Question

Should Justice A of the Florida Supreme Court be retained in office? Questions concerning retention of various Supreme Court Justices occasionally appear on the Florida ballot. You randomly sample voters to determine if the majority of registered voters favor retention of Justice A. From your sample you find the test-statistic = 1.21.

What is the p-value?

State the administrative decision.

State the Type I error for this problem in terms of retention of Justice A.

Answer 1

Here we want to test that "whether the majority of registered voters favor retention of Justice or not".

So null hypothesis ( H₀) and the alternative hypothesis ( H_a ) are as follows:

H₀ : P = 05

H_a : P > 05

So here we can use one sample proportion test.

Also from the alternative hypothesis, it is a right tailed test.

A. From your sample you find the test-statistic = 1.21.

We want to find p-value.

P-value = P( Z > 1.21) = 1 - P{ Z < 1.21) ......( 1 )

From the Z-table we get P(Z < 1.21 ) = 0.8869

So p-value = 1 - 0.8869 = 0.1131

If level of significance ( ) is not given then we take it as 0.05

Decision rule:

1) If p-value < level of significance (alpha) then we reject null hypothesis

2) If p-value > level of significance (alpha) then we fail to reject null hypothesis.

Here p value = 0.1131 which is > 0.05 so we used first rule.

That is we fail to reject null hypothesis

Conclusion: At 5% level of significance there are not sufficient evidence to conclude that

the majority of registered voters favor retention of Justice.

If we failed to reject null hypothesis then there is no Type I eeror.