Question

After surveying brokers at an insurance firm, the results showed that out of 6 brokers only 30% of the brokers were bringing in most of the sales, while the remainders were only able to renew with their same companies. I claim that 50% of all brokers are able to bring in most of sales. Use a 0.05 significant level to test the stated claim about population proportion." In your second posting, you need to manually state the null and alternate hypotheses for the claim you have made in your question and type of hypothesis test, by indicating whether the test is right-tailed, left-tailed, or two-tailed test. Then, calculate the related Test Statistic and p-value by StatCrunch along with the summary table or by using manual calculations followed by comparing the related p-value versus the level of significance to determine whether to reject or not to reject the null hypothesis. Based on this comparison, you can make a decision whether the stated claim inside your question about the population proportion is valid or not.

Answer 1

Solution:-

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

Null hypothesis: P = 0.50
Alternative hypothesis: P $\neq$ 0.50

Note that these hypotheses constitute a two-tailed test.

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 (S.D) and compute the z-score test statistic (z).

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

S.D = 0.20412
z = (p - P) /S.D

z = - 0.9798

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 two-tailed test, the P-value is the probability that the z-score is less than -0.9798 or greater than 0.9798.

Thus, the P-value = 0.3272

Interpret results. Since the P-value (0.3272) is greater than the significance level (0.05), we cannot reject the null hypothesis.

From the above test we have sufficient evidence in the favor that stated claim inside your question about the population proportion is valid