In: Statistics and Probability
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%
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%.