Question

(1 point) Randomly selected 28 student cars have ages with a mean of 7.3 years and a standard deviation of 3.6 years, while randomly selected 17 faculty cars have ages with a mean of 5.5 years and a standard deviation of 3.3 years. 1. Use a 0.05 significance level to test the claim that student cars are older than faculty cars.

(a) The test statistic is _______?

(b) The critical value is _______ ?

(c) Is there sufficient evidence to support the claim that student cars are older than faculty cars? A. No B. Yes

2. Construct a 95% confidence interval estimate of the difference μs−μf, where μs is the mean age of student cars and μf is the mean age of faculty cars.

_______ <(μs−μf) < ___________

Answer 1

To Test -

H0 :- µ1 = µ2
H1 :- µ1 > µ2

Part a)

t = (X̅1 - X̅2) / SP √ ( ( 1 / n1) + (1 / n2))

SP = 3.4914

t = 1.68

Part b)

Critical value t(α, n1 + n1 - 2) = t( 0.05 , 28 + 17 - 2) = 1.681

Part c)

t < t(α, n1 + n2 - 2) = 1.6768 < 1.681
Result :- Fail to Reject Null Hypothesis

NO

Question 2

Confidence interval is :-
( X̅1 - X̅2 ) ± t( α/2 , n1+n2-2) SP √( (1/n1) + (1/n2))
t(α/2, n1 + n1 - 2) = t( 0.05/2, 28 + 17 - 2) = 2.017
Lower limit = -0.3649

Upper limit = 3.9649

95% Confidence Interval is ( -0.3649 , 3.9649 )