Question

In: Statistics and Probability

Randomly selected 2929 student cars have ages with a mean of 77 years and a standard...

Randomly selected 2929 student cars have ages with a mean of 77 years and a standard deviation of 3.43.4 years, while randomly selected 1515 faculty cars have ages with a mean of 5.95.9 years and a standard deviation of 3.73.7 years.

1. Use a 0.010.01 significance level to test the claim that student cars are older than faculty cars.

(a) The null hypothesis is H0:μs=μfH0:μs=μf. What is the alternate hypothesis?

A. HA:μs<μfHA:μs<μf
B. HA:μs≠μfHA:μs≠μf
C. HA:μs>μfHA:μs>μf

(b) The test statistic is

(c) The p-value is

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

A. Yes
B. No

Expert Solution

a) Option - C) H_A:

b) The test statistic t = ()/sqrt(s1^2/n1 + s2^2/n2)

= (7 - 5.9)/sqrt((3.4)^2/29 + (3.7)^2/15)

= 0.961

c) df = (s1^2/n1 + s2^2/n2)^2/((s1^2/n1)^2/(n1 - 1) + (s2^2/n2)^2/(n2 - 1)

= ((3.4)^2/29 + (3.7)^2/15)^2/(((3.4)^2/29)^2/28 + ((3.7)^2/15)^2/14)

= 26

P-value = P(T > 0.961)

= 1 - P(T < 0.961)

= 1 - 0.8273 = 0.1727

d) Since the P-value is greater than the significance level(0.1727 > 0.01), so we should not reject H₀.

Option - B) No, there is not sufficient evidence to support the claim that the student cars are older than faculty cars.

orchestra answered 2 years ago

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