Question

It has long been stated that the mean temperature of humans is 98.698.6degrees°F. ​However, two researchers currently involved in the subject thought that the mean temperature of humans is less than 98.698.6degrees°F. They measured the temperatures of 4444 healthy adults 1 to 4 times daily for 3​ days, obtaining 200200 measurements. The sample data resulted in a sample mean of 98.398.3degrees°F and a sample standard deviation of 11degrees°F. Use the​ P-value approach to conduct a hypothesis test to judge whether the mean temperature of humans is less than 98.698.6degrees°F at the alphaαequals=0.010.01 level of significan

Answer 1

Answer:

The claim is false that the mean temperature of humans is less than 98.6°F

Step-by-step explanation:

Claim :The mean temperature of humans is less than 98.6°F

$H_0:\mu \geq 98.6^{\circ}F\\H_a:\mu< 98.6^{\circ}F$

They obtained 200 measurements

Sample size n =200

x = 98.3°F

$\sigma = 11^{\circ}F$

Since n > 30

So we will use  z test

Formula : $z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

Substitute the values in the formula :

$z=\frac{98.3-98.6}{\frac{11}{\sqrt{200}}}$

$z=−0.385$

Refer the z table for p value

p value = 0.3520

α= 0.01

p value > α

So, we accept the null hypothesis.

So, the claim is false that the mean temperature of humans is less than 98.6°F .