A car manufacturer is concerned that dealers conceal unhappy customers by keeping them out of surveys conducted by the factory. The manufacturer suspects that certain dealers enter incorrect addresses for dissatisfied customers so that they do not receive the satisfaction survey that is mailed by the manufacturer. If a current survey of the 65 customers at a dealership indicates 55% rate its service as exceptionally good, can the manufacturer estimate the proportion of all customers at this dealership who feel that its service is exceptionally good? Can it estimate the proportion at other dealerships?

Question

wheelervm1916 wheelervm1916

12-02-2020
Mathematics

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A car manufacturer is concerned that dealers conceal unhappy customers by keeping them out of surveys conducted by the factory. The manufacturer suspects that certain dealers enter incorrect addresses for dissatisfied customers so that they do not receive the satisfaction survey that is mailed by the manufacturer. If a current survey of the 65 customers at a dealership indicates 55% rate its service as exceptionally good, can the manufacturer estimate the proportion of all customers at this dealership who feel that its service is exceptionally good? Can it estimate the proportion at other dealerships?

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warylucknow warylucknow · Answer 1 · 2020-02-12T11:58:32+01:00

Answer:

Yes, the manufacturer can estimate the proportion of all customers at this dealership who feel that its service is exceptionally good.

No, the manufacturer cannot estimate, the proportion of customers who rated the service as exceptionally good, about the other dealerships.

Step-by-step explanation:

A sample of 65 customers from a dealership is selected and it is determined that 55% of the customers rated the service as exceptionally good.

According to the central limit theorem if a large random sample selected from an unknown population then the sampling distribution of sample proportion ([tex]\hat p[/tex]) follows a normal distribution.

Then the population proportion can be estimated by the sample proportion value.

That is, [tex]p=\hat p=0.55[/tex].

Thus, the manufacturer can estimate the proportion of all customers at this dealership who feel that its service is exceptionally good using the sample proportion value of [tex]\hat p=0.55[/tex].

Since the sample is selected from a specific dealership, he cannot estimate, the proportion of customers who rated the service as exceptionally good, about the other dealerships.