When subjects were treated with a drug, their systolic blood pressure readings (

Question

When subjects were treated with a drug, their systolic blood pressure readings (in mm Hg) were measured before and after the drug was taken. Results are given in the table below. Assume that the paired sample dat is a simple random sample and that the differences have a distribution that is approximately normal. Using a 0.05 significance level, is there sufficient evidence to support the claim that the drug is effective in lowering systolic blood pressure? 169 188 158 157 175 164 159 210 179 208 192 155 Before 186 179 159 152 162 148 163 179 147 153 155 156 After In this example, Hd is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the systolic blood pressure reading before the drug was taken minus the reading after the drug was taken. What are the null and alternative hypotheses for the hypothesis test? B. Ho: Hd O A. Ho: d -0 H1: Hd 0 O D. Ho: Hd #0 O C. Ho: d H1: Hd >0 H1: Hd Identify the test statistic. (Round to two decimal places as needed.) Identify the P-value. P-value (Round to three decimal places as needed.) Since the P-value is Y than the significance level, Ho. There is evidence Click to select your answer(s).

Explanation / Answer

Hypothesis: Option A. Since the difference is before drug minus after drug and the test is for evidence to support the after drug has reduced the systolic blood pressure, the alternative hypothesis will check for the mean of difference being greater than 0. Null hypothesis is assumed that the mean of difference is 0.

Standard deviation, sd = sqrt [ ((di - d)2 / (n - 1) ] = 20.59328
SE = sd / sqrt( n ) = 20.59328/sqrt(12) = 5.9448

Degree of freedom, df = n - 1 = 11

t = (d - D) / SE where d is the sample mean and D is the hypothesized mean.
t = (14.58333 - 0)/5.9448 = 2.45

p = 0.016(for right tailed)

Since the p value is less than the significance level, reject H0. There is sufficient evidence to support the claim that the drug is effective in lowering systolic blood pressure.

Before 169 188 158 157 175 164 159 210 179 208 192 155 After 186 179 159 152 162 148 163 179 147 153 155 156 Difference -17 9 -1 5 13 16 -4 31 32 55 37 -1

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