The customer services manager of a bank wants to estimate the true average time it takes for a teller to serve a customer. A random sample of the service time for 14 individual customers is collected. The results are listed as follows (in minutes):

1.7 1.9 1.7 1.5 1.6 1.4 1.6 1.0 1.0 2.0 1.3 1.2 0.8 2.3

a With respect to the above given information:

i Explain why a Student’s t distribution should be used in constructing a confidence interval for the true average amount of time it takes to serve a customer. What assumption(s) must be made initially?

ii State the condition(s) when a normal distribution can be used instead.

b Find a 90% confidence interval estimate for the true average time it takes to serve a customer. Keep your final answers to two decimal places.

c Given that the service times are normally distributed and the population standard deviation is known to be 0.45 minutes, what sample size is required if the manager wishes to be 98% confident that the sample average is correct to within ±0.2 minutes of the true average service time?

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A digital camera manufacturer is choosing between two brands of rechargeable battery to be used in its latest model to be released this fall. To compare the durability, ten batteries of each of the two brands were

randomly selected. After being fully charged, the standby times of the ten batteries selected for each brand were recorded as follows:

BRAND A 91 99 103 94 129 87 118 85 84 82

BRAND B 98 103 108 107 96 109 90 87 121 94

a At the 5% level of significance, test whether there is any difference in

the variance of the standby times between the batteries of the two brands.

b At the 5% level of significance, test whether there is any difference in the average standby time between the batteries of the two brands.

What assumption(s) must be made?

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The buyers of a brand of smart phone were asked to mail a registration card in order to put a one-year warranty into effect. The card contains several questions relating to the purchase. From a large number of these registration cards, a random sample of 130 is drawn. The following table

summarizes the results regarding which feature of the smart phone the purchasers like most and the model being purchased:

-----------------------MODEL

FEATURE --------------A B C

EASY TO USE--------- 9 7 12

APPEARANCE --------14 13 194

CONNECTIVITY-------- 8 7 10

RESOLUTION 10 12 9

At a 5% level of significance, test whether the two variables: *Feature *and

*M**odel*are independent or not.