Determine the p-value for a hypothesis test for the mean (population standard deviation unknown)

Question

The mean body temperature of the human body under normal conditions is accepted to be98.6

F

. Jason is a pre-med student who is skeptical of this claim. To test this claim, he selects a random sample of47

people to record their body temperatures. The following is the data from this study:

• The alternative hypothesisHa:98.6.
• The sample mean body temperatureof the47 people is98.3F.
• The sample standard deviation is0.80F.
• The test statistic is calculated as2.57.

Using the information above andthe portion of thet

table below, choose the correctp

value and interpretationfor this hypothesis test.

Values forright-tail areas under thet

-distribution curve

Probability0.100.050.0250.010.005Degrees of Freedom401.3031.6842.0212.4232.704411.3031.6832.0202.4212.701421.3021.6822.0182.4182.698431.3021.6812.0172.4162.695441.3011.6802.0152.4142.692451.3011.6792.0142.4122.690461.3001.6792.0132.4102.687471.3001.6782.0122.4082.685481.2991.6772.0112.4072.682491.2991.6772.0102.4052.680

Select the correct answer below:

The probability of observing a value oft0=2.57

or more if the null hypothesis is true is between0.005

and0.01.

The probability of observing a value oft0=2.57 or less or observing a value oft0=2.57

or moreif the null hypothesis is true is between0.01

and0.02.

The probability of observing a value oft0=2.57

or less or observing a value oft0=2.57 or moreif the null hypothesis is true is between0.05

and0.10.

The probability of observing a value oft0=2.57

or less if the null hypothesis is true is between0.005

and0.01