Test the given claim using the traditional method of hypothesis testing. Assume

Question

Test the given claim using the traditional method of hypothesis testing. Assume that the sample has been randomly selected from a population with a normal distribution. A public bus company official claims that the mean waiting time for bus number 14 during peak hours is less than 10 minutes. Karen took bus number 14 during peak hours on 18 different occasions. Her mean waiting time was 7 minutes with a standard deviation of 2.3 minutes. At the 0.01 significance level, test the claim that the mean is less than 10 minutes.

Explanation / Answer

THE NULL HYPOTHESIS = HO =U = 10

THE ALTERNATE HYPOTHESIS = Ha = u<10

as the n = 14

degree of freedom = 14-1

for significance = 0.01

the critical region = t <-2.65

the t test = (7-10)/(2.3/sqrt(14))

= -4.88

as the t stat = -4.88 <-2.65

therefore we will reject the null hypothesis

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