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 :
mm hg
mm hg
We shall use one sample t-test to test the above given hypothesis. The test statistic will be given by,
Where, is sample mean, is hypothesized value of population mean, n is sample size and s is sample standard deviation.
We are given that,
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 (H0) 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.
Data Summaries Sample Mean Sample Std Dev Sample Size 79.998 11.588 1000 Hypothesis Testing Confidence Interval...
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