Question

It is commonly believed that the mean body temperature of a healthy adult is 98.6 F. You are not entirely convinced. You collected data using 43 healthy people and found that they had a mean body temperature of 98.21 F with a standard deviation of 1.14 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. Please do not use a table, use calculator.

Answer 1

Solution :

Given that,

Population mean = = 98.6

Sample mean = = 98.21

Sample standard deviation = s = 1.14

Sample size = n = 43

Level of significance = = 0.05

This is a two tailed test.

The null and alternative hypothesis is,

Ho: 98.6

Ha: 98.6

The test statistics,

t = ( - )/ (s/)

=( 98.21 - 98.6 ) / ( 1.14 /43)

= -2.243

Critical value of  the significance level is α = 0.05, and the critical value for a two-tailed test is

= 2.018

Since it is observed that |t| = 2.243 > = 2.018, it is then concluded that the null hypothesis is rejected.

P- Value = 0.0302

The p-value is p = 0.0302 < 0.05, it is concluded that the null hypothesis is rejected.

Conclusion :

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population

mean μ is different than 98.6, at the 0.05 significance level.