It is assumed that the mean systolic blood pressure is mu = 120 mm Hg in the gen
ID: 3396905 • Letter: I
Question
It is assumed that the mean systolic blood pressure is mu = 120 mm Hg in the general population. In the Honolulu Heart Study, a sample of n = 25 people had an average systolic blood pressure of 130 mm Mg with a standard deviation of 20mm Hg. Is the group significantly different from the regular population? What are the null and alternative hypothesis? Ho: mu = 130 HA: mu > 130 Ho: mu = 130 HA: mu 130 Ho: mu = 120 HA: mu > 120 Ho: mu = 120 HA: mu 120 What is the test statistic? 2.5 -2.5 0.5 -0.5 What is the result of your test? alpha = 0.01Explanation / Answer
a)
Formulating the null and alternative hypotheses,
Ho: u1 - u2 = 0
Ha: u1 - u2 =/ 0 [ANSWER, IV]
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b)
At level of significance = 0.05
As we can see, this is a two tailed test.
Calculating the means of each group,
X1 = 50
X2 = 35
Calculating the standard deviations of each group,
s1 = 18
s2 = 12
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):
n1 = sample size of group 1 = 12
n2 = sample size of group 2 = 15
Thus, df = n1 + n2 - 2 = 25
Also, sD = 6.049793385
Thus, the t statistic will be
t = [X1 - X2 - uD]/sD = 2.479423518 = 2.5 [ANSWER, I]
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c)
where uD = hypothesized difference = 0
Now, the critical value for t is
tcrit = +/- 2.05953855
As t > 2.0595, WE REJECT THE NULL HYPOTHESIS.
Hence,
OPTION I: There is enough evidence that the group is significantly different from the regular population.
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