Question

Question 3 Background: Blood Pressure versus Position Does the position of patient in which the patient's blood pressure is measured affect the result of the measurement? standing position results in lower readings than measuring systolic blood pressures in supine position. Let the parameter Pd represent the An experiment was designed to assess whether measuring systolic blood pressure population mean difference in systolic blood measurement readings (Standing less Supine, i.e., Standing Supine) for the population of all adults. The researcher would like to test Ho: Hd = 0 verus Ha Hd 0. A random sample of nineteen adults was takes and their blood pressures, in mmHg, were measured in both positions. Here are some summary measures of the variables associated with blood pressure measurements sd se(mean) IQR 0% 25% 50% 75% 100% mean Difference -1.8461 4.7232 1.0836 6.5744 -10,0967 -4.8526 -1.9643 1.7217 5.8031 19 126.0448 131.4719 Standing 140.8871 10.3778 2.3808 18.0854 143.0283 149.5573 157.0217 19 Supine 142.7332 12.6771 2.9083 15,6067 120.5047 134.7589 147.3576 150.3656 165.9995 19 Question 3 Subquestions 3.a Which of the following (slightly rounded) values from this summary output correctly completes this interpretation 0.5 statement? point(s) We would estimate the possible sample mean differences in blood pressure readings (d values) to be about mmHg away from population mean difference in blood pressure rea Hd, on average. 4 7232 10.3778 12.6771 1.0836 2.3808 2,9083 3.b Which of the following (slightly rounded) values from this summary output corectly completes this interpretation 0.5 statement? point(s) The sample mean differerence in blood pressure readings is standard errors from the hypothes ized population mean difference in blood pressure readings of 0 mmHg. 0.3909, below 1.7037, below n59.1764, above 13.5758, above 49.0779, above 11.2591, above 3.c What distribution is used to find the p-value for the test? 0.5 point(s) standard normal N(0,1) distribution a t(19) distribution a t(18) distribution 3.d Provide the bounds for the p-value. 0.5 point(s) 0.05> p-value >0.075 0.05

Answer 1

a)
se(mean) = 1.0836

b)
TS = mean/se
TS = -1.8461/1.0836
= - 1.7037

hence 1.7037 below

c)
this is paired t-test
t-distribution
df =n-1 = 19-1 = 18

d)
p-value = P(T < -1.7037)
= =t.dist(-1.7037,18,1)
= 0.0528

hence
option A) is correct