Question

Loretta, who turns 91 this year, has heard that the mean systolic blood pressure among the elderly is 120 millimeters of mercury (mmHg), but she believes that the actual value is higher. She bases her belief on a recently reported study of 16 randomly selected, elderly adults. The sample mean systolic blood pressure of the adults in the study was 131 mmHg, and the sample standard deviation was 21 mmHg. Assume that the population of systolic blood pressures of elderly adults is normally distributed. Based on the study, at the 0.1 level of significance, can it be concluded that , the mean systolic blood pressure among elderly adults, is greater than 120 mmHg?

Answer 1

We can perform a t-test using the sample data to determine if the mean systolic blood pressure is greater than 120 mmHg. If the p-value is less than 0.1, we can conclude that the actual value is higher.

Step-by-step explanation:

In order to determine whether the mean systolic blood pressure among elderly adults is greater than 120 mmHg, we can perform a hypothesis test using the sample data. Since the population standard deviation is not known, we'll use a t-test.

1. Step 1: State the null and alternative hypotheses.

   Null hypothesis (H0): μ = 120 mmHg

   Alternative hypothesis (H1): μ > 120 mmHg

2. Step 2: Set the level of significance (alpha).

   Alpha (α) = 0.1

3. Step 3: Conduct the hypothesis test.

   We'll use a t-test with the sample mean (131 mmHg), sample standard deviation (21 mmHg), sample size (16), and the hypothesized population mean (120 mmHg).

   Calculate the t-value: t = (x - μ)/(σ/√n), where x is the sample mean, μ is the hypothesized population mean, σ is the sample standard deviation, and n is the sample size.

   t = (131 - 120)/(21/√16) = 11/5 = 2.2

   Compare the t-value to the critical value from the t-distribution table or use statistical software to find the p-value. If the p-value is less than the level of significance (alpha), we reject the null hypothesis in favor of the alternative hypothesis.

4. Step 4: Interpret the results.

   If the p-value is less than 0.1, we can conclude that there is sufficient evidence to suggest that the mean systolic blood pressure among elderly adults is greater than 120 mmHg.