PLEASE SOLVE FOR T NOT Z · Find the best point estimate of the population mean.

Question

PLEASE SOLVE FOR T NOT Z

·         Find the best point estimate of the population mean.

·         Construct a 95% confidence interval for the population mean. Assume that your data is normally distributed and ÃÆ’ is unknown.

Please show your work for the construction of this confidence interval and be sure to use the Equation Editor to format your equations.

·         Write a statement that correctly interprets the confidence interval in context of your selected topic.

·         Construct a 99% confidence interval for the population mean. Assume that your data is normally distributed and is unknown.

·         Please show your work for the construction of this confidence interval and be sure to use the Equation Editor to format your equations.

·         Write a statement that correctly interprets the confidence interval in context of your selected topic.

Compare and contrast your findings for the 95% and 99% confidence interval.

·         Did you notice any changes in your interval estimate? Explain.

·         What conclusion(s) can be drawn about your interval estimates when the confidence level is increased? Explain

Mean 62,306

Standard Error 1003.69153

Median 56,520

Midrange 80,010

Mode 46,100

Standard Deviation 19149.21386

Sample Variance 366692391.3

Range 79,680

Minimum 40,170

Maximum 119,850

Sample Size = 364

Explanation / Answer

Solution:

We are given,

Xbar = 62306

SD = 19149.21386

n = 364

df = n – 1 = 364 – 1 = 363

First of all we have to find 95% confidence interval.

Confidence interval = Xbar -/+ t*SD/sqrt(n)

Critical value = t = 1.9665 (by using t-table)

Confidence interval = 62306 -/+ 1.9665*19149.21386/sqrt(364)

Confidence interval = 62306 -/+ 1973.7800

Lower limit = 62306 - 1973.7800 = 60332.22

Upper limit = 62306 + 1973.7800 = 64279.78

Confidence interval = (60332.22, 64279.78)

We are 95% confident that the population mean will lies between the two values 60332.22 and 64279.78.

Now, we have to find 99% confidence interval.

Critical value = t = 2.5894 (by using t-table)

Confidence interval = 62306 -/+ 2.5894*19149.21386/sqrt(364)

Confidence interval = 62306 -/+ 2598.9998

Lower limit = 62306 - 2598.9998 = 59707.00

Upper limit = 62306 + 2598.9998 = 64905.00

Confidence interval = (59707, 64905)

We are 99% confident that the population mean will lies between the two values 59707 and 64905.

We notice the changes in the interval estimate.

The width of the 95% confidence interval is less than the width of the 99% confidence interval.

As we increase the confidence level, the width of the confidence interval also increases.

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