For this project you will be conducting two hypothesis tests similar to the ones

Question

For this project you will be conducting two hypothesis tests similar to the ones you ran in your Chapter 8 homework. I want to see that you can show all the steps for the P-value method of Hypothesis Testing A small part of the federal budget is prepared by estimating the proportion of veterans who will take advantage of the educational benefit (The Montgomery Gl Bill provides money for college, technical and vocational school for active-duty personnel and veterans.) A random sample of 470 veterans was obtained, and 178 indicated that they intended to use the education benefit within the next year. Use a 0.05 significance level to test the claim that less than 40% of all veterans will use their educational benefit within the next year. 1. k) Show all the steps of your hypothesis test including a) the claim being tested , b) the null and alternative hypothesis, c) the test statistic, d) the p value, e) initial cnclician and a final conclusion about the,original claim

Explanation / Answer

Solution:-

a) The claim is p < 0.40.

b)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P > 0.40
Alternative hypothesis: P < 0.40

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected only if the sample proportion is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method, shown in the next section, is a one-sample z-test.

Analyze sample data. Using sample data, we calculate the standard deviation () and compute the z-score test statistic (z).

= sqrt[ P * ( 1 - P ) / n ]

= 0.0226
c)

z = (p - P) /

z = - 0.94

where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

Since we have a one-tailed test, the P-value is the probability that the z-score is less than - 0.94.

d) Thus, the P-value = 0.1736

Interpret results. Since the P-value (0.1736) is greater than the significance level (0.05), we cannot accept the null hypothesis.

e) The initial claim is that less than 40% of the veterans will use their educational benefits within the next year.

d) Final conclusion from the above test we do not have sufficient evidence in the favor of the claim that less than 40% of the veterans will use their educational benefits within the next year.

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