Question

The table below contains information pertaining to the gasoline mileage for random samples of trains of two different types X and Y. Assume their population standard deviations are known (as given) and the two distributions are normal.

Brand X Brand Y
Number of Trains    14 11
Mean mileage 20.04 24.03
Pop. St Dev. σ 2.18 1.76

A) Name and Find the 95% Confidence Interval for the difference of two pop. means (μx - μY).

B) What can you conclude (if anything) from the confidence interval above concerning the mean gasoline mileage of Brand X compared to Brand Y. Write a complete sentence.

Answer 1

GIVEN:

Sample size of trains of brand X

Sample size of trains of brand Y

Sample mean mileage of brand X trains

Sample mean mileage of brand Y trains

Population standard deviation of brand X trains

Population standard deviation of brand Y trains

HYPOTHESIS:

The hypothesis is given by,

(That is, there is no significant difference in mean gasoline mileage between brand X and brand Y trains.)

(That is, there is significant difference in mean gasoline mileage between brand X and brand Y trains.)

LEVEL OF SIGNIFICANCE:

FORMULA USED:

The formula for % confidence interval for difference between two population means is,

where is the two tailed z critical value at .

CRITICAL VALUE:

The two tailed z critical value at is .

(A) % CONFIDENCE INTERVAL FOR DIFFERENCE BETWEEN TWO POPULATION MEANS:

The % confidence interval for difference between two population means is,

  

  

  

  

Thus the % confidence interval for difference between two population means is .

(B) CONCLUSION:

Since the value specified by the null hypothesis () is not in the interval , the null hypothesis can be rejected at the significance level . Thus we can conclude that there is significant difference in mean gasoline mileage between brand X and brand Y trains.