Homework SourseConsider the hypothesis test given by Ho 650 Ha 650 Assume
Consider the hypothesis test given by
Ho: = 650
Ha: > 650
Assume the population is normally distributed. In a random sample of 25 subjects, the sample mean is found to be x = 655 and the sample standard deviation is s = 28
(a) (1 pt) Is this test for population proportion, mean or standard deviation? What distribution should you apply for the critical value?
(b) (1 pt) Is the test a right-tailed, left-tailed or two-tailed test?
(c) (2 pts) Find the test statistic. (Show work and round the answer to two decimal places)
(d) (2 pts) Determine the P-value for this test. (Show work and round the answer to three decimal places)
(e) (1 pt) Is there sufficient evidence to justify the rejection of Ho at the a = 0.02level? Explain.
Solution
(a)
Is this test for population proportion, mean or standard deviation? What distribution should you apply for the critical value?
It is a test for MEAN, as can be seen in the hypotheses.
The distribution, as there are just 25 subjects, is a t distribution.
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(b) (1 pt) Is the test a right-tailed, left-tailed or two-tailed test?
By the use of the > sign in Ha, it is a RIGHT TAILED test.
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(c) (2 pts) Find the test statistic. (Show work and round the answer to two decimal places)
Formulating the null and alternative hypotheses,
Ho: u <= 650
Ha: u > 650
As we can see, this is a right tailed test.
Getting the test statistic, as
X = sample mean = 655
uo = hypothesized mean = 650
n = sample size = 25
s = standard deviation = 28
Thus, t = (X - uo) * sqrt(n) / s = 0.892857143 [ANSWER, TEST STATISTIC]
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D)
Also, the p value is, as df = 25 - 1 = 24,
p = 0.190399677 = 0.19 [ANSWER]
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As p > 0.02, we FAIL TO REJECT THE NULL HYPOTHESIS.
No, there no sufficient evidence to justify the rejection of Ho at the a = 0.02 level.
