Did I do this right and should i show more work?
Listed below are body temperatures for four subjects measured at two different times in a day.
Body Temperature (ยฐ๐น) ๐๐ก 6 ๐๐: 98.0,97.0,98.6,97.4
Body Temperature (ยฐ๐น) ๐๐ก 6 ๐๐: 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 ๐ฏ๐ FAIL TO REJECT ๐ฏ๐
Reason:
e. State a conclusion within the context of the scenario:
a. Ho: ยตd โฅ 0
Ha: ยตd < 0;
D = Temperature at 6 AM - Temperature at 6 PM
b. -2.333
Sample size = 4
Average = -0.35
Std. Dev = 0.3
(-0.35 -0)/0.3/โ4 = -2.333
c. 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 9pm is higher than the body temperature measured at 6am.