## [answered] A study compared the maximum speed (km/hour) of two types o

A study compared the maximum speed (km/hour) of two types of children?s bikes: brand A and brandB. A sample of four Brand A bikes resulted in a sample mean of 13.9 km/hour with sample standarddeviation of 1.2247 km/hour. A sample of four Brand B bikes resulted in a sample mean of 12.2km/hour with sample standard deviation of 1.009951 km/hour. Assume the populations are normalwith equal variances; and the two populations are independent.

(i) Suppose a hypothesis test is conducted to look for evidence that the two brands of children?s bikeshave a different population mean maximum speed. Determine the test-statistic.

(ii) Find the 95% confidence interval for the difference in the population mean maximum speed

.(iii) Let ?A be the population mean for the maximum speed of Brand A bikes. Let ?B be the populationmean for the maximum speed of Brand B bikes. Suppose H0 : ?A ??B = 0 and Ha : ?A ??B 6= 0. Usethe confidence interval constructed in (ii) to decide if there is a difference in mean maximum speedbetween the two brands. Explain your decision.

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