Discussion below along with example

The objective of this assignment is for you to personally create a fully documented artificial (i.e. you make it up) example of a hypothesis test of a claim about a population proportion parameter using the Critical Value Method just like you might see in a textbook. Please do not copy an example from the Internet or a textbook. Also, while I expect you to learn from other students' submissions, if in my opinion your post too closely resembles another student's I will ask you to revise it.

Please use the following outline for your response:

I) Description of problem and statement of claim and test.

The proportion of kindergarten students in the DEF School District who walk to school is equal to 10%

The proportion of drivers who live in the city of GHI who listen to the radio while driving is less than 40%

B) State the claim symbolically (i.e. using mathematical symbols). For the above example claims this would look like:

p > 0.75

p = 0.10

p < 0.40

II) Statement of null hypothesis.

State H0. (Hint: Given your symbolic claim above, follow the flowchart in Figure 8-2 (p. 385) to identify H0. It will be a mathematical expression with p and an equal sign.)

III) Statement of alternative hypothesis.

State H1. (Hint: Given your symbolic claim above, follow the flowchart in Figure 8-2 (p. 385) to identify H1. It will be a mathematical expression with p and either a greater-than sign, a less-than sign, or a not-equal sign.)

IV) Description of sampling plan

(Hint: You should describe a procedure for obtaining a random sample from the stated population and since you are testing a population proportion, the end result should be some number of "successes", say x, out of a sample size of n where you create x and n for the purpose of this example. )

A) Describe how a sample of data for testing the claim was obtained.

B) State the sample size, n, and what was recorded for each item in the sample. 

V) Verification of requirements, calculation of test statistic, statement of critical value(s).

Chapter 8-3 describes a number of ways to test the claim about the proportion given the sample data. For this assignment, use the Critical Value Method (p. 402).

A) First tell why the three requirements on the top of p. 400 are satisfied.

B) Calculate and show the test statistic.

VI) State the conclusion about the null hypothesis and then in words using the original claim.

Enter your discussion response by clicking RESPOND on this post and put your name in the title. You can discuss other students' input by clicking on RESPOND for their posts. If you change your response based on my comments, please be aware that I am not notified automatically when you modify a post, only when you make a new post using Respond, so you will have to let me know of your modification. Also, all responses should be written - not audio or video.

Here is an example: Please don't copy if you do I can't use it and please don't use the explanation becase it's wrong.

I.  State the Claim

a. The proportion of families in the U.S with more than 2 children is less than 35%. P > .35 and the significance level is .01

II. State the Null hypothesis

a. H₀: P = .35

III. State the alternative hypothesis

a. H₁: P > .35

IV.  Description of sampling plan

a. After sampling 40,650 families randomly in the U.S it is found that 12,230 of them have more than 2 children. N=40,650 and x=12,230

V. Verification of requirements, calculation of test statistic, and statement of critical values.

a. The requirements for this test are met. First, the sample is a simple random sample as all variations of n were able to happen. Second, the requirements for a binomial distribution are met. There is a fixed number of independent tests in which the options yield either a success or a failure. Finally, np is greater than or equal to 5 and nq is also greater than or equal to 5. Therefore all requirements to run the test are met.

b. z = .300861 - .35 / srt[(.35 * .65) / 40,650] = -.049139/.0023657 = -20.7714  (P value is .0000)

c. The critical value is 2.33

VI. State the conclusion

a.     Because the P-value is less then the significance level, reject the null hypothesis. There is sufficient evidence to support the claim that the proportion of families in the U.S with more than 2 children is less than 35%.