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
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:
Putting the values, we get,
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.