A study was conducted to examine the impact of speaking in public on college stu

Question

A study was conducted to examine the impact of speaking in public on college students. A class of 15 statistics students participated in the study. At the beginning of a lecture the students recorded their systolic blood pressure. During the lecture the instructor called on each student to stand and answer questions about topics in the lecture. After speaking the students once again recorded their blood pressure. The resulting values are given below along with summary statistics. Does this information indicate that blood pressure increased because of speaking? Conduct an appropriate hypothesis test and show appropriate steps. A. Let mean systolic blood pressure before speaking in public, and mean systolic blood pressure after speaking in public. The hypothesis for this test are:_ a. H_0: mu_1 - mu_2 = 0 vs H_A: mu_1 - mu_2 notequalto 0 b. H_0: mu_1 - mu_2 = 0 vs H_A: mu_1 - mu_2 > 0 c. H_0: mu_1 - mu_2 = 0 VS H_A: mu_1 - mu_2

Explanation / Answer

there are n=15 students.

hence sample size=n=15

let X denotes the systolic blood pressure before public speaking and Y denotes the same after public speaking

since here the observations are same in both the cases

hence (X,Y) follows bivariate normal distribution with parameters (u1,u2,sigma1,sigma2,r)

A. u1 is the mean systolic blood pressure before public speaking and u2 be the systolic blood pressure after public speaking

we want to test whether blood pressure increases due to speaking

or whether u2>u1

hence the hypothesis is H0: u1-u2=0 vs H1:u1-u2<0   

B. since here X and Y are dependent since the sample units are same in both the cases.

hence this is a two sample paired t test

C. the test statistic is given by T=(mean of difference-0)*sqrt(n)/(sd of difference) which under H0 follows a t distribution with df n-1

now the value of the test statistic is t=(-8.2-0)*sqrt(15)/13.24=-2.399 [answer]

since the alternative hypothesis is left tailed

hence p value is p=P[T<-2.398675] where T~t15-1

p=.015 [answer]

D. so we have level of significance=alpha=0.05

here p=0.015 so p<alpha

hence H0 is rejected

hence

there is sufficient statistical evidence, at the 5% to indicate that blood pressure is increased because of public speaking

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.