Question

A study found that, in 2005, 12.5% of U.S. workers belonged to unions (The Wall Street Journal, January 21, 2006). Suppose a sample of 400 U.S. workers is collected in 2006 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 2006.(b) If the sample results show that 52 of the workers belonged to unions, what is the p-value for your hypothesis test? Round your answers to four decimal places.

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 = 12.5% = 0.125

Alpha, α = 0.05

Number of women belonging to union , x = 52

First, we design the null and the alternate hypothesis  

$H_{0}: p = 0.125\\H_A: p > 0.125$

The null hypothesis sates that 12.5% of U.S. workers belong to union and the alternate hypothesis states that there is a increase in union membership.

This is a one-tailed(right) test.  

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,

$z = \displaystyle\frac{0.13-0.125}{\sqrt{\frac{0.125(1-0.125)}{400}}} = 0.3023$

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

P-value = 0.3812

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

Conclusion:

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