Deliverable 3 - Confidence Intervals

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 interval can be defined as interval estimate that is calculated from the statistics of the data available for observation, that may contain a true value of the unknown size of a population.

Point estimate is process of using a sample data when calculating one value which will be used as the best guess of the unknown population parameter.

Sample mean us the best estimate for the population mean.

It gives a range of possible values that the sample may take when controlling the probability that might be lower or higher than the estimated range.

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.

i. Standard deviation (from excel for whole population) = 22644.46

ii. Sample mean (20 samples were used) = 77529

iii. Confidence interval is given by the formula; CI = where is the sample mean, z is obtained from table (1.96 for 95%) is the estimate standard deviation and n is the size of the population

CI = 77529 (1.96 * )

= 77529 2326.308

= 75202.69128 to 79855.30872

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.

All the steps above are followed only that z value changes to 2.58

Ow calculating the value

CI = 77529 (2.58 * )

= 77529 3062.1819

= 74466.8181 to 80591.1819

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.

The higher confidence interval gives a higher probability to cover the true value.

With a narrower confidence interval, a lower variability is realized and thereby a higher precision is achieved.

For instance, in the above case, the confidence interval is 77529 2326.308 for 95% and 77529 3062.1819 for 99%. It can be seen that 77529 2326.308 has lower variability and thereby higher precision.

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 364 in the data set in our Excel workbook large enough? Explain.

Answer and Explanation:

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

Population mean is 72224.34066 and the confidence interval is 72224.34066 126

126 = 1.96 *

N= 320

Yes the data is large enough since the value of n is less than 364