Homework SourseConsider the following hypotheses H0 068 H1 068 Given that
Consider the following hypotheses.
H0: = 0.68
H1: 0.68
Given that P overbar = 0.57, n =160, and = 0.05, answer the following questions.
a. What conclusion should be drawn?
b. Determine the p-value for this test.
a. Determine the critical value(s) of the test statistic.
___________
(Use a comma to separate answers as needed. Round to two decimal places as needed.)
Calculate the test statistic.
___________
(Round to two decimal places as needed.)
Choose the correct answer below.
A. Reject H0. There is sufficient evidence that p 0.68.
B. Do not reject H0. There is insufficient evidence that p 0.68.
C. Reject H0. There is insufficient evidence that p 0.68.
D. Do not reject H0. There is sufficient evidence that P 0.68.
b. p-value = ________
(Round to three decimal places as needed.)
Solution
a)
Formulating the null and alternatuve hypotheses,
Ho: p = 0.68
Ha: p =/= 0.68
As we see, the hypothesized po = 0.68
Getting the point estimate of p, p^,
p^ = x / n = 0.57
Getting the standard error of p^, sp,
sp = sqrt[po (1 - po)/n] = 0.036878178
Getting the z statistic,
z = (p^ - po)/sp = -2.982793795 [ANSWER, TEST STATISTIC]
As this is a 2 tailed test, then, getting the p value,
p = 0.002856304
significance level = 0.05
Comparing p and the significance value, we REJECT THE NULL HYPOTHESIS.
There is significant evidence that the population proporiton is not 0.68. [CONCLUSION]
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b)
From above:
As this is a 2 tailed test, then, getting the p value,
p = 0.002856304 [ANSWER]
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c)
As this is a two tailed z test at 0.05 level, then by table/technology,
critical values = -1.96, 1.96 [ANSWER]
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d)
A. Reject H0. There is sufficient evidence that p 0.68. [ANSWER, A]
