Question

Minimum wage, Part I. Do a majority of US adults believe raising the minimum wage will help the economy, or is there a majority who do not believe this? A Rasmussen Reports survey of 1,000 US adults found that 42% believe it will help the economy.24 Conduct an appropriate hypothesis test to help answer the research question.

Answer 1

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: Not majority of US adults believe raising the minimum wage will help the economy.

Alternative hypothesis: Ha: A majority of US adults believe raising the minimum wage will help the economy.

H0: p ≤ 0.5 versus Ha: p > 0.5

This is an upper 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

n = sample size = 1000

p̂ = x/n = 0.42

p = 0.5

q = 1 - p = 0.5

Z = (p̂ - p)/sqrt(pq/n)

Z = (0.42 – 0.5)/sqrt(0.5*0.5/1000)

Test statistic = Z = -5.0596

P-value = 1.000

(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 a majority of US adults believe raising the minimum wage will help the economy.