Exercises. 1. Check if the sample size is large enough to use the normal distribution to make a confidence interval for p for each of the following cases

1. Check if the sample size is large enough to use the normal distribution to make a confidence interval for p for each of the following cases

a) n = 60 and

b) n = 180 and

c) n = 200 and

d) n = 65 and

2. A sample of 500 observations selected from a population gave a sample proportion equal to 0.72.

a) make a 90 % confidence interval for p.

b) construct a 95 % confidence interval for p.

c) make a 99 % confidence interval for p.

Interpret your results.

3. A sample selected from a population gave a sample proportion equal

to 0.73

a) make a 98 % confidence interval for p assuming n = 90

b) construct a 98 % confidence interval for p assuming n = 500

c) construct a 98 % confidence interval for p assuming n = 100

Interpret your results.

4. A sample of 87 university students revealed that 53 carried their books and notes in a backpack. Obtain a 95 % confidence interval for the population of students who use backpacks.

5. The Beverage Company has been experiencing problems with the automatic machine that places labels on bottles. A sample of 300 bottles resulted in 27 bottles with improperly applied labels. Using these data, develop a 90 % confidence interval for the population proportion of bottles with improperly applied labels.

6. If 65 persons in a random sample of 180 required lawyer services, then find and interpret 96 % confidence interval for proportion of persons in the population who required a lawyer services.

7. Let sample proportion . How large a sample should be taken to be 95 % sure that the error of estimation does not exceed 0.02 when estimating a proportion?

8. A sample of 20 managers was taken and they were asked whether or not they usually take work home. The responses are given below:

Yes Yes No No No Yes No No

No No Yes Yes No Yes Yes No

No No No Yes

Make a 99 % confidence interval for the percentage of all managers who take work home.

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