Question

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.

14) 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:

n1 = 85 n2 = 75 = 124.1 mmHg = 138.7 mmHg s1 = 38.7 mmHg s2 = 39.2 mmHg

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.

Answer 1

we have given that

for vegetarians

n1=85 m1=124.1 S1=38.7

for non-Vegetarians

n2=75 m2=138.7 S2=39.2

we need to test whether the blood pressure of vegetarians is, on average, lower than the blood pressure of nonvegetarians

Hence

Since both sample sizes are more than 30 so we will use Z statistics

also since it is assumed that both population standard deviations are not equal hence test statistics is given by

since test is left tailed so

P-Value=P(Z<-2.365)=0.009

since P Value is less than level of significance hence we reject H0 hence there is sufficient statistical evidence to conclude that the blood pressure of vegetarians is, on average, lower than the blood pressure of nonvegetarians.