Answer:
The Null Hypothesis is ![H_o:k_o = 0.07](https://tex.z-dn.net/?f=H_o%3Ak_o%20%3D%200.07)
The alternative hypothesis is ![H_a :k_o \ne 0.07](https://tex.z-dn.net/?f=H_a%20%3Ak_o%20%5Cne%200.07)
Decision rule
If the test staistics is greater than the critical value of significance level then
is accepted else
is rejected
With the above in mind
The critical value of the significance level which is obtained from the table is
![t_{0.05} = 1.645](https://tex.z-dn.net/?f=t_%7B0.05%7D%20%3D%201.645)
Now since the critical value of significance level is greater than the test staistics then the null hypothesis will be rejected
Conclusion
The information is not enough to back the claim that state differs from the nation
Step-by-step explanation:
From the question we are told that
The percentage of US female workers paid at the minimum wage or less is
7% = 0.07
The sample size is
The number paid minimum wage or less is x = 42
The significance level is
5% = 0.05
Now the probability of getting a US female workers paid at the minimum wage or less is mathematically represented as
![\= k = \frac{x}{n}](https://tex.z-dn.net/?f=%5C%3D%20k%20%3D%20%5Cfrac%7Bx%7D%7Bn%7D)
substituting value
![\= k = \frac{42}{500}](https://tex.z-dn.net/?f=%5C%3D%20k%20%3D%20%5Cfrac%7B42%7D%7B500%7D)
![\= k = 0.084](https://tex.z-dn.net/?f=%5C%3D%20k%20%3D%200.084)
The Null Hypothesis is ![H_o:k_o = 0.07](https://tex.z-dn.net/?f=H_o%3Ak_o%20%3D%200.07)
The alternative hypothesis is ![H_a :k_o \ne 0.07](https://tex.z-dn.net/?f=H_a%20%3Ak_o%20%5Cne%200.07)
Generally the test statistics is mathematically evaluated as
![z = \frac{\= k - k_o}{\sqrt{\frac{k_o(1-k_o)}{n} } }](https://tex.z-dn.net/?f=z%20%3D%20%20%5Cfrac%7B%5C%3D%20%20k%20%20-%20k_o%7D%7B%5Csqrt%7B%5Cfrac%7Bk_o%281-k_o%29%7D%7Bn%7D%20%7D%20%7D)
substituting value
![z = \frac{0.084 - 0.07}{\sqrt{\frac{0.07 (1-0.07)}{500} } }](https://tex.z-dn.net/?f=z%20%3D%20%20%5Cfrac%7B0.084%20%20-%200.07%7D%7B%5Csqrt%7B%5Cfrac%7B0.07%20%281-0.07%29%7D%7B500%7D%20%7D%20%7D)
![z = 1.23](https://tex.z-dn.net/?f=z%20%3D%20%201.23)
Now the Decision rule is stated as
If the test staistics is greater than the critical value of significance level then
is accepted else
is rejected
With the above in mind
The critical value of the significance level which is obtained from the table is
![t_{0.05} = 1.645](https://tex.z-dn.net/?f=t_%7B0.05%7D%20%3D%201.645)
Now since the critical value of significance level is greater than the test staistics then the null hypothesis will be rejected
So the conclusion will be
The information is not enough to back the claim that state differs from the nation