Question

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.

1. 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

Vegetarians   Nonvegetarians n ⁼ 85  

             x1 = 124.1 mmHg x2 = 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.

1. Set up the null hypothesis and alternative hypothesis and indicate the claim.
2. Calculate the test statistic. Be sure to set up the equation. Round to three decimal places.
3. Find the _p-value. Round to four decimal places.
4. Make a decision about the null hypothesis. Be sure to explain how you make the decision.
5. 1. Wrrite a complete a conclusion about the original claim.

Answer 1

a) H₀:

H₁:

b) The test statistic

  

= -2.365

C)



  

= 155

P-value = P(T < -2.365)

= 0.0096

d) since the p-value is less than the significance level (0.0096 < 0.01), so we should reject the null hypothesis.

e) At 0.01 significance level, 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 .