PART
1. An opinion poll asks a random sample of 100 college juniors how they view their job prospects once they graduate. Out of the 100 students 53 said Excellent. Find a 95% confidence interval to estimate the proportion of college juniors who think their job prospects are excellent. Assume large samples.
The random sample is equivalent to 100 college juniors
From this sample, 53 of them considered their job prospects to be excellent, which is equivalent to 0.53.
A 95% confidence interval implies that in the event that 100 different kinds of samples are taken into consideration and a 95% confidence interval is calculated for every sample, then roughly 95 out of the 100 confidence intervals will have the true mean value, which is
To construct a 95% confidence interval for a population, mean , the correct critical value of z* (Sprinthall, 2003) is P (-1.96 < Z < 1.96) = 0.95
The test statistic is 0.7019
The confidence interval is (0.6808, 0.7019)
2. In 1999, the Bureau of Justice Statistics3 indicated that 14% of violent crimes are committed by women. Suppose that a random sample of 400 people who committed violent crimes was taken and it was determined that 65 of the 400 were women. Find a large-sample 95% confidence interval based on the sample data. Determine if the 14% is contained in the confidence interval.
65/400 = 16.25% or 0.1625
To construct a 95% confidence interval for a population, mean , the correct critical value of z* is P (-1.96 < Z < 1.96) = 0.95
The test statistic is 0.5636
The confidence interval is (0.5636, 0.7967)
The 14 percent which is equivalent is not contained within the confidence interval
3. The IRS is trying to determine which percentage of tax returns claim itemized deductions. A random sample of 2,000 returns was taken and the IRS found...
…claims that 30% of tax filers claim itemized deductions. A random sample of 2,000 returns was taken and the IRS found that 663 claimed itemized deductions. Test the claim using the four-step process. Use a significance level of 0.10. Then, compare this problem to Problem 3 of Part 1.State:
Null Hypothesis: 30% of the tax filers claim itemized deductions
Alternate Hypothesis: 30% of the tax filers do not claim itemized deductions
Plan:
A sample is selected from the population, and a sample mean is measured. The random sample taken encompasses a total of 2,000 returns. From this figure, the IRS determined that 663 tax filers claimed itemized deductions.
Solve:
This is equivalent to:
(663 / 2,000) * 100 = 33.15% or 0.3315
Conclude:
A member of the IRS makes a claim that 30% of the tax filers claim itemized deductions. This is equivalent to 0.3. From the question, the test statistic is 0.3315. The significance level used is 0.10. Taking…
References
Seber, G. A. (2013). Statistical models for proportions and probabilities. New York: Springer.
Sprinthall, R. C. (2003). Basic statistical analysis. Allyn & Bacon.
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