Systolic blood pressure levels above $120 \mathrm{~mm} \mathrm{Hg}$ are considered to be high. For the 100 systolic blood pressure levels listed in the accompanying data set, the mean is $121.36000 \mathrm{~mm}$ $\mathrm{Hg}$ and the standard deviation is $17.15498 \mathrm{~mm} \mathrm{Hg}$. Assume that a simple random sample has been selected. Use a 0.10 significance level to test the claim that the sample is from a population with a mean greater than $120 \mathrm{~mm} \mathrm{Hg}$.
Click the icon to view the data set of systolic blood pressure levels.
Identify the null and alternative hypotheses.
(Type integers or decimals. Do not round.)
Identify the test statistic.
(Round to two decimal places as needed)
Identify the P-value.
(Round to three decimal places as needed.)
State the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim.
the null hypothesis. There $\mathbf{\nabla}$ sufficient evidence at the 0.10 significance level to the claim that the sample is from a population with a mean systolic blood pressure level greater than $120 \mathrm{~mm} \mathrm{Hg}$.
Answer
State the conclusion in the context of the problem. There is not enough evidence at the 0.10 significance level to support the claim that the sample is from a population with a mean systolic blood pressure level greater than 120 mm Hg.
Step 1 ：Set up the null and alternative hypotheses. The null hypothesis is that the population mean is equal to 120 mm Hg, and the alternative hypothesis is that the population mean is greater than 120 mm Hg.
Step 2 ：Calculate the test statistic using the formula for a one-sample t-test, which is (sample mean - population mean) / (standard deviation / sqrt(sample size)). The test statistic is approximately \(\boxed{0.79}\).
Step 3 ：Find the p-value associated with this test statistic. The p-value is approximately \(\boxed{0.215}\).
Step 4 ：Compare the p-value with the significance level. Since the p-value is greater than the significance level of 0.10, we do not reject the null hypothesis.
Step 5 ：State the conclusion in the context of the problem. There is not enough evidence at the 0.10 significance level to support the claim that the sample is from a population with a mean systolic blood pressure level greater than 120 mm Hg.
