# Hypothesis testing of Proportion & Paired T Test

1. Union Membership Nationwide 13.7% of employed wage and salary workers are union members (down from 20.1% in 1983). A random sample of 300 local wage and salary workers showed that 50 belonged to a union. At ?=0.05, is there sufficient evidence to conclude that the proportion of union membership differs from 13.7%?

2. Free School Lunches It has been reported that 59.3% of U.S. school lunches served are free and at a reduced price. A random sample of 300 children in a large metropolitan area indicated that 156 of them received lunch free or at a reduced price. At the 0.01 level of significance, is there sufficient evidence to conclude that the proportion is less then 59.3%?

3. Automobile Part Production In an effort to increase production of an automobile part, the factory manager decides to play music in the manufacturing area. Eight workers are selected, and the number of items each produced for a specific day is recorded. After on week of music, the same workers are monitored again. The data are given in the table. At ?=0.05 can the manager conclude that the music has increased production?

Worker 1 2 3 4 5 6 7 8

Before 6 8 10 9 5 12 9 7

After 10 12 9 12 8 13 8 10

https://brainmass.com/statistics/students-t-test/hypothesis-testing-proportion-paired-t-test-364435

#### Solution Summary

The solution provides step by step method for the calculation of testing of hypothesis. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.