Question

Keiko recently switched her primary doctor to one specializing in caring for elderly patients. On her new doctor's website, it says that the mean systolic blood pressure among elderly females is 120 millimeters of mercury (mmilg). Keiko believes the value is actually higher She bases her belief on a recently reported study of 20 randomly selected, elderly females. The sample mean systolic blood pressure was 122 mmHg, and the sample standard deviation was 25 mmHg: Assume that the systolic blood pressures of elderly females are approximately normally distributed. Based on the study. at the 0.05 level of significance, can it. be conduded that μ, the population mean systolic blood pressure among elderly females, is greater than 120 mamlig? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (if necessary. consult a list of formutias.) (a) State the null hypothesis. H 6 and the altemative hypothesis. H1 (b) Determine the type of test statistic to use. (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the p-value. (Round to three or more decimal places.) (e) Can it be concluded that the mean systolic blood pressure among elderly females is greater than 120mmHg ? Yes No

Answer 1

The null hypothesis states that the population mean systolic blood pressure among elderly females is equal to 120 mmHg. The alternative hypothesis states that the population mean systolic blood pressure among elderly females is greater than 120 mmHg. Using the t-test as the appropriate test statistic, the calculated value is 0.894, and the p-value is greater than 0.05, indicating that we fail to reject the null hypothesis. Therefore, it cannot be concluded that the mean systolic blood pressure among elderly females is greater than 120 mmHg.

Step-by-step explanation:

(a) The null hypothesis, H0, is that the population mean systolic blood pressure among elderly females is equal to 120 mmHg. The alternative hypothesis, H1, is that the population mean systolic blood pressure among elderly females is greater than 120 mmHg.

(b) The appropriate test statistic to use is the t-test because we have a sample mean and sample standard deviation.

(c) To find the value of the test statistic, we can use the formula: t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size)). Plugging in the values, we get: t = (122 - 120) / (25 / sqrt(20)) = 0.894. So the value of the test statistic is 0.894.

(d) To find the p-value, we can compare the test statistic to the critical value from the t-distribution table. The critical value for a one-tailed test with a significance level of 0.05 and 19 degrees of freedom is 1.729. Since the test statistic (0.894) is less than the critical value (1.729), the p-value is greater than 0.05. Therefore, we fail to reject the null hypothesis.

(e) Based on the study, it cannot be concluded that the mean systolic blood pressure among elderly females is greater than 120 mmHg.