Statistics 3 fixing of a couple questions:

Inferential Statistics and Analytics

Rasmussen College

11/20/17

Deliverable 03 Worksheet

1. Discuss the importance of constructing confidence intervals for the population mean by answering these questions.

· What are confidence intervals?

· What is a point estimate?

· What is the best point estimate for the population mean? Explain.

· Why do we need confidence intervals?

Answer and Explanation:

Enter your step-by-step answer and explanations here.

· Confidence intervals refers to a measure of probability that a given population parameter will fall between the two set values. It expresses both uncertainty and precision of a sampling method used by giving a range of values. It consist of confidence level, margin of error and a statistic.

· Point estimate is a single value used as static, which is to estimate a parameter in a given population. For example a sample mean of a population, standard deviation and sample variance.

· Sample means is the best point estimate for population means.

· Confidence intervals are important in statistics as they help in explaining uncertainty that is associated with any sampling method used. Usually, there is an error associated with sampling method used. This marginal error is expressed by use of confidence intervals.

2. Using the data from the Excel workbook, construct a  95%  confidence interval for the population mean. Assume that your data is normally distributed and σ is unknown. Include a statement that correctly interprets the confidence interval in context of the scenario.

Hint: Use the sample mean and sample standard deviation from Deliverable 1.

Answer and Explanation:

Enter your step-by-step answer and explanations here.

· At 95% confidence level, the coefficient is 1.96.

· Confidence interval is therefore calculated as;

Sample mean coefficient X (sample standard deviation/square roof of sample size.

From the calculation, the salary upper bound is $64,273 while the lower bound is $60,338. It means we are 95% confident that the mean salary of people working in Minnesota is between $60,338- $64,273.

3. Using the data from the Excel workbook, construct a  99%  confidence interval for the population mean. Assume that your data is normally distributed and σ is unknown. Include a statement that correctly interprets the confidence interval in context of the scenario.

Hint: Use the sample mean and sample standard deviation from Deliverable 1.

Answer and Explanation:

Enter your step-by-step answer and explanations here

We are 99% confident that the mean salary for workers in Minnesota is between $64,896 and $59,717.

4. Compare your answers for (2) and (3). You notice that the 99% confidence interval is wider. What is the advantage of using a wider confidence interval? Why would you not always use the 99% confidence interval? Explain with an example.

Answer and Explanation:

Enter your step-by-step answer and explanations here.

At 95% confidence interval is between $64,273 and $60,338 while at 99%, confidence interval is $64,896 and $59,717. This show that at 99%, confidence interval range is $5,179. Compared to 95%, confidence interval range is $3,935. This confirms that as we increase confidence level, confidence interval widens.

At 99% confidence interval is not the best. Wider interval does not give a better estimate.

5. We want to estimate the mean salary in Minnesota. How many jobs must be randomly selected for their respective mean salaries if we want 95% confidence that the sample mean is within $126 of the population mean and σ = $1150.

Is the current sample size of the data set in our excel document of 364 large enough? Explain.

Answer and Explanation:

Enter your step-by-step answer and explanations here.

At 95% confidence interval is $64,273

Sample mean should be $126+$62306=$62,422

Therefore

64,273=62,422+196 X 19149/n^0.5

n^0.5=20.2766

Therefore the five jobs can be randomly selected

The sample size of 364 is large enough for our analysis. It allow is to use Central Limit Theorem