MATH 225N Week 6 Confidence Intervals Questions and Answers

MATH 225N Week 6 Confidence Intervals Questions and Answers Week 6 Questions on Confidence Intervals 1. On a busy Sunday morning, a waitress randomly sampled customers about their preference for morning beverages, Specifically, she wanted to find out how many people preferred coffee over tea. The proportion of customers that preferred coffee was 0.42 with a margin of error 0.07. Construct a confidence interval for the proportion of customers that preferred coffee. (0.42 - 0.07), (0.42 + 0.07) = (0.35), (0.49) 2. A company sells juice in 1quart bottles. In a quality control test, the company found the mean volume of juice in a random sample of bottles was X = 31 ounces, with a marginal error of 3 ounces. Construct a confidence interval for the mean number of ounces of juice bottled by this company. (31-3), 31+3) = (28), (34) 3. Randomly selected employees at an office were asked to take part in a survey about overtime. The office manager wanted to find out how many employees worked overtime in the last week. The proportion of employees that worked overtime was 0.83, with a margin of error of 0.11. (0.83 – 0.11), (0.83 + 0.11) = (0.72), (0.94) 4. A random sample or garter snakes were measured, and the proportion of snakes that were longer than 20 inches in length recorded. The measurements resulted in a sample proportion of p = 0.25 with a sampling standard deviation of Op = 0.05. Write a 68% confidence interval for the true proportion of garter snakes that were over 20 inches in length. (.25 - .05). (.25 + .05) = (0.20), (.30) 5. The average number of onions needed to make French onion soup from the population of recipes is unknown. A random sample of recipes yields a sample mean of x = 8.2 onions. Assume the sampling distribution of the mean has a standard deviation of 2.3 onions. Use the Empirical Rule to construct a 95% confidence interval for the true population mean number of onions. Since 95% falls in 2 SD’s the calculation would be (8.2 – 4.6) “4.6 is the margin of error”, (8.2 + 4.6) = (3.6) , (12.8) 6. In a survey, a random sample of adults were asked whether a tomato is a fruit or vegetable. The survey resulted in a sample proportion of 0.58 with a sampling standard deviation of 0.08 who stated a tomato is a fruit. Write a 99.7 confidence interval for the true proportion of number of adults who stated the tomato is a fruit. (0.58 – 3 x 0.08), (0.58 + 3 x 0.08) =(0.58 – .24), (0.58 + .24) = 0.34 + 0.82 7. A college admissions director wishes to estimate the mean number of students currently enrolled. The age of random sample of 23 students is given below. Assume the ages are approximately normally distributed. Use Excel to construct a 90% confidence interval for the population mean age. Round your answer to 2 decimal places and use increasing order. Use week 6 worksheet to get mean and SD. Data 25.8 Mean 23.1043 22.2 Sample Standard Deviation 1.3693 22.5 22.8 24.6 24 22.6 23.6 22.8 23.1 21.5 21.4 22.5 24.5 21.5 22.5 20.5 23 25.1 25.2 23.8 21.8 24.1 Confidence Level 0.900 n 32 Mean 23.1043 StDev 1.3693 pop stdev no SE 0. t 1.696 Margin of Error 0. Lower Limit 22. Upper Limit 23. Lower margin of error = 22.69 and upper limit is 23.51 8. Suppose that the scores of bowlers in a particular league follow a normal distribution such that a standard deviation of the population is 12. Find the 95% confidence interval of the mean score for all bowlers in this league using the accompanying data set of 40 random scores. Round your answers to 2 decimal places using ascending order. Lower Limit = 90.78 Upper Limit = 98.22 Confidence Level 0.950 n 40 Mean 94.5000 StDev 12.0000 pop stdev yes SE 1. z 1.960 Margin of Error 3. Lower Limit 90. Upper Limit 98. 9. In the survey of 603 adults, 98 said that they regularly lie to people conducting surveys. Create a 99% confidence interval for the proportion of adults who regularly lie to people conducting surveys. Use excel to create the confidence interval rounding to 4 decimal places. Lower Limit = 0.1238 Upper Limit = 0.2012 Confidence Level 0.990 n 603 Number of Successes 98 Sample Proportion 0. SE 0. z 2.576 Margin of Error 0. Lower Limit 0. Upper Limit 0. 10. In a random sampling of 350 attendees at a minor league baseball game, 184 said that they bought food from the concession stand. Create a 95%confidence interval for the proportion of fans who bought food from the concession stand. Use excel to create the confidence interval rounding to 4 decimal places. Lower limit = 0.4734 Upper Limit = 0.5780 Confidence Level 0.950 n 350 Number of Successes 184 Sample Proportion 0. SE 0. z 1.960 Margin of Error 0. Lower Limit 0. Upper Limit 0. 11. Suppose that the weight of tight ends in a football league are normally distributed such that sigma squared = 1,369. A sample of 49 tight ends was randomly selected and the weights are given in the table below. Use Excel to create a 95% confidence interval for the mean weight of the tight ends in this league. Rounding your answers to 2 decimal places and using ascending order. (Have to get square root of 1369 which is 37). Population sample is yes . Lower limit = 241.42 Upper Limit = 262.14 Confidence Level 0.950 n 49 Mean 251.7755 StDev 37.0000 pop stdev yes SE 5. z 1.960 Margin of Error 10. Lower Limit 241. Upper Limit 262. 12. Suppose heights, in inches of orangutans are normally distributed and have a known population standard deviation of 4 inches. A random sample of 16 orangutans is taken and gives a sample mean of 56 inches. Find the confidence interval of the population mean with a 95% confidence level. Lower limit = 54.04 and Upper Limit = 57.96 13. The population standard deviation for the total snowfalls per year in a city is 13 inches. If we want to be 95% confident that the sample mean is within 3 inches of the true population mean, what is the minimum sample size that should be taken? Answer: 73 snowfalls Minimum Sample Size μ for population mean Confidence Level 0.950 StDev 13 Error 3 z-Value 1.960 Minimum Sample Size 73 14. The population standard deviation for the body weights for employees of a company is 10 pounds. If we want to be 95% confident that the sample mean is within 3 pounds of the true population mean, what is the minimum sample size that should be taken. Answer: 43 employees Minimum Sample Size μ for population mean Confidence Level 0.950 StDev 10 Error 3 z-Value 1.960 Minimum Sample Size 43 15. The length, in words, of the essays written for a contest are normally distributed with a population standard deviation of 442 words and an unknown population mean. If random sample of 24 essays is taken and results in a sample mean of 1330 words, find a 99% confidence interval for the population mean. Round to two decimal places. Answer: Lower limit = 1097.59 upper Limit = 1562.41 16. Brenda wants to estimate the percentage of people who eat fast food at least once per week. She wants to create a 95% Confidence interval which has an error bound of at most 2%. How many people should be polled to create the confidence interval? Answer: 2401 Minimum Sample Size p for Proportion Confidence Level 0.950 Enter decimal Sample Proportion 0.5 If sample proportion unknown enter 0.5 Error 0.02 Write percentage as decimal z-Value 1.960 Minimum Sample Size 2401 17. Suppose a clothing store wants to determine the current percentage of customers who are over the age of forty. How many customers should the company survey in order to be 92% confident that the estimated (sample) proportion is within 5% of the true population proportion of customers who are over the age of 40? Answer: 307 Minimum Sample Size p for Proportion Confidence Level 0.920 Enter decimal Sample Proportion 0.5 If sample proportion unknown enter 0.5 Error 0.05 Write percentage as decimal z-Value 1.751 Minimum Sample Size 307 18. Suppose the scores of a standardized test are normally distributed. If the population standard deviation is 2 points, what minimum sample size is needed to be 90% confident that the sample mean is within 1 point of the true population mean? Be sure to round up to the nearest integer. Provide your answer below: 11 Minimum Sample Size μ for population mean Confidence Level 0.900 StDev 2 Error 1 z-Value 1.64