Question

Speeding Tickets (The data is from a sample of randomly selected subjects.)

Yes No

Women 27 473

Men 26 224

Compute row totals. Test the claim that the percentage of women ticketed for speeding is less than the percentage of men at LaTeX: \alphaα = 2%. State the hypotheses, find the proportions(including the pooled) then Z. Include a sketch, state the p-value followed by your conclusion.

Answer 1

As we are testing here whether the  percentage of women ticketed for speeding is less than the percentage of men, therefore the null and the alternative hypothesis here are given as:

The sample proportions here are computed as:
p₁ = 27/ (27 + 473) = 0.054
p₂ = 26 / (26 + 224) = 0.104

The pooled proportion here is computed as:
P = (27 + 26) / (500 + 250) = 0.0707

The standard error here is computed as:

The test statistic now is computed here as:

Therefore -2.52 is the test statistic value here.

As this is a one tailed test, the p-value here is computed from the standard normal tables as:
p = P(Z < -2.52) = 0.0059

Therefore 0.0059 is the required p-value here.

The graph here is given as:

As the p-value here is 0.0059 < 0.02 which is the level of significance, therefore the test is significant here and we can reject the null hypothesis here. Therefore we have sufficient evidence here that the percentage of women ticketed for speeding is less than the percentage of men​​​​​​​