Question

# Use the below to solve 8,10,12 1. Identify n, p, and q. Verify that np 5...

Use the below to solve 8,10,12 1. Identify n, p, and q. Verify that np 5 and nq 5. 2. State the claim both verbally and mathematically. Identify the null and alternative hypotheses. (State H0 and Ha) 3. Determine what type of test you will be doing: If Ha is < then left tailed If Ha is > then right tailed If Ha is then two tailed 4. Specify the level of significance, α. This represents the area under the curve that lies in the shaded region of the tail. Sketch a graph of this. 5. Determine the critical value(s) by looking up the appropriate area based on the level of significance on the INSIDE of the standard normal distribution chart (table 4) to find the z-value corresponding to that area. For a left-tailed test, you will be finding the closest area to α on the INSIDE of the table and finding the corresponding z-score. For a right-tailed test you will be finding the closest area to 1 – α on the INSIDE of the table and finding the corresponding z-score. For a two-tailed test you will be finding the closest area to ½ α on the INSIDE of the table, finding the corresponding z-score, and using the negative and positive values of the z-score. 6. Determine the rejection region(s) based on the critical value(s) and shaded area of the graph. 7. Determine the test statistic, which is the sample proportion ?̂. Remember that ?̂= ? ? if you have to compute it. 8. Find the standardized test statistic, z = ?̂−? √ ?? ? . 9. Make a decision to reject or fail to reject the null hypothesis. Reject H0 if z is in the rejection region. Fail to reject H0 if z is not in the rejection region. 10. Interpret the decision in the context of the original claim 8) Internal Revenue Service Audits A research center claims that at least 27% of U.S. adults think that the IRS will audit their taxes. In a random sample of 1000 U.S. adults in a recent year, 23% say they are concerned that the IRS will audit their taxes. At α = 0.01, is there enough evidence to reject the center’s claim? 10) Working Students An education researcher claims that 57% of college students work year-round. In a random sample of 300 college students, 171 say they work year-round. At α = 0.10, is there enough evidence to support the researcher’s claim? 12) Changing Jobs A research center claims that more than 29% of U.S. employees have changed jobs in the past three years. In a random sample of 180 U.S. employees, 63 have changed jobs in the past three years. At α = 0.10, is there enough evidence to support the center’s claim?

Solution:-

12)

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

Null hypothesis: P < 0.29
Alternative hypothesis: P > 0.29

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.10. 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 = 0.03382
z = (p - P) / S.D

z = 1.774

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 greater than 1.774.

Thus, the P-value = 0.038.

Interpret results. Since the P-value (0.038) is less than the significance level (0.10), we cannot accept the null hypothesis.

From the above test we have sufficient evidence in the favor of the center's claim.