Test the indicated claim about the means of two populations. Assume that the two
ID: 2907302 • 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 3) 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 x1- 73.2 beats/min x2-68.9 beats/min 1 10.9 beats/min s2-8.2 beats/min n1-16 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
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: u1< u2
Alternative hypothesis: u1 > u2
Note that these hypotheses constitute a one-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.025. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 3.60956
DF = 26
t = [ (x1 - x2) - d ] / SE
t = 1.19
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is thesize of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.
The observed difference in sample means produced a t statistic of 1.19.
Therefore, the P-value in this analysis is 0.245.
Interpret results. Since the P-value (0.245) is greater than the significance level (0.025), we cannot reject the null hypothesis.
From the above test we do not have sufficient evidence in the favor of the claim that the mean resting pulse of people who do not exercise regularly is larger than the mean resting pulse rate of people who exercise regularly.
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