Question

Two different models of a car manufacturer are compared to see if Model A has a higher average miles per gallon (mpg) than Model B. A sample of size 14 Model A cars found a sample average of 28.2 mpg and a standard deviation 3.0 mpg. A sample of size 10 Model B cars found a sample average of 22.6 mpg and a standard deviation of 5.1 mpg. Conduct the appropriate hypothesis test.

a. Ho: μ_A = μ_B Ha: μ_A μ_B

b. Test statistic (t or z):   =  Round to 2 decimals.

c. p-value =   Round to 4 decimals.

d. Interpretation of the p-value: If the null hypothesis is   , then there is a  (4 decimals) probability that the sample difference in means is   (1 decimal) mpg. (Instructions: first box: True or False, second box: p-value, third box: >, < or not equal, fourth box: sample statistic)

e. Decision:   (Reject H₀ or do not reject H₀)

f. Conclusion: There is  (sufficient / insufficient) evidence to conclude that Model A has   (a higher / a lower) average mpg as/than Model B.

Answer 1

For sample 1 : x̅1 = 28.2, s1 = 3, n1 = 14

For sample 2 : x̅2 = 22.6, s2 = 5.1, n2 = 10

α = 0.05

a) Null and Alternative hypothesis:

Ho : µA = µB

H1 : µA > µB

b) Test statistic:

t = (x̅1 - x̅2)/√(s1²/n1 + s2²/n2) = (28.2 - 22.6)/√(3²/14 + 5.1²/10) = 3.1093

c) df = ((s1²/n1 + s2²/n2)²)/[(s1²/n1)²/(n1-1) + (s2²/n2)²/(n2-1) ] = 13.4306 = 13

p-value = T.DIST.RT(3.1093, 13) = 0.0041

d) If the null hypothesis is true, then there is a 0.0041 probability that the sample difference in means is 0 mpg.

e) Decision: Reject H₀

f) Conclusion:

There is sufficient evidence to conclude that Model A has a higher average mpg as/than Model B.