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
[tex]H_{0}: p = 0.113\\H_A: p > 0.113[/tex]
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:
[tex]\hat{p} = \dfrac{x}{n} = \dfrac{52}{400} = 0.13[/tex]
[tex]z = \dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]
Putting the values, we get,
[tex]z = \displaystyle\frac{0.13-0.113}{\sqrt{\frac{0.113(1-0.113)}{400}}} = 1.073[/tex]
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.
The evidence isn't sufficient enough to support the claim that union membership increased.
This is a statistical measurement used to validate a hypothesis against observed data.
Sample size, n = 400
p = 11.3% = 0.113
Alpha, α = 0.05
Number of women belonging to union = 52
H₀ : p = 0.113
Hₐ : p > 0.113
This means 11.3% of U.S. workers belong to union and there was an increase.
p = x / n
z = p - p /(( √p(1-p) /n
= 53/400 = 0.13
z = p - p /(( √p(1 - p) /n)).
Substitute the values into the equation.
z = 0.13 - 0.113 / ((√0.113(1-0.113)/400)) = 1.073
P-value = 0.141636 from the table which is greater than the significance level, hence we accept the null hypothesis.
The evidence is therefore not sufficient enough to support the claim that union membership increased.
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