Math

StatisticsQ&A Library5. 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

44 views

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?

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 *x̄* = 2.10 is:

*z* = (*x̄* – *μ*)/* σ/*(*√n*)

= (2.10 – 2.34)/(0.38/√87)

= &nd...

Tagged in

Find answers to questions asked by student like you

Show more Q&A

Q: Describe the shape, expected value and standard error for the distribution of sample means for sampl...

A: Given datan = 36mean = 80SD = 24Points on sampling distribution of the sample mean:If the true popul...

Q: The age of children in kindergarten on the first day of school is uniformly distributed between 4.8 ...

A: 1. The mean of the distribution is 5.3200 and it is obtained below: From the given information, the...

Q: Discuss the differences between probability and nonprobability sampling. What are their comparative ...

A: The differences has been shown in the table

Q: Nancy and Karen play a game of cards as follows. Nancy draws 3 cards out of a regular deck of 52 car...

A: From the given information,Total cards = 52.Number of aces = 4,Number of draws (without replacement)...

Q: Suppose that the duration of a particular type of criminal trial is known to be normally distributed...

A: a) The distribution of X ~ N(22,36) is and it is identified below: Let X be the number of days for a...

Q: Problem in photo

A: Precision: The precision of the confidence interval is obtained by the width of the confidence inter...

Q: Explain how you can quickly calculate the average of the following list of test scores without addin...

A: Given data81, 78, 79, 82All the data are centered about 8081 – 80 = 178 – 80 = -279 – 80 = -182 – 80...

Q: Imagine you construct three confidence intervals for the same scenario: a 90%the confidence interval...

A: The confidence intervals are 90% and 95% and 99%.

Q: Is it correct to say that in the long run, if you computed many, many confidence intervals using the...

A: The 99% confidence level gives the long-run of confidence intervals. That is, the large number of sa...