Question

choose the the correct answer

3.A Sample of ten house owners is drawn and the following values of their incomes are obtained .Mean Rs.6000;Standard deviation Rs.650.Test the hypothesis that the average income of house owners of the town is Rs.5500 *



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=2.31, Null hypothesis rejected at 5% level

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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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