Homework SourseSystolic blood pressure of adults has a normal distribution
Systolic blood pressure of adults has a normal distribution with mean 130 and standard deviation 35. Someone makes the claim that statistics teachers have a higher average systolic blood pressure than 130. A random sample of 100 statistics teachers is obtained and the mean is 135. Assume that 35 is the standard deviation for the population of statistics teachers. Suppose the claim was that statistics teachers have a different average systolic blood pressure than 130. The research and null hypotheses are as follows.
Ha :=(doesn\'t equal)130 H0 :=130
(a) Calculate a two sided p-value
(b) For = 0.05 is the test statistic you calculated in 2(a) larger or smaller than the critical value?
(c) If = 0.05, is there enough evidence to reject H0 and conclude that the Ha is true? (d) If = 0.1, what is the critical value of Z.
(d) For = 0.1 is the test statistic you calculated in 2(a) larger or smaller than the critical value?
(e) If = 0.1, is there enough evidence to reject H0 and conclude that the Ha is true?
Solution
a)
Formulating the null and alternative hypotheses,
Ho: u = 130
Ha: u =/ 130
As we can see, this is a two tailed test.
Getting the test statistic, as
X = sample mean = 135
uo = hypothesized mean = 130
n = sample size = 100
s = standard deviation = 35
Thus, z = (X - uo) * sqrt(n) / s = 1.428571429
Also, the p value is
p = 0.153127451 [ANSWER, p value]
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b)
As P > 0.05, then the test statistic is SMALLER THAN THE CRITICAL VALUE at 0.05 level.
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C)
NO, as P > 0.05.
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d)
As this is a two tailed test, at 0.1 level,
zcrit = +/- 1.645 [ANSWER]
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d)
As P > 0.1, then the test statistic is SMALLER THAN THE CRITICAL VALUE at 0.1 level.
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e)
As P > 0.1, NO.
Comparing z and zcrit (or, p and significance level), we FAIL TO REJECT THE NULL HYPOTHESIS.
