Question

Use the following data for Questions 6. 7. 8. and 9: Past data show the mean temperature of humans to be 98.6 degrees F. Some recent data for a sample of 26 females 1 to 4 times daily for three days yielded a total of 123 measurements. This sample data had a mean temperature of 98.4 degrees F with a standard deviation of 0.7 degrees F. Perform a hypothesis test to judge whether the normal body temperature of women is less than 98.6 degrees F at a 0.01 level of significance State the null and alternative hypotheses: (A)H: u = 98.6; H: > 98.6 (B) H: p = 98.6; H: < 98.6 (C)H: y = 98.6; H: # 98.6 (D) H: > 98.6; H: > 98.6

pls I need help.with the solution as soon as possible

Answer 1

Solution:

Given

n = 26 sample size

$\mu= 98.6$ degrees F population mean

$\bar x= 98.4$. degrees F sample mean

s = 0.7 degrees F sample standard deviation

$\alpha=0.01$. Level of significance

To test the hypothesis

$Ho:\mu= 98.6$. Vs.   $Ha:\mu< 98.6$

Option B is correct.

Test statistic

$t = \frac{\bar x-\mu}{s/\sqrt n}$

$t = \frac{98.4-98.6}{0.7/\sqrt 26}$

$t = \frac{98.4-98.6}{0.7/5.0990195}$

$t = \frac{-2}{0.1372812}$

t = -1.4568637

Test statistic t = -1.457

P Value = 0.078782 from online P value calculator

P Value = 0.0788

Decision : P Value  $> \alpha=0.01$

Fail to reject Ho.

Conclusion: fail to reject Ho , there is insufficient evidence to conclude that the normal body temperature of women is less than 98.6 degrees F.