Question

2)

Human Body Temperature. A sample of 112 body temperatures with a mean of 98.20°F and a standard deviation of 0.62°F. Use a 0.05 significance level to test the claim that the mean body temperature of the population is equal to 99.6°F, as is commonly believed. Is there sufficient evidence to conclude that the common belief wrong?

Answer 1

Given that a sample of n = 112 body temperatures with a mean of = 98.20°F and a standard deviation of s = 0.62°F.

Now we have to test the claim that the mean body temperature of the population is equal to 99.6°F, as is commonly believed.

Thus based on the claim the hypotheses are:

Based on the hypothesis it will be a two-tailed test since the population standard deviation is unknown hence t-distribution is applicable:

Rejection region:

Based on the type of hypothesis and given significance level which is 0.05 the critical value for the rejection region is calculated using the excel formula for t-distribution which takes the significance level and the degree of freedom df = n-1= 112-1 =111, the formula used is =T.INV.2T(0.05, 111), thus the tc = 1.982.

Reject the Ho if t < -tc or t >tc.

Test statistic:

Conclusion:

Since the t << -tc hence we can reject the null hypothesis and conclude that there is enough evidence to warrant the rejection of the claim that the mean body temperature of the population is equal to 99.6°F, as is commonly believed.

Note: Feel free to ask in query remains