothesis, Ha: μ ≠ 98.6

b)

two tailed

c)

0.05

d)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (98.26 - 98.6)/(1.16/sqrt(54))
t = -2.15

e)

P-value Approach
P-value = 0.0361
As P-value < 0.05, reject the null hypothesis.

f)

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

g)

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