The mean income per person in the United States is $44,000, and the distribution of incomes follows a normal distribution. A random sample of 15 residents of Wilmington, Delaware, had a mean of $48,000 with a standard deviation of $10,500. At the 0.100 level of significance, is that enough evidence to conclude that residents of Wilmington, Delaware, have more income than the national average?a) State the null hypothesis and the alternate hypothesis.b) State the decision rule for 0.100 significance level. (Round your answer to 3 decimal places.) Reject Ho if t >_____________c) Compute the value of the test statistic. (Round your answer to 2 decimal places.) Value of the test statistic _______________

Question
Asked Nov 18, 2019
29 views

The mean income per person in the United States is $44,000, and the distribution of incomes follows a normal distribution. A random sample of 15 residents of Wilmington, Delaware, had a mean of $48,000 with a standard deviation of $10,500. At the 0.100 level of significance, is that enough evidence to conclude that residents of Wilmington, Delaware, have more income than the national average?

a) State the null hypothesis and the alternate hypothesis.

b) State the decision rule for 0.100 significance level. (Round your answer to 3 decimal places.) Reject Ho if t >_____________

c) Compute the value of the test statistic. (Round your answer to 2 decimal places.) Value of the test statistic _______________

 

check_circle

Expert Answer

Step 1

Part (a):Null and alternative hypothesis:

The hypotheses to be tested are:

H0: μ ≤ 44,000, that is, the mean income of residence of Wilmington, Delaware is less than or equal to 44,000.

Versus:

H0: μ > 44,000, that is, the residence of Wilmington, Delaware have more income than the national average.

Step 2

Part (b): Decision rule:

The decision rule is given by:

 Reject the null hypothesis if t >critical value. Otherwise fail to reject the null hypothesis.

The level of significance is 0.10.

It is given that test is right tailed. α = 0.10, n=15.

Note that the Excel formula =T....

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Statistics

Other

Related Statistics Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: Forbes magazine published data on the best small firms in 2012. These were firms that had been publi...

A: The mean is calculated using the Excel software. After entering the data in cells A1 to A30 (there a...

question_answer

Q: During the 2009 holiday season, 436 randomly sampled American adults were surveyed regarding their a...

A: c) The sample mean is 84.71 and it is calculated below: From the given information, the 95% confiden...

question_answer

Q: Assume that a sample is used to estimate a population proportion p. Find the 99.9% confidence interv...

A: Solution:From the given information, in a random sample of 235 number of success is 97.The sample pr...

question_answer

Q: Suppose that the number of Facebook friends users have is normally distributed with a mean of 128 an...

A: (b)The conditions for the t-distribution is appropriate as given below:If the sample size is larger ...

question_answer

Q: The lengths of pregnancies in a small rural village are normally distributed with a mean of 261 days...

A: The range would you expect to find the middle 95% of most pregnancies is,Step-by-step procedure to o...

question_answer

Q: THIS NOT GRADED ASSIGIMENT , IT IS AN OLD EXAM QUESTION.

A: (a)Let  is the variance assembly time for men and  the variance assembly time for women.The hypothes...

question_answer

Q: a marketing firm asked a random set of married and single men how much they were willing to spend on...

A: The null and alternative hypotheses are stated below:Null hypothesis: There is no difference in the ...

question_answer

Q: To determine whether caffeine consumption affects the ability to solve math problems, a researcher h...

A: Introduction:If the population standard deviation is unknown so that the sample standard deviation h...

question_answer

Q: Pollsters are concerned about declining levels of cooperation among persons contacted in surveys. A ...

A: The age bracket table is shown below: