The p-value for the hypothesis test with a claim that the mean body temperature at 12 am is greater than 98.6 °F, a sample size of n=8, and a test statistic t=2.671 is approximately 0.018.
In hypothesis testing, the p-value is the probability of observing a test statistic as extreme as the one calculated from the sample, assuming the null hypothesis is true.
Given the hypothesis:
Null hypothesis (H0):
μ=98.6 °F (mean body temperature is equal to 98.6 °F)
Alternative hypothesis (H1):
μ>98.6 °F (mean body temperature is greater than 98.6 °F)
The sample size is n=8, and the test statistic (t) is 2.671.
Using statistical software or a t-table, you can find the p-value associated with the test statistic. In this case, the p-value is approximately 0.018.
Interpretation:
If the p-value is less than the significance level (commonly 0.05), you would reject the null hypothesis.
In this scenario, since 0.018<0.05, you would reject the null hypothesis in favor of the alternative hypothesis.
This means there is enough evidence to suggest that the mean body temperature at 12 am is significantly greater than 98.6 °F. The smaller the p-value, the stronger the evidence against the null hypothesis.