Claim: The average income for college students is below $10,000. What would the
ID: 3022040 • Letter: C
Question
Claim: The average income for college students is below $10,000. What would the null and alternative hypotheses be for this test? H_0: H_A: Explain what a Type 1 error would be for this test. What would the decision rule for this test be? Suppose that a survey of 450 students had an average of $9550 with a standard deviation of However, the sample data suggests that the population has a distribution that is not normal. What would the p-value be for this test? (Show your work.) Given an interpretation of what the p-value means in the context of the problem. If alpha = 0.05, state your conclusion.Explanation / Answer
A)
Ho: u >= 10000
Ha: u < 10000
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b)
It is concluding that the average income for students is below $10000, when in fact, it is not.
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c)
If we use 0.05 level, then we reject Ho if z < -1.645.
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d)
Formulating the null and alternative hypotheses,
Ho: u >= 10000
Ha: u < 10000
As we can see, this is a left tailed test.
Getting the test statistic, as
X = sample mean = 9550
uo = hypothesized mean = 10000
n = sample size = 450
s = standard deviation = 600
Thus, z = (X - uo) * sqrt(n) / s = -15.90990258
Also, the p value is
p = 2.70488*10^-57 [ANSWER, P VALUE]
We can still use the normal distirbution because the sampling distribution of the mean is approimately normal by Central Limit Theorem, and we have a big sample size here.
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e)
If the null hypothesis is true, there is only 2.705*10^-57 chance of getting a sample mean this far from 10000.
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f)
There is significant evidence that the true mean income for college students is below $10000 at 0.05 level. [CONCLUSION]
Comparing z and zcrit (or, p and significance level), we REJECT THE NULL HYPOTHESIS.