Question

1. Out of samples of 100 residents in certain area 73 found to own their homes. Test the hypothesis that proportion of house owners is 80 % against the alternative that it is less than 80 %. Subject :- Research Methedology

Answer 1

TRY BY

YOUR OWN ...............DONT disturrb ME....

UNDERSTAND

Answer 2

Answer:

The answer is that we reject the null hypothesis of 80% house owners.

Explanation:

i) Stating the hypothesis:

Null Hypothesis $H_{0}$: At least 80% of the residents own their houses.

$H_{0}$ suggests that P ≥ 80

Alternative Hypothesis $H_{a}$: Less than 80% residents do not own their houses.

$H_{a}$ suggests P ≤ 80

ii) Data Sampling

A sample of 100 residents is taken randomly.

iii) Data Analysis

The proportion of residents who say that they own house is 73% or .73.

iv) Data investigation

Let’s assume that the mean of sample data is .80, which is hypothesized proportion of sample which own their houses.

Standard deviation (σ) =

Where,

P = test value specified in $H_{0}$

n = sample size

N = population size

Hence,

σ = $\sqrt{{\frac{0.8(1-0.8)}{100} } {\frac{(1,000,000-100)}{1,000,000-1} }}$

σ = √0.0016 = 0.04

v) Finding the lower and upper limits of region of acceptance

The upper limit will be equal to 100% or 1 since this is the highest proportion of the population.

The lower limit (LL) = P(X’ ≤LL) = α = 0.05

If we put the values in a statistical normal distribution calculator, LL comes out to be 0.734.

This means that the region of acceptance lies between 0.734 and 1.

vi) Testing the Hypothesis

The survey on sample proportion suggested that 73% residents own their homes. But the region of acceptance is between 0.734 and 1. It means that .73 falls out of the region of acceptance and falls in the region of rejection on the left hand side. Therefore, we reject the null hypothesis that 80% of the voters will turn out to vote in upcoming elections.

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