Question

A researcher wishes to determine whether the blood pressure of vegetarians is, on average, lower than the blood pressure of nonvegetarians. Independent simple random samples of 85 vegetarians and 75 nonvegetarians yielded the following sample statistics for systolic blood pressure:

Sample 1:
Sample size (n1) = 85
Sample mean (x̄1) = 124.1 mmHg
Sample standard deviation (s1) = 38.7 mmHg

Sample 2:
Sample size (n2) = 75
Sample mean (x̄2) = 138.7 mmHg
Sample standard deviation (s2) = 39.2 mmHg

Use a significance level of 0.01 to test the claim that the mean systolic blood pressure of vegetarians (μ1) is lower than the mean systolic blood pressure of nonvegetarians (μ2) using the p-value method of hypothesis testing.

Null hypothesis: The mean systolic blood pressure of vegetarians is not lower than the mean systolic blood pressure of nonvegetarians.

Alternative hypothesis: The mean systolic blood pressure of vegetarians is lower than the mean systolic blood pressure of nonvegetarians.

Test statistic (rounded to 2 decimal places): ________

P-value (rounded to 4 decimal places): ________

Reject or fail to reject null hypothesis: ________

Final conclusion that addresses the original claim: ________

Answer 1

To test whether the mean systolic blood pressure of vegetarians is lower than nonvegetarians, we can use the p-value method of hypothesis testing. The test statistic is -4.13 and the p-value is less than 0.0001. Therefore, we reject the null hypothesis and conclude that the mean systolic blood pressure of vegetarians is lower than nonvegetarians.

Step-by-step explanation:

To test whether the mean systolic blood pressure of vegetarians is lower than the mean systolic blood pressure of nonvegetarians, we can use the p-value method of hypothesis testing. The null hypothesis is that the mean systolic blood pressure of vegetarians is not lower than the mean systolic blood pressure of nonvegetarians, while the alternative hypothesis is that the mean systolic blood pressure of vegetarians is lower than the mean systolic blood pressure of nonvegetarians.

Using the given sample statistics, we can calculate the test statistic and the p-value. The test statistic is the z-score, which is calculated as (sample mean 1 - sample mean 2) / sqrt((s1^2 / n1) + (s2^2 / n2)). In this case, the test statistic is -4.13 (rounded to 2 decimal places).

The p-value is the probability of obtaining the observed test statistic or a more extreme test statistic, assuming that the null hypothesis is true. To find the p-value, we can compare the test statistic to the critical value for a one-tailed test at a significance level of 0.01. If the p-value is less than or equal to 0.01, we reject the null hypothesis. In this case, the p-value is less than 0.0001 (rounded to 4 decimal places).

Therefore, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the mean systolic blood pressure of vegetarians is lower than the mean systolic blood pressure of nonvegetarians.