Exam 12: Confidence Intervals for Means

Find the standard error of the mean. -A small business ships specialty homemade candies to anywhere in the world. Past Records indicate that the weight of orders is normally distributed. Suppose a random Sample of 16 orders is selected and each is weighed. The sample mean was found to be 110 grams with a standard deviation of 14 grams. The standard error of the mean is

Find the margin of error. -A manufacturer of cheese filled ravioli supplies a pizza restaurant chain. Based on Data collected from its automatic filling process, the amount of cheese inserted into the Ravioli is normally distributed. To make sure that the automatic filling process is on Target, quality control inspectors take a sample of 25 ravioli and measure the weight of Cheese filling. They find a sample mean weight of 15 grams with a standard deviation of 1.5 grams. What is the margin of error at 90% confidence?

Find the confidence interval. -A large software development firm recently relocated its facilities. Top management is Interested in fostering good relations with their new local community and has encouraged Their professional employees to engage in local service activities. They wish to Determine the average number of hours the firm's professionals volunteer per month. A Random sample of 24 professionals yields a mean of 16.6 hours and a standard deviation Of 2.22 hours. The 95% confidence interval is

Find the confidence interval. -In a metal fabrication process, metal rods are produced to a specified target length of 15 feet. Suppose that the lengths are normally distributed. A quality control specialist Collects a random sample of 16 rods and finds the sample mean length to be 14.8 feet and A standard deviation of 0.65 feet. The 95% confidence interval for the true mean length Of rods produced by this process is

Find the confidence interval. -A small business ships specialty homemade candies to anywhere in the world. Past Records indicate that the weight of orders is normally distributed. Suppose a random Sample of 16 orders is selected and each is weighed. The sample mean was found to be 110 grams with a standard deviation of 14 grams. The 90% confidence interval for the True mean weight of orders is

Find the confidence interval. -Grandma Gertrude's Chocolates, a family owned business, has an opportunity to Supply its product for distribution through a large coffee house chain. However, the Coffee house chain has certain specifications regarding cacao content as it wishes to Advertise the health benefits (antioxidants) of the chocolate products it sells. In order to Determine the mean % cacao in its dark chocolate products, quality inspectors sample 36 Pieces. They find a sample mean of 55% with a standard deviation of 4%. The 90% confidence interval for the true mean % cacao is

Interpret the confidence interval. -A manufacturer of cheese filled ravioli supplies a pizza restaurant chain. Based on Data collected from its automatic filling process, the amount of cheese inserted into the Ravioli is normally distributed. To make sure that the automatic filling process is on Target, quality control inspectors take a sample of 25 ravioli and measure the weight of Cheese filling. They find the 99% confidence interval of 14.16 to 15.84 grams. Which of The following is the correct interpretation?

Find the margin of error. -Grandma Gertrude's Chocolates, a family owned business, has an opportunity to Supply its product for distribution through a large coffee house chain. However, the Coffee house chain has certain specifications regarding cacao content as it wishes to Advertise the health benefits (antioxidants) of the chocolate products it sells. In order to Determine the mean % cacao in its dark chocolate products, quality inspectors sample 36 Pieces. They find a sample mean of 55% with a standard deviation of 4%. What is the margin of error at 95% confidence?

Find the sample size. -ABI Insurance wants to estimate the average life expectancy to within one year with 95% confidence. Previous studies have shown the mean age life expectancy of its clients To be 78.6 with a standard deviation of 4.48 years. How many randomly selected Recently paid policies would they need to sample to achieve the desired level of accuracy?

Interpret the confidence interval. -A large software development firm recently relocated its facilities. Top management is Interested in fostering good relations with their new local community and has encouraged Their professional employees to engage in local service activities. They wish to Determine the average number of hours the firm's professionals volunteer per month. They find the 95% confidence interval of 14.62 to 15.78. Which of the following is the Correct interpretation?

Find the confidence interval. -Insurance companies track life expectancy information to assist in determining the cost Of life insurance policies. ABI Insurance randomly sampled 100 recently paid policies And determined the average age of clients in this sample to be 77.7 years with a standard Deviation of 3.6. The 90% confidence interval for the true mean age of its life insurance Policy holders is

Describe t-distributions. -In a metal fabrication process, metal rods are produced to a specified target length of 15 feet. Suppose that the lengths are normally distributed. A quality control specialist Collects a random sample of 16 rods and finds the sample mean length to be 14.8 feet and A standard deviation of 0.65 feet. Which of the following statement is true?

Grandma Gertrude's Chocolates, a family owned business, has an opportunity to supply its product for distribution through a large coffee house chain. However, the coffee house chain has certain specifications regarding cacao content as it wishes to advertise the health benefits (antioxidants) of the chocolate products it sells. In order to determine the mean % cacao in its dark chocolate products, quality inspectors sample 36 pieces. They find a sample mean of 55% with a standard deviation of 4%. a. Describe the sampling distribution for the sample mean. b. What is the standard error? c. What is the margin of error for 90% confidence? d. What is the margin of error for 95% confidence? e. Based on the sample results, find the 90% confidence interval and interpret. f. Based on the sample results, find the 95% confidence interval and interpret. g. For a more accurate determination of the mean weight, the quality control inspectors wish to estimate it within 1% with 95% confidence. How many pieces of dark chocolate should they sample?

Find the standard error of the mean. -In a metal fabrication process, metal rods are produced to a specified target length of 15 feet. Suppose that the lengths are normally distributed. A quality control specialist Collects a random sample of 16 rods and finds the sample mean length to be 14.8 feet and A standard deviation of 0.65 feet. The standard error of the mean is

Describe t-distributions. -A small business ships specialty homemade candies to anywhere in the world. Past Records indicate that the weight of orders is normally distributed. Suppose a random Sample of 16 orders is selected and each is weighed. The sample mean was found to be 110 grams with a standard deviation of 14 grams. Which of the following statements is True?

Find the sample size. -Top management at a large software company wishes to estimate the average number Of hours its firm's professional employees volunteer in the local community. Based on Past similar studies, the standard deviation was found to be 2.22 hours. If top Management wants to estimate the average number of hours volunteered per month by Their professional staff to within one hour with 99% confidence, how many randomly Selected professional employees would they need to sample?

Check conditions / assumptions of confidence intervals for means. -Which of the following is not an assumption and / or condition required for constructing A confidence interval for the mean?

Find correct t* values. -A manufacturer of cheese filled ravioli supplies a pizza restaurant chain. Based on Data collected from its automatic filling process, the amount of cheese inserted into the Ravioli is normally distributed. To make sure that the automatic filling process is on Target, quality control inspectors take a sample of 25 ravioli. The correct value of t* to Construct a 99% confidence interval for the true mean amount of cheese filling is

Find the sample size. -A manufacturer of cheese filled ravioli wants to make sure that its automatic filling Process is on target. Based on a sample of 25 ravioli the mean weight of cheese filling is Estimated to be 15 grams with a standard deviation of 1.5 grams. However, the quality Control inspectors wish to estimate the mean weight of cheese filling more accurately so That they can be 99% confident that it is within .25 grams of the true mean. How many Ravioli should they sample?

Find the sample size. -Grandma Gertrude's Chocolates, a family owned business, has an opportunity to Supply its product for distribution through a large coffee house chain. However, the Coffee house chain has certain specifications regarding cacao content as it wishes to Advertise the health benefits (antioxidants) of the chocolate products it sells. Past data Indicate a standard deviation of 4%. If quality control inspectors wish to estimate the % Cacao to within 1% of the true mean with 95% confidence, how many pieces of Chocolate should they sample?