Question

In: Statistics and Probability

A recent study indicated of 50 cdddvcvvo people indicated that 53.5% of people vote. Test the...

A recent study indicated of 50 cdddvcvvo people indicated that 53.5% of people vote.
Test the Hypothesis at the α =.05 level that the proportion of people that vote is > 50%

Solutions

Expert Solution

Here, we have to use one sample z test for the population proportion.

The null and alternative hypotheses for this test are given as below:

Null hypothesis: H0: the proportion of people that vote is 50%.

Alternative hypothesis: Ha: the proportion of people that vote is not 50%.

H0: p = 0.5 versus Ha: p ≠ 0.5

This is a two tailed test.

We are given

Level of significance = α = 0.05

Test statistic formula for this test is given as below:

Z = (p̂ - p)/sqrt(pq/n)

Where, p̂ = Sample proportion, p is population proportion, q = 1 - p, and n is sample size

n = sample size = 50

p̂ = x/n = 0.535

p = 0.5

q = 1 - p = 0.5

Z = (p̂ - p)/sqrt(pq/n)

Z = (0.535 - 0.5)/sqrt(0.5*0.5/50)

Z = 0.4950

Test statistic = 0.4950

P-value = 0.6206

(by using z-table)

P-value > α = 0.05

So, we do not reject the null hypothesis

There is sufficient evidence to conclude that the proportion of people that vote is 50%.


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