It has long been stated that the mean temperature of humans is 98.6 degrees F. However, two researchers currently involved in the subject thought that the mean temperature of humans is less than 98.6 degrees F. They measured the temperatures of 56 healthy adults 1 to 4 times daily for 3 days, obtaining 250 measurements. The sample data resulted in a sample mean of 98.2 degrees F and a sample standard deviation of 0.9 degrees F. Use the P-value approach to conduct a hypothesis test to judge whether the mean temperature of humans is less than 98.6 degrees F at the alpha = 0.01 level of significance.1. State the hypotheses.A. Upper H 0H0:▼▼ 98.6 FB. Upper H 1H1:▼▼ 98.6 F2. Find the test statistic.a. t0 = ?b. the P-value is:____.3. What can be concluded?A. RejectUpper H0 since the P-value is less than the significance level.B. Reject Upper H0 since the P-value is not less than the significance level.C. Do not reject Upper H0 since the P-value is less than the significance level.D. Do not reject Upper H0 since the P-value is not less than the significance level.

We are given that it has long been stated that the mean temperature of humans is 98.6 degrees F. However, two researchers currently involved in the subject thought that the mean temperature of humans is less than 98.6 degrees F.

The sample data resulted in a sample mean of 98.2 degrees F and a sample standard deviation of 0.9 degrees F.

Let [tex]\mu[/tex] = mean temperature of humans.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu\geq[/tex] 98.6°F {means that the mean temperature of humans is more than or equal to 98.6°F}

Alternate Hypothesis, [tex]H_A[/tex] : p < 98.6°F {means that the mean temperature of humans is less than 98.6°F}

The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;

T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean temperature = 98.2°F

[tex]\sigma[/tex] = sample standard deviation = 0.9°F

n = sample of healthy adults = 56

So, test statistics = [tex]\frac{98.2-98.6}{\frac{0.9}{\sqrt{56} } }[/tex] ~ [tex]t_5_5[/tex]

= -3.326

The value of t test statistics is -3.326.

Now, P-value of the test statistics is given by following formula;

P-value = P( [tex]t_5_5[/tex] < -3.326) = 0.00077 or 0.08%

Since, P-value of the test statistics is less than the level of significance as 0.08% < 1%, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the mean temperature of humans is less than 98.6°F.