# Hypothesis Testing and Confidence Interval

Based on data from USA Today, tax returns include an option of designating $3 for presidential election campaigns, and it does not cots the taxpayer anything to make that designation. In a simple random sample of 250 taxpayer returns from 1976, 27.6% of the returns designated the $3 for the campaign. In a simple random of 300 recent returns, 7.3% of the returns designated the $3 for the campaign.

Construct a 98% confidence interval estimate for the difference of the percentages of returns designating the $3 for the campaign in 1976 and that of the recent returns. What conclusion does the confidence interval suggest?

https://brainmass.com/statistics/correlation-and-regression-analysis/hypothesis-testing-confidence-interval-613355

#### Solution Preview

Based on data from USA Today, tax returns include an option of designating $3 for presidential election campaigns, and it does not cots the taxpayer anything to make that designation. In a simple random sample of 250 taxpayer returns from 1976, 27.6% of the returns designated the $3 for the campaign. In a simple random of 300 recent returns, 7.3% of the returns designated the $3 for the campaign.

Construct a 98% confidence interval estimate for the difference of the percentages of returns designating the $3 for the campaign in 1976 and that of the recent returns. What conclusion does the confidence interval suggest?

Answer

98% confidence interval is given by,

Confidence Interval Estimate

of the Difference Between Two Proportions

Data

Confidence Level 98%

Intermediate Calculations

Z Value -2.3263

Std. Error of the Diff. between two Proportions 0.0320

Interval Half Width 0.0745

Confidence Interval

Interval Lower Limit 0.1285

Interval Upper Limit 0.2775

Since the confidence interval does not include zero, we can conclude that there is significant difference ...

#### Solution Summary

The solution provides step by step method for the calculation of confidence interval and testing of hypothesis. Formula for the calculation and Interpretations of the results are also included.