Question

The systolic blood pressure (BP) of the women was measured in 2011 and in a follow-up in 2014. The researcher wants to know, if, on average, the systolic BP of the poorest women in 2014 is significantly greater than the systolic BP of the same cohort in 2011.

2011 - sample size = 104, mean = 115.04, standard deviation = 14.934, std error mean = 1.464

2014 - sample size = 104, mean = 127, standard deviation = 13.350, std error mean 1.309

1. State appropriate hypotheses (define any symbols used).

2. State (but do not check) the assumptions for carrying out this test. Describe the assumptions in the context of this question.

3. Calculate the value of a suitable test statistic for this test. Show all working out and define any symbols used.

4.Calculate the P-value of this test. Show all working out and define any symbols used.

5.Interpret the P-value and describe the outcome of the test in the context of this question.

Answer 1

1. The null and alternative hypotheses are Ho. μ2014-u2011- 2. The assumptions are as written below: Dependent variable is continuous i. Independent variable consists of two categorical independent groups iii. Observations are independent of each other iv. Variances of both the samples are same v. There are no significant outliers vi Dependent variable should be approximately normally distributed for both the groups 3. The R command to perform the test is >library (BSDA) > tsun. test (mean . x=127, s.x=13.350,n·x=104,mean . y-115.04, s. 14.934,n.y=104, + alternative="greater") Welch Modified Two-Sample t-Test data: Summarized x and y t6.0889, df203.46, p-value-2.789e-09 alternative hypothesis: true difference in means is greater than 0 95 percent confidence interval: 8.714375 sample estimates: mean of x mean of y NA 127.00 115.04 4. The p-value for the test is 2.789e-09 5. Since, the p-value is less than the level of significance if considered 0.05, we will reject the null hypothesis and conclude that the on average, the systolic BP of the poorest women in 2014 is significantly greater than the systolic BP of the same cohort in 2011