Randomly selected 70 student cars have ages with a mean of 8 years and a standar

Question

Randomly selected 70 student cars have ages with a mean of 8 years and a standard deviation of 3.4 years, while randomly selected 65 faculty cars have ages with a mean of 5.3 years and a standard deviation of 3.5 years.
1. Use a 0.04 significance level to test the claim that student cars are older than faculty cars.
a) The test statistic is
b) The critical value is

Is there sufficient evidence to support the claim that student cars are older than faculty cars? YES

2. Construct a 96 % confidence interval estimate of the difference 12 , where 1 is the mean age of student cars and 2 is the mean age of faculty cars.

      ___________<(12)<____________

Explanation / Answer

1- studen car age

2 -faculty car age

1) n1= 70 ,x1bar = 8 ,s1 = 3.4

n2 = 65 ,x2bar = 5.3 ,s2 = 3.5

s_pooled^2 = (s1^2 * (n1-1) + s2^2(n2-1))/(n1+n2-1)

=(69*3.4*3.4+643.5*3.5)/(69+64)

=22.9315038

s_pooled =sqrt(22.9315038) = 4.788

T = (x1bar -x2bar)/(s_pooled *sqrt(1/70+1/65))

=(8-5.3)/(4.788*sqrt(1/70+1/65))

=3.273

this follow t-distribution with 69+64 df

b)critical value = P(T<0.96) = 1.764

since TS> t-critical

we reject te null annd conclude that there is sufficient evidence to support the claim that student cars are older than faculty cars

2)

confidence interval is

(8-5.3) - 1.764*4.788*sqrt(1/70+1/65)) , (8-5.3) + 1.764*4.788*sqrt(1/70+1/65)) ,

(1.245 ,4.15483)

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