Question

A vehicle repair shop wants to determine the satisfaction level of their customers. In order to do so, they randomly select 60 of their customers and send them a satisfaction survey. 43 of the individuals surveyed state that they are “Very Satisfied” with the service they received. Assume that the repair shop has more than 2000 customers.

a.Verify that we can construct a confidence interval for the proportion of the vehicle repair shop’s customers who are Very Satisfied.

b.Construct a 90% confidence interval for the proportion of the vehicle repair shop’s customers who are Very Satisfied.

Answer 1

given data and some necessary calculations are:-

sample size (n) = 60

sample proportion () = 43/60 = 0.7167

a).conditions :-

the sample is stated to be a simple random sample , the value of is 12.182 ,which is greater than or equal to 10 and the sample size can be assumed to be less than or equal to 5% of the population size.all the requirements are satisfied.

[

n = 60 < 5% of 2000 = 100 ]

b).z critical value for 90% confidence level, both tailed test be:-

The 90% confidence interval for the proportion of the vehicle repair shop’s customers who are Very Satisfied is :-

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