Question

It has long been stated that the mean temperature of humans is 98.6degreesF. ​However, two researchers currently involved in the subject thought that the mean temperature of humans is less than 98.6degreesF. They measured the temperatures of 61 healthy adults 1 to 4 times daily for 3​ days, obtaining 275 measurements. The sample data resulted in a sample mean of 98.3degreesF and a sample standard deviation of 1degreesF. Use the​ P-value approach to conduct a hypothesis test to judge whether the mean temperature of humans is less than 98.6degreesF at the alphaequals0.01 level of significance. State the hypotheses. Upper H 0​: ▼ sigma p mu ▼ equals not equals less than greater than 98.6degreesF Upper H 1​: ▼ sigma mu p ▼ less than not equals greater than equals 98.6degreesF Find the test statistic. t 0equals nothing ​(Round to two decimal places as​ needed.) The​ P-value is nothing. ​(Round to three decimal places as​ needed.) What can be​ concluded? A. Do not reject Upper H 0 since the​ P-value is less than the significance level. B. Reject Upper H 0 since the​ P-value is less than the significance level. C. Reject Upper H 0 since the​ P-value is not less than the significance level. D. Do not reject Upper H 0 since the​ P-value is not less than the significance level.

Answer 1

Explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 98.6

For the alternative hypothesis,

µ < 98.6

This is a left tailed test.

Since the population standard deviation is not given, the distribution is a student's t.

Since n = 275

Degrees of freedom, df = n - 1 = 275 - 1 = 274

test statistic, t = (x - µ)/(s/√n)

Where

x = sample mean = 98.3

µ = population mean = 98.6

s = samples standard deviation = 1

t = (98.3 - 98.6)/(1/√275) = - 4.97

We would determine the p value using the t test calculator. It becomes

p < 0.00001

Since alpha, 0.01 > than the p value, then we would reject the null hypothesis. Therefore, the correct option is

B. Reject Upper H 0 since the​ P-value is less than the significance level.