Test the indicated claim about the means of two populations. Assume that the two
ID: 3205561 • Letter: T
Question
Test the indicated claim about the means of two populations. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. A researcher was interested in comparing the resting pulse rates of people who exercise regularly and of those who do not exercise regularly. Independent simple random samples of 16 people who do not exercise regularly and 12 people who exercise regularly were selected, and the resting pulse rates (in beats per minute) were recorded. The summary statistics are as follows. Do not exercise regularly Exercise regularly x_1 = 73.0 beats/min X_2 = 68.4 beats/min s_1 = 10.9 beats/min S_2 = 8.2 beats/min n_1 = 16 n_2 = 12 Use a 0.025 significance level to test the claim that the mean resting pulse rate of people who do not exercise regularly is larger than the mean resting pulse rate of people who exercise regularly. Use the traditional method of hypothesis testing.Explanation / Answer
Given that,
mean(x)=73
standard deviation , s.d1=10.9
number(n1)=16
y(mean)=68.4
standard deviation, s.d2 =8.2
number(n2)=12
null, Ho: u1 = u2
alternate, people who don't exercise regularly is larger than mean resting pulse rate of people H1: u1 > u2
level of significance, = 0.025
from standard normal table,right tailed t /2 =2.056
since our test is right-tailed
reject Ho, if to > 2.056
calculate pooled variance s^2= (n1-1*s1^2 + n2-1*s2^2 )/(n1+n2-2)
s^2 = (15*118.81 + 11*67.24) / (28- 2 )
s^2 = 96.9919
we use test statistic (t) = (x-y)/sqrt(s^2(1/n1+1/n2))
to=73-68.4/sqrt((96.9919( 1 /16+ 1/12 ))
to=4.6/3.7609
to=1.2231
| to | =1.2231
critical value
the value of |t | with (n1+n2-2) i.e 26 d.f is 2.056
we got |to| = 1.2231 & | t | = 2.056
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value: right tail -ha : ( p > 1.2231 ) = 0.11613
hence value of p0.025 < 0.11613,here we do not reject Ho
ANSWERS
---------------
null, Ho: u1 < u2
alternate, H1: u1 > u2
test statistic: 1.2231
critical value: 2.056
decision: do not reject Ho
p-value: 0.11613
we don't have enough evidence to support people who don't exercise regularly is larger than
mean resting pulse rate of people
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.