Question

The U.S. Bureau of Labor Statistics reports that 11.3% of U.S. workers belong to unions (BLS website, January 2014). Suppose a sample of 400 U.S. workers is collected in 2014 to determine whether union efforts to organize have increased union membership. a. Formulate the hypotheses that can be used to determine whether union membership increased in 2014. H 0: p H a: p b. If the sample results show that 52 of the workers belonged to unions, what is the p-value for your hypothesis test (to 4 decimals)? c. At = .05, what is your conclusion?

Answer 1

Answer:

There is not enough evidence to support the claim that union membership increased.

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 400

p = 11.3% = 0.113

Alpha, α = 0.05

Number of women belonging to union , x = 52

First, we design the null and the alternate hypothesis

$H_{0}: p = 0.113\\H_A: p > 0.113$

The null hypothesis sates that 11.3% of U.S. workers belong to union and the alternate hypothesis states that there is a increase in union membership.

Formula:

$\hat{p} = \dfrac{x}{n} = \dfrac{52}{400} = 0.13$

$z = \dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}$

Putting the values, we get,

$z = \displaystyle\frac{0.13-0.113}{\sqrt{\frac{0.113(1-0.113)}{400}}} = 1.073$

now, we calculate the p-value from the table.

P-value = 0.141636

Since the p-value is greater than the significance level, we fail to reject the null hypothesis and accept the null hypothesis.

Thus, there is not enough evidence to support the claim that union membership increased.