Question

A random sample of n = 1,400 observations from a binomial population produced x = 667 successes. You wish to show that p differs from 0.5.

Calculate the appropriate test statistic. (Round your answer to two decimal places.)

z =

Calculate the p-value. (Round your answer to four decimal places.)

p-value =

Answer 1

Question 7

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 p not differs from 0.5.

Alternative hypothesis: Ha: The p differs from 0.5.

H0: p = 0.5 versus Ha: p ≠ 0.5

This is a two tailed test.

We assume

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

x = number of items of interest = 667

n = sample size = 1400

p̂ = x/n = 667/1400 = 0.476428571

p = 0.5

q = 1 - p = 0.5

Z = (p̂ - p)/sqrt(pq/n)

Z = (0.476428571 – 0.5)/sqrt(0.5*0.5/1400)

Z = -1.7639

Test statistic = -1.76

P-value = 0.0777

(by using z-table)

P-value > α = 0.05

So, we do not reject the null hypothesis

There is not sufficient evidence to conclude that the population proportion p differs from 0.5.