# Estimated proportion defective, 95% confidence interval

Schadek Silkscreen Printing, Inc. purchases plastic cups on which to print logos for sporting events, proms, birthdays, and other special occasions. Zack Schadek, the owner, received a large shipment this morning. To ensure the quality of the shipment, he selected a random sample of 300 cups. He found 15 to be defective.

a. What is the estimated proportion defective in the population?

b. Develop a 95% confidence interval for the proportion defective.

c. Zack has a an agreement with his supplier that he is to return lots that are 10% or more defective. Should he return this lot? Explain your decision.

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#### Solution Preview

Please see the attached file.

a) Proportion of defective in the sample is

p=0.05

Hence estimated proportion of defective in the ...

#### Solution Summary

The expert estimates proportion defective with a 95% confidence interval.

Statistics Problems: Mean, probability, standard deviation, confidence interval

1. You are a manager of a Starbucks located at Southcenter Mall. Recently, a new local coffee shop specializing in lattes has opened in the Mall. You are wondering what the impact on your latte sales may be. You know from previous data tracking that the largest number of lattes sold at your location is during the morning. Thus, you decide to pull data from the last 2 weeks on the number of lattes sold between 7:00 - 10:00 am on weekdays. The raw data is as follows:

65 70 53 57 81 79 77 68 88 85

a) Find the arithmetic mean and the standard deviation of lattes sold from 7:00-10:00am. Discuss the meaning of these numbers within the context of the problem.

b) Are the values in part (a) called statistics or parameters? Why?

2. A quality control procedure for testing Ready-Flash flash bulbs consists of drawing two bulbs at random from each lot of 100. If both are defective, the entire lot is rejected. Find the probability that both bulbs are defective if the lot contains 10 defective flash bulbs. Since we are drawing bulbs at random, assume each bulb in the lot has an equal chance of being drawn.

a) What is the probability of getting a defective bulb on the first draw?

b) If the first bulb drawn is not replaced, what is the probability of getting a defective bulb on the second draw if the first bulb was defective?

c) Are the probabilities computed in parts a and b different? Does drawing a defective bulb on the first draw change the probability of getting a defective bulb on the second draw? Are the events dependent or independent?

d) Compute: P(1st bulb defective and 2nd bulb defective).

3. The American Restaurant Association collected information on the number of meals eaten outside the home per week by young married couples. A survey of 60 couples showed the sample mean number of meals eaten outside the home was 2.76 meals per week, with a standard deviation of .75 meals per week.

a) Construct a 95% confidence interval for the population mean.

b) How would the interval change if you lowered the confidence level from 95% to 90%?

4. The First National Bank of Wilson has 650 checking account customers. A recent sample of 50 of these customers showed 26 to have a Visa card with the bank. Construct the 99 percent confidence interval for the proportion of checking account customers who have a Visa card with the bank.

5. The Tennessee Tourism Institute (TTI) plans to sample information center visitors entering the state to learn the fraction of visitors who plan to camp in the state. Current estimates are that 35 percent of visitors are campers. How large a sample would you take to estimate at a 95 percent confidence level the population proportion with an allowable error of 2 percent?

6. The Myers Summer Casual Furniture Store tells customers that a special order will take six weeks (42 days). During recent months the owner has received several complaints that the special orders are taking longer than 42 days. A sample of 12 special orders delivered in the last month showed that the mean waiting time was 51 days with a standard deviation of 8 days. At the .05 significance level, are customers waiting an average of more than 42 days?

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