Question

Use technology to find the Pivalue for the hypothesis test described below The claim is that for 12AM body temperatures, the mean is μ>98.6F. The sample aize is n=9 and the test atatistic is t=1.564. P.value

Answer 1

To calculate the p-value for a hypothesis test with sample size n=9 and test statistic t=1.564 using a TI-83 or TI-84 calculator, access the T-Test function, enter the necessary parameters for a right-tailed test, and the calculator will provide the p-value.

Step-by-step explanation:

To find the p-value for the hypothesis test where the claim is that the mean body temperature at 12 AM is greater than 98.6°F, and given a sample size of n=9 and a test statistic t=1.564, one would typically use a Student's t-distribution because the population standard deviation is unknown. Since the sample is small (n=9), the t-distribution is the appropriate choice over the normal distribution.

To calculate the p-value using a technology tool like the TI-83 or TI-84 calculator:

1. Press STAT and arrow over to TESTS.
2. Select 2: T-Test.
3. Enter the test statistic (t=1.564).
4. Set μ: to be > μ0 (the mean under the null hypothesis).
5. Choose Calculate and then press ENTER.

The calculator will then provide the p-value, which is the probability of obtaining a test statistic as extreme as, or more extreme than, the observed value when the null hypothesis is true.

For this data, as the alternative hypothesis is that μ > 98.6°F, this will be a right-tailed test. The p-value is the area under the t-distribution curve to the right of the test statistic value.