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According to the US Bureau of labor statistics, 7% of US female workers between 16 and 24 years old are paid at the minimum wage or less. A state politician wants to verify this statement for his state. He uses a sample of 500 female workers and finds 42 are paid at the minimum wage or less. Use a 5% significance level to test to test whether that state differs from the nation.

State clearly the null and the alternative hypothesis, the test statistic, the decision rule and the conclusion.

User Toumash
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Answer:

The Null Hypothesis is
H_o:k_o = 0.07

The alternative hypothesis is
H_a :k_o \\e 0.07

Decision rule

If the test staistics is greater than the critical value of significance level then
H_o is accepted else
H_o 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

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

Explanation:

From the question we are told that

The percentage of US female workers paid at the minimum wage or less is
k_o = 7% = 0.07

The sample size is
n = 500

The number paid minimum wage or less is x = 42

The significance level is
\alpha =5% = 0.05

Now the probability of getting a US female workers paid at the minimum wage or less is mathematically represented as


\= k = (x)/(n)

substituting value


\= k = (42)/(500)


\= k = 0.084

The Null Hypothesis is
H_o:k_o = 0.07

The alternative hypothesis is
H_a :k_o \\e 0.07

Generally the test statistics is mathematically evaluated as


z = \frac{\= k - k_o}{\sqrt{(k_o(1-k_o))/(n) } }

substituting value


z = \frac{0.084 - 0.07}{\sqrt{(0.07 (1-0.07))/(500) } }


z = 1.23

Now the Decision rule is stated as

If the test staistics is greater than the critical value of significance level then
H_o is accepted else
H_o 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

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

User Daniel Broekman
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