Question

The stopping distances of a random sample of nf=16 Fire-Hawk compact cars have a mean of xf=57.2 and standard deviation of sf=4.81. The stopping distances of a random sample of nl=14 Lance compact cars have a mean of xl=62.7 and standard deviation of sL=7.56 feet. Here, each stopping distance is measured from a speed of 35mph. Test whether the variance of the stopping distances of population of all the fire-Hawk cars is less than the variance of the stopping distances of population of all lance cars.

	State the hypothesis
	Decide the level of significance α	=0. 05
	Take a sample and calculate your test statistic
	Critical value rule	Reject H0 if _____________________
	P-value rule	Reject H0 if___________________

b) Attach your MegaStat output for this problem, here (Take a snapshot and put it here)

c) Interpret the 95% confidence interval for uF-uL that is reported in your Megastat output.

If you could post Megastat output too it would be helpful! Just snip it!

Answer 1

Hypotheses are :

Test is right tailed.

Test statistics wil be

Degree of freedom of numerator is df1=14-1=13 and degree of freedom of denominator is df2=16-1=15.

The critical value of F is: 2.448

Rejection region:

If F > 2.448, reject H0

Since F lies in the rejection region so we reject the null hypothesis. That is we can conclude that the variance of the stopping distances of population of all the fire-Hawk cars is less than the variance of the stopping distances of population of all lance cars.

The p-value is: 0.0484

b)

Following is the output of t test:

Hypothesis Test: Independent Groups (t-test, unequal variance)
	Fire Hawk	Lance cars
	57.2	62.7	mean
	4.81	7.56	std. dev.
	16	14	n
		21	df
		-5.5000	difference (Fire Hawk - Lance cars)
		2.3513	standard error of difference
		0	hypothesized difference
		-2.34	t
		.0293	p-value (two-tailed)
		-10.3897	confidence interval 95.% lower
		-0.6103	confidence interval 95.% upper
		4.8897	margin of error

c)

The 95% confidence interval for uF-uL is (-10.39, -0.61).

Since confidence interval does not contain zero so there is a signficant difference between the population means.