5. According to the 2010 US Census, the average number of residents per housingunit for the n=87 counties in Minnesota was 2.10, and the standard deviationwas 0.38. Test whether the true mean number of residents per housing unitin Minnesota in 2010 is less than the national value of 2.34 at the level α = 0.05.a. Show all five steps of this test.b. What type of error could we be making in this context?c. What is the minimum average number of residents per household neededin order to fail to reject H0? Assume the sample standard deviation is the same.d. Suppose the true number of residents per household in Minnesota is normallydistributed with a mean of 2.0 and standard deviation of 0.4. Suppose we rejectnull hypothesis if the sample mean number of residents is less than 2.27. Whatis the probability of making a type II error?

Question
Asked Nov 10, 2019
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5. According to the 2010 US Census, the average number of residents per housing
unit for the n=87 counties in Minnesota was 2.10, and the standard deviation
was 0.38. Test whether the true mean number of residents per housing unit
in Minnesota in 2010 is less than the national value of 2.34 at the level α = 0.05.
a. Show all five steps of this test.
b. What type of error could we be making in this context?

c. What is the minimum average number of residents per household needed
in order to fail to reject H0? Assume the sample standard deviation is the same.
d. Suppose the true number of residents per household in Minnesota is normally
distributed with a mean of 2.0 and standard deviation of 0.4. Suppose we reject
null hypothesis if the sample mean number of residents is less than 2.27. What
is the probability of making a type II error?

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Expert Answer

Step 1

Note:

Thank you for the question. We have solved the first 3 parts for you. If you need help with another one, please re-post the question and mention the part.

Step 2

Part a:

Assuming μ to be the true mean no. of residents per housing unit and σ = 0.38 to be the population standard deviation, the hypotheses are:

H0: μ = 2.34 vs H1: μ < 2.34.

The level of significance is, α = 0.05.

The one-sample z-test is to be used in this situation.

The test statistic for testing, using the sample mean = 2.10 is:

z = (μ)/ σ/(√n)

= (2.10 – 2.34)/(0.38/√87)

= &nd...

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