Question

Complete this homework by R and put the syntaxes of R and corresponding outputs under respective question

[Example Question] Find the mean and the variance of milk yield data.

> mean(task)

[1] 36.15385

A medical researcher wishes to determine if a pill has the undesirable side effect of reducing the blood pressure of the user. The study involves recording the initial blood pressure of 15 college-age women. After they use the pill regularly for six months, their blood pressures are again recorded. The researcher wishes to draw inferences about the effect of the pill on blood pressure from the observations given in the table below. (You need to create your own data file based on the observations in the table.) ID 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Before 70 80 72 76 76 76 72 78 82 64 74 92 74 68 84 After 68 72 62 70 58 67 68 59 66 72 74 65 74 72 73 (a) Calculate a 95% confidence interval for the mean reduction in blood pressure. (b) Test whether the data substantiate the claim that use of the pill reduces blood pressure at a =0.01. (Follow all the necessary steps)

I apologized i put the wrong qs

Answer 1

## R command

Before=c(70,80,72,76,76,76,72,78,82,64,74,92,74,68,84)
After=c(68,72,62,70,58,67,68,59,66,72,74,65,74,72,73)

## a) The 95% Confidence interval include in output of this test
t.test(x=Before, y =After, alternative = "greater", paired =TRUE,
conf.level = 0.95)

## End

Let, d=Before=After

Hypothesis

$H_{o}:~\mu_{d}=0$

$H_{1}:~\mu_{d}>0$

> Before=c(70,80,72,76,76,76,72,78, 82, 64,74,92,74, 68, 84) > After=c(68,72,62,70, 58, 67, 68, 59, 66, 72,74,65,74,72,73) > ## a) The 95% Confidence interval include in output of this test > t.test(x=Before, y =After, alternative = "greater", paired =TRUE, conf.level = 0.95) + Paired t-test data: Before and After t = 3.2325, df = 14, p-value = 0.003009 alternative hypothesis: true difference in means is greater than o 95 percent confidence interval: 3.580295 Inf sample estimates: mean of the differences 7.866667

The 95% confidence interval for the true population mean reduction in blood pressure is (3.580296, infinity). Hence, the true population mean reduction in blood pressure falls in this interval with 95% confidence.

b) The p-value of the test is 0.003009 and less than 0.01 significance level. Hence, we can reject the null hypothesis and accept the claim that the pill has the undesirable side effect of reducing the blood pressure of the user at the 0.01 significance level.