Question

A random sample of 42 taxpayers claimed an average of ​$ 9,698 in medical expenses for the year. Assume the population standard deviation for these deductions was ​$2,380. Construct confidence intervals to estimate the average deduction for the population with the levels of significance shown below. a. 2 % b. 5% c. 20 %

Please help me to solve this problem using PhStat ( NOT FORMULAS)

Answer 1

Solution:

Given:

Sample Size = n = 42

Sample mean =

8696 = X

The population standard deviation for these deductions = $\sigma$ = $2,380.

We have to construct confidence intervals to estimate the average deduction for the population with the levels of significance shown below. a. 2 % b. 5% c. 20 %

We are given levels of significance, then corresponding confidence levels are:

a) 100 - 2 = 98%

b) 100 - 5 = 95%

c) 100 - 20 = 80%

Part a) 98% confidence interval

Use following steps in PhStat (Excel)

Book1 - Excel Page Layout Formulas Data Review View Add-ins File Home Insert MegaStat About Kadd PHStat- Data Preparation Descriptive Statistics Decision-Making Probability & Prob. Distributions Sampling Confidence Intervals E F G H I Sample Size Estimate for the Mean, sigma known... Estimate for the Mean, sigma unknown.... Estimate for the population Variance... Estimate for the Proportion... One-Sample Tests Two-Sample Tests (Unsummarized Data) Two-Sample Tests (Summarized Data) Multiple-Sample Tests Estimate for the population Total... Estimate for the Total Difference... Control Charts Regression

Select and Enter Numbers:

About Kadd MegaStat PHStat KADD- Menu Commands Estimate for the Mean, sigma kno... X D7 A B C D % Data Population Standard Deviation: 2380 Confidence Level: 98 Input Options Sample Statistics Known Sample Size: Sample Mean: 9698 Sample Statistics Unknown Sample Cell Range: First cell contains label OUW No 00 OU WN- Output Options Title: Finite Population Correction Population Size: Help OK Cancel

Click on OK

Thus we get following output:

Confidence Interval Estimate for the Mean
Data
Population Standard Deviation	2380
Sample Mean	9698
Sample Size	42
Confidence Level	98%
Intermediate Calculations
Standard Error of the Mean	367.2420
Z Value	-2.3263
Interval Half Width	854.3326
Confidence Interval
Interval Lower Limit	8843.67
Interval Upper Limit	10552.33

Part b) 95% confidence interval:

Estimate for the Mean, sigma kno... X % Data Population Standard Deviation: 2380 Confidence Level: 95 Input Options Sample Statistics Known Sample Size: Sample Mean: 96981 Sample Statistics Unknown Sample Cell Range: First cell contains label Output Options Title: Finite Population Correction Population Size: 1 Help OK Cancel

Confidence Interval Estimate for the Mean
Data
Population Standard Deviation	2380
Sample Mean	9698
Sample Size	42
Confidence Level	95%
Intermediate Calculations
Standard Error of the Mean	367.2420
Z Value	-1.9600
Interval Half Width	719.7810
Confidence Interval
Interval Lower Limit	8978.22
Interval Upper Limit	10417.78

Part c) 80% confidence interval:

Estimate for the Mean, sigma kno... X % Data Population Standard Deviation: 2380 Confidence Level: 80 Input Options Sample Statistics Known Sample Size: Sample Mean: 9698 Sample Statistics Unknown Sample Cell Range: First cell contains label Output Options Title: Finite Population Correction Population Size: Help OK Cancel

Confidence Interval Estimate for the Mean
Data
Population Standard Deviation	2380
Sample Mean	9698
Sample Size	42
Confidence Level	80%
Intermediate Calculations
Standard Error of the Mean	367.2420
Z Value	-1.2816
Interval Half Width	470.6395
Confidence Interval
Interval Lower Limit	9227.36
Interval Upper Limit	10168.64