Consider the following hypotheses: H_0: mu le 20.4 H_A: mu > 20.4 A sample of 50
ID: 3159804 • Letter: C
Question
Consider the following hypotheses: H_0: mu le 20.4 H_A: mu > 20.4 A sample of 50 observations yields a sample mean of 21. Assume that the sample is drawn from a normal population with a known population standard deviation of 5.3 and that alpha = 0.10 we're going to conduct this test using the P-value approach. The hypotheses have already been given to you, but tell me what type of test this is left-tailed, right-tailed, or two-tailed? What is the significance level? Under what conditions will we reject H_0 Calculate the test statistic and p-value. What is your conclusion?Explanation / Answer
a)
Formulating the null and alternative hypotheses,
Ho: u <= 20.4
Ha: u > 20.4
As we can see, this is a right tailed test. [ANSWER]
We can tell as Ha used >.
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b)
Thus, getting the critical z, as alpha = 0.1 ,
alpha = 0.1 [SIGNIFICANCE LEVEL]
Hence, by table/technology,
zcrit = + 1.281551566
Hence, we reject Ho when z > 1.282. [REJECTION REGION]
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c)
Getting the test statistic, as
X = sample mean = 21
uo = hypothesized mean = 20.4
n = sample size = 50
s = standard deviation = 5.3
Thus, z = (X - uo) * sqrt(n) / s = 0.800498243 [ANSWER, TEST STATISTIC]
Also, the p value is
Pvalue = 0.211711091 [ANSWER, P VALUE]
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d)
As z < 1.282, P > 0.10, we FAIL TO REJECT THE NULL HYPOTHESIS.
There is no significant evidence that the true mean is greater than 20.4 at 0.10 level. [CONCLUSION]
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