Test the indicated claim about the means of two populations. Assume that the two
ID: 3205504 • 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.
2) 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 x1 = 73.0 beats/min s1 = 10.9 beats/min n1 = 16 Exercise regularly x2 = 68.4 beats/min s2 = 8.2 beats/min n2 = 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
Data:
n1 = 16
n2 = 12
x1-bar = 73
x2-bar = 68.4
s1 = 10.9
s2 = 8.2
Hypotheses:
Ha: 1 2
Ha: 1 > 2
Decision Rule:
= 0.025
Degrees of freedom = MIN((16 - 1),(12 - 1)) = 11
Critical t- score = 2.200985159
Reject Ho if t > 2.200985159
Test Statistic:
SE = {(s1^2 /n1) + (s2^2 /n2)} = ((10.9^2)/16) + ((8.2^2)/12)) = 3.6096
t = (x1-bar -x2-bar)/SE = (73 - 68.4)/3.6095648398849 = 1.2744
p- value = 0.1143943
Decision (in terms of the hypotheses):
Since 1.27439185 < 2.200985159 we fail to reject Ho
Conclusion (in terms of the problem):
There is no sufficient evidence 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.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.