Question

George is curious. He has been told that the average body temperature of humans is 98.6 degrees Fahrenheit.​ However, he believes it is much lower than that. He randomly selects 60 people from those passing by him on a street and takes their temperature. The average temperature of these 60 people is 98.2 degrees Fahrenheit. The standard​ deviation, sigma Subscript x​,is known to be 0.62 degrees Fahrenheit. The​ p-value is less than 0.0001. What is the correct​ conclusion?

Answer 1

`p_v =P(t_((59))>t_(calc))<0.0001`

Since the p value is a very low value we have enough evidence to reject the null hypothesis in favor of the alternative hypothesis and we can conclude that the true mean for this case is significantly different from 98.6 F at any usual significance level used.

Explanation:

Information given

`\bar X=98.2` represent the sample mean

`\sigma=0.62` represent the population standard deviation

`n=60` sample size

`\mu_o =98.6` represent the value that we want to test

t would represent the statistic

`p_v` represent the p value

System of hypothesis

We want to verify if the true mean is equal to 98.6 F, the system of hypothesis would be:

Null hypothesis:
`\mu = 98.6`

Alternative hypothesis:
`\mu \\eq 98.6`

The statistic is given by:

`t=(\bar X-\mu_o)/((s)/(√(n)))` (1)

The degrees of freedom, on this case:

`df=n-1=60-1=59`

The p value would be given by:

`p_v =P(t_((59))>t_(calc))<0.0001`

Since the p value is a very low value we have enough evidence to reject the null hypothesis in favor of the alternative hypothesis and we can conclude that the true mean for this case is significantly different from 98.6 F at any usual significance level used.