Test the Indicated Claim About the Means of Two Populations

question 63

Essay

Test the indicated claim about the means of two populations. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations
are equal. Use the traditional method or P-value method as indicated.
-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:
$$\begin{array} { l l } \text { Vegetarians } & \text { Nonvegetarians } \\\hline \mathrm { n } _ { 1 } = 85 & { \mathrm { n } _ { 2 } } = 75 \\\overline { \mathrm { x } _ { 1 } } = 124.1 \mathrm { mmHg } & \overline { \mathrm { x } _ { 2 } } = 138.7 \mathrm { mmHg } \\\mathrm { s } _ { 1 } = 38.7 \mathrm { mmHg } & \mathrm { s } _ { 2 } = 39.2 \mathrm { mmHg }\end{array}$$ Use a significance level of 0.01 to test the claim that the mean systolic blood pressure of vegetarians is lower than the mean systolic blood pressure of nonvegetarians. Use the P-value method of hypothesis testing.

Calculate population size using the finite population correction factor.

Utilize the formula of the standard error of the mean to calculate probabilities related to sample means from infinite populations.

Describe the properties of the sampling distribution of the sample mean.

Determine the relationship between sample size, standard error, and the distribution shape of the sample mean.

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Definitions:

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