Question 1076811: Need help finding p-value, thank you! I can't seem to get it right!
Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with σ = 2.8%. A random sample of 10 bank stocks gave the following yields (in percents).
5.7 4.8 6.0 4.9 4.0 3.4 6.5 7.1 5.3 6.1
The sample mean is x = 5.38%. Suppose that for the entire stock market, the mean dividend yield is μ = 4.2%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.2%? Use α = 0.01.
(a) What is the level of significance?
0.01
Correct: Your answer is correct.
State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?
H0: μ = 4.2%; H1: μ ≠ 4.2%; two-tailed
H0: μ = 4.2%; H1: μ < 4.2%; left-tailed
H0: μ = 4.2%; H1: μ > 4.2%; right-tailed
H0: μ > 4.2%; H1: μ = 4.2%; right-tailed
Correct: Your answer is correct.
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
The standard normal, since we assume that x has a normal distribution with unknown σ.
The standard normal, since we assume that x has a normal distribution with known σ.
The Student's t, since n is large with unknown σ.
The Student's t, since we assume that x has a normal distribution with known σ.
Correct: Your answer is correct.
What is the value of the sample test statistic? (Round your answer to two decimal places.)
1.33
Correct: Your answer is correct.
(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)
.1065
Incorrect: Your answer is incorrect.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! What is the value of the sample test statistic? (Round your answer to two decimal places.)
1.33
Correct: Your answer is correct.
(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)
p-value = P(z > 1.33) = normalcdf(1.33,100) = 0.09176
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Conclusion::
Since the p-value is greater than 1%, fail to reject Ho.
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Cheers,
Stan H.
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