Question

A sample of ten house owners is drawn and the following values of their incomes are obtained. Mean Rs.6,000 SD Rs.650. Test the hypothesis that the average income of house owners of the town is Rs.5,500.

Answer 1

Given : A sample of ten house owners is drawn and the following values of their incomes are obtained.  

Mean Rs.6,000 SD Rs.650.

To Find : Test the hypothesis that the average income of house owners of the town is Rs.5,500.

a. Calculated value of t=1.04, Null hypothesis accepted at 5% level

b. Calculated value of t=6.14, Null hypothesis rejected at 5% level

c. Calculated value of t=16.04, Null hypothesis rejected at 5% level

d. Calculated value of t=2.43, Null hypothesis rejected at 5% level

Solution:

Sample Mean  $\overline{x}$ = 6000

Sample  SD   s = 650

n = Sample size = 10

df = 10 - 1 = 9  ( degree of freedom)

Population Mean $\mu_{0}$ = 5500

t = T score

t =  ( $\overline{x}$ -  $\mu_{0}$) / ( s/√n)

=> t = (6000 - 5500)/(650/√10)

=> t = 2.43

Check Value of t for 5 % level for 9 degree of freedom and compare..

Calculated value of t=2.43 hence Null hypothesis rejected at 5% level

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