Listed below are body temperatures for four subjects measured at two different times in a day.

Question

Body Temperature (°𝐹) 𝑎𝑡 6 𝑎𝑚: 98.0,97.0,98.6,97.4
Body Temperature (°𝐹) 𝑎𝑡 6 𝑝𝑚: 98.0,97.6,98.8,98.0
Assume the sample data are simple random samples and that the differences have a distribution that is approximately normal. Test the claim that body temperature measured at 6 pm is higher than the body temperature measured at 6 am. Use a 0.10 significance level. Show your work.
a. Give the symbolic null & alternative hypotheses. Use correct notation.
H0: HA:
b. Determine the test statistic (round to 3 decimal places): __________________
c. Determine the p-value (round to 3 decimal places):
d. Result (Circle one & justify): REJECT 𝑯𝟎 FAIL TO REJECT 𝑯𝟎
Reason:
e. State a conclusion within the context of the scenario

Did I solve this correctly?

a. H0: µd ≥ 0
HA: µd < 0;
D = Temperature at 6 AM - Temperature at 6 PM

b. -2.333
Sample size = 4
Average = -0.35
Std. Dev = 0.3

Test statistic = (-0.35-0)/0.3/√4=-2.333

c. 0.051
Df = 4-1 = 3
P-value = P(t(3) < -2.333) = 0.051

d. Reject Ho
Reason: The P value of 0.051 is smaller than the significance level of 0.05

e. We reject the null hypothesis due to the data providing enough evidence that the body temperature measured at 6pm is higher than the body temperature measured at 6am.