Question

Loretta, who turns 91this 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 22 randomly selected, elderly adults. The sample mean systolic blood pressure of the adults in the study was 131mmHg, and the sample standard deviation was 22 mmHg.

Assume that the population of systolic blood pressures of elderly adults is normally distributed. Based on the study, at the 0.05 level of significance, can it be concluded that μ, the mean systolic blood pressure among elderly adults, is greater than 120 mmHg?

Perform a one-tailed test. Then fill in the table below.

Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)

Top of Form

Bottom of Form

The null hypothesis: H0: The alternative hypothesis: H1: The type of test statistic: (Choose one)ZtChi squareF The value of the test statistic: (Round to at least three decimal places.) The critical value at the 0.05 level of significance: (Round to at least three decimal places.) Can it be concluded, at the 0.05 level of significance, that the mean systolic blood pressure among elderly adults is greater than 120 mmHg? Yes No

Answer 1

This is the right tailed test .

The null and alternative hypothesis is

H₀ : $\mu$ = 120

H_a : $\mu$ > 120

The type of test statistic is t .Test statistic = t

= ($\bar x$ - $\mu$ ) / s / $\sqrt$ n

= (131 - 120) / 22 / $\sqrt$ 22

Test statistic = 2.345

df = 21

P-value = 0.0145

$\alpha$ = 0.05

t _0.025,21 = +/-2.080

Critical value = +/-2.080

P-value < $\alpha$

Reject the null hypothesis .

Yes