Question

A yellow light technically means to stop but many people ignore it and drive through. It is thought that men are more aggressive drivers than women and are more prone to go through yellows. Experimenters stood by one traffic light at various times of the day and monitored a random sample of drivers. One experimenter took note of whether the driver stopped or went through the light and the other noted the gender. Here are the results: Drivers Percentage going through yellow Men 71 76% Women 53 65% Run a hypothesis test at the 2% level to check out the conjecture as well as finding a 98% confidence interval for the data?

Answer 1

The hypothesis being tested is:

H₀: p₁ = p₂

H_a: p₁ > p₂

p1	p2	pc
0.76	0.65	0.713	p (as decimal)
54/71	34/53	88/124	p (as fraction)
53.96	34.45	88.41	X
71	53	124	n
	0.11	difference
	0.	hypothesized difference
	0.0821	std. error
	1.34	z
	.0902	p-value (one-tailed, upper)
	-0.0827	confidence interval 98.% lower
	0.3027	confidence interval 98.% upper
	0.1927	margin of error

The p-value is 0.0902.

Since the p-value (0.0902) is greater than the significance level (0.02), we cannot reject the null hypothesis.

Therefore, we cannot conclude that men are more aggressive drivers than women and are more prone to go through yellows.

The 98% confidence interval for the proportion difference is between -0.0827 and 0.3027. Since the confidence interval contains a negative value, we cannot conclude that men are more aggressive drivers than women and are more prone to go through yellows.