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2. The mean diameter of a...

2. The mean diameter of a ball bearing produced by a certain manufacturer is 0.80 cm with a population standard deviation of 0.03 cm. A sample of 36 ball bearings is randomly selected from a production run. What is the probability that the sample of ball bearings will have a mean within ±0.005 cm of the population mean (that is, the mean is between 0.795 cm and 0.805 cm)? (8pts)

3. A new soft drink is being market tested. It is estimated that 60% of consumers will like the new drink. A sample of 96 taste-tested the new drink.

a. Determine the standard error of the proportion. (4pts)

0.05

b. What is the probability that the sample proportion will be within ±0.0725 of the population proportion (that is, the proportion is between 0.5275 and 0.6725)? (8pts)

4. Use the t-distribution table to find the t- value for a sample size of n = 15 with a 90% confidence level. (2pts)

5. Use the t-distribution table to find the t- value for a sample size of n = 30 with a level of significance,

α = 0.05. (2pts)

6. A random sample of 100 credit sales in a department store showed an average sale of $120.00. From past data, it is known that the population standard deviation is $40.00.

a. Determine the standard error of the mean. (4pts)

b. At 95% confidence, determine the margin of error. (4pts)

c. Find the 95% confidence interval of the population mean. (8pts)

7. A sample of 25 patients in a doctor's office showed that they had to wait an average of 35 minutes with a sample standard deviation of 10 minutes before they could see the doctor. Construct a 95% confidence interval estimate for the average waiting time of all the patients who visit this doctor. Assume the population of waiting times is normally distributed. (8pts)

8. A new brand of breakfast cereal is being market tested. One hundred (100) boxes of the cereal were given to consumers to try. The consumers were asked whether they liked or disliked the cereal. A total of 60% of the customers stated they liked the cereal. Construct a 95% confidence interval for the proportion of all consumers who will like the cereal. (8pts)

9. A coal company wants to determine a 95% confidence interval estimate for the average daily tonnage of coal that they mine. Assuming that the company reports that the standard deviation of daily output is 100 tons, how many days should they sample (i.e. find the sample size) so that the margin of error will be 20 tons or less? (4pts)

Bonus (4pts):

For each of the following, identify the type of sampling used as random sampling from an infinite population, stratified random sampling, cluster sampling, or systematic sampling.

a) In the study of managers at a large firm, managers are categorized into one of three groups according to their division (field, production, or corporate). A simple random sample of managers is taken from each group.

b) A physician is selected at random from the American Medical Association directory. Every 100th physician thereafter is selected to be in the sample.

DUE BY 11PM TONIGHT PLEASE HELP. SORRY FOR LAST MINUTE.

3. A new soft drink is being market tested. It is estimated that 60% of consumers will like the new drink. A sample of 96 taste-tested the new drink.

a. Determine the standard error of the proportion. (4pts)

0.05

b. What is the probability that the sample proportion will be within ±0.0725 of the population proportion (that is, the proportion is between 0.5275 and 0.6725)? (8pts)

4. Use the t-distribution table to find the t- value for a sample size of n = 15 with a 90% confidence level. (2pts)

5. Use the t-distribution table to find the t- value for a sample size of n = 30 with a level of significance,

α = 0.05. (2pts)

6. A random sample of 100 credit sales in a department store showed an average sale of $120.00. From past data, it is known that the population standard deviation is $40.00.

a. Determine the standard error of the mean. (4pts)

b. At 95% confidence, determine the margin of error. (4pts)

c. Find the 95% confidence interval of the population mean. (8pts)

7. A sample of 25 patients in a doctor's office showed that they had to wait an average of 35 minutes with a sample standard deviation of 10 minutes before they could see the doctor. Construct a 95% confidence interval estimate for the average waiting time of all the patients who visit this doctor. Assume the population of waiting times is normally distributed. (8pts)

8. A new brand of breakfast cereal is being market tested. One hundred (100) boxes of the cereal were given to consumers to try. The consumers were asked whether they liked or disliked the cereal. A total of 60% of the customers stated they liked the cereal. Construct a 95% confidence interval for the proportion of all consumers who will like the cereal. (8pts)

9. A coal company wants to determine a 95% confidence interval estimate for the average daily tonnage of coal that they mine. Assuming that the company reports that the standard deviation of daily output is 100 tons, how many days should they sample (i.e. find the sample size) so that the margin of error will be 20 tons or less? (4pts)

Bonus (4pts):

For each of the following, identify the type of sampling used as random sampling from an infinite population, stratified random sampling, cluster sampling, or systematic sampling.

a) In the study of managers at a large firm, managers are categorized into one of three groups according to their division (field, production, or corporate). A simple random sample of managers is taken from each group.

b) A physician is selected at random from the American Medical Association directory. Every 100th physician thereafter is selected to be in the sample.

DUE BY 11PM TONIGHT PLEASE HELP. SORRY FOR LAST MINUTE.

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