Homework SoursePlease explain all parts A wine producer claims that the pro
Please explain all parts!
A wine producer claims that the proportion of its customers who cannot distinguish its product from frozen grape juice is about 0.1. The producer decides to test this null hypothesis against the alternative that the true proportion is more than 0.1. He then selects a random sample of 101 from his customers, and 14 of them fail to distinguish its product from frozen grape juice.
What should the appropriate hypotheses one should test?
Incorrect H0: p = 0.1, Ha: p < 0.1
Incorrect H0: p = 0.14, Ha: p 0.14
Incorrect H0: p = 0.1, Ha: p 0.1
Correct: H0: p = 0.1, Ha: p > 0.1
Incorrect H0: p = 0.14, Ha: p > 0.14
The value of the test-statistic is
We should reject at 6% level of significance if
Correct: test-statistic > 1.555
Incorrect test-statistic > 1.881
Incorrect | test-statistic | > 1.881
Incorrect test-statistic < -1.555
If = 0.06, what will be your conclusion?
Incorrect Reject H0
Correct: Do not reject H0
Incorrect not enough information to reach a decision
The p-value of the test is equal to
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Solution
1.
Formulating the null and alternatuve hypotheses,
Ho: p = 0.1
Ha: p > 0.1 [ANSWER]
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2.
As we see, the hypothesized po = 0.1
Getting the point estimate of p, p^,
p^ = x / n = 0.138613861
Getting the standard error of p^, sp,
sp = sqrt[po (1 - po)/n] = 0.029851116
Getting the z statistic,
z = (p^ - po)/sp = 1.293548347 [ANSWER, TEST STATISTIC]
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3.
At 0.06 level, right tailed, by table/technology, we reject Ho if
z > 1.554773595 [ANSWER]
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4.
As z < 1.555, WE DO NO REJECT HO. [ANSWER]
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5.
The right tailed area of z = 1.2935 is, by table/technology,
P = 0.0979 [ANSWER]
As this is a 1 tailed test, then, getting the p value,
p = 0.097910737
