Question

Data Summaries Sample Mean Sample Std Dev Sample Size 79.998 11.588 1000 Hypothesis Testing Confidence Interval Creation Level of Confidence: 95% Alpha (a) Value: 0.05 MOE 0.719 9 - MOE: 79.279 9 + MOE: 80.717 Confidence Interval Question What is the confidence interval telling you about the population parameter? Use the formula: df = n-1 Use the formula: (9-4_0)/(s/sqrt(n)) Degrees of Freedom: Alpha (a) Value: Test Statistic Value: Is your test statistic a z value or at value? P-Value Method P-value: Is your p-value <a? Decision: Hypothesis Test Reject H_O What would you Do Not Reject HO regarding his belief auuut tie average diastolic blood pressure?

Answer 1

Solution :

You have already calculated the 95% confidence interval. Your confidence interval is correct.

95% confidence interval is (79.279, 80.717).

Interpretation : We are 95% confident that the average diastolic blood pressure of the people in the USA lies between 79.279 and 80.717.

Hypothesis testing :

The null and alternative hypotheses are as follows :

$\large H_{0} : \mu = 81$ mm hg

$\large H_{1} : \mu < 81$ mm hg

We shall use one sample t-test to test the above given hypothesis. The test statistic will be given by,

t = α – μ s/νη

Where, $\large \bar{x}$ is sample mean, $\large \mu$ is hypothesized value of population mean, n is sample size and s is sample standard deviation.

We are given that, $\large \bar{x}=79.998, \mu = 81, n = 1000, s =11.588$

$\large \therefore t = \frac{79.998-81}{11.588/\sqrt{1000}} =-2.7344$

Test statistic value : -2.7344

Degrees of freedom = (1000 - 1) = 999

Alpha value = 0.03

Our test statistic is a t value.

The test is left-tailed test, so we must obtain left-tailed p-value, which is given by,

p-value = P(T < t)

p-value = P(T < -2.7344)

p-value = 0.0032

The p-value is 0.0032

Significance level (alpha) = 0.03

(0.0032 < 0.03)

P-value < alpha

Since, p-value is less than the significance level of 0.03, therefore the null hypothesis (H​​​​​​0) will be rejected at 0.03 significance level.

Conclusion : At 0.03 significance level, there is sufficient evidence to conclude that the average systolic blood pressure is less than 81 mm hg.