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8. [-/1 Points] DETAILS BBUNDERSTAT12 7.2.014.MI.S. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER How much does a sleeping bag cost? Let's say you want a sleeping bag that should keep you warm in temperatures from 20OF to 450F. A random sample of prices ($) for sleeping bags in this temperature range is given below. Assume that the population of x values has an approximately normal distribution. 80 85 70 90 100 60 30 23 100 110 105 95 105 60 110 120 95 90 60 70 LA USE SALT (a) Use a calculator with mean and sample standard deviation keys to find the sample mean price x and sample standard deviation s. (Round your answers to four decimal places.) x = $ S = (b) Using the given data as representative of the population of prices of all summer sleeping bags, find a 90% confidence interval for the mean price & of all summer sleeping bags. (Round your answers to two decimal places.) lower limit upper limit Need Help? Read It Master It9. [-/1 Points] DETAILS BBUNDERSTAT12 7.2.016.5. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Do you want to own your own candy store? Wow! With some interest in running your own business and a decent credit rating, you can probably get a bank loan on startup costs for franchises such as Candy Express, The Fudge Company, Karmel Corn, and Rocky Mountain Chocolate Factory. Startup costs (in thousand s of dollars) for a random sample of candy stores are given below. Assume that the population of x values has an approximately normal distribution. 92 178 126 91 75 94 116 100 85 LO USE SALT (a) Use a calculator with mean and sample standard deviation keys to find the sample mean startup cost x and sample standard deviation s. (Round your answers to four decimal places.) X = thousand dollars thousand dollars (b) Find a 90% confidence interval for the population average startup costs u for candy store franchises. (Round your answers to one decimal place.) lower limit thousand dollars upper limit thousand dollars Need Help? Read it Watch it10. [0.2/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 7.2.017.MI.S. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Over the past several months, an adult patient has been treated for tetany (severe muscle spasms). This condition is associated with an average total calcium level below 6 mg/dl. Recently, the patient's total calcium tests gave the following readings (in mg/dI). Assume that the population of x values has an approximately normal distribution. 9.10 9.60 10.50 9.30 9.40 9.80 10.00 9.90 11.20 12.10 In USE SALT (a) Use a calculator with mean and sample standard deviation keys to find the sample mean reading x and the sample standard deviation s. (Round your answers to four decimal places.) x = mg/d mg/dl (b) Find a 99.9% confidence interval for the population mean of total calcium in this patient's blood. (Round your answer to two decimal places.) lower limit mg/dl upper limit mg/dl (c) Based on your results in part (b), do you think this patient still has a calcium deficiency? Explain. Yes. This confidence interval suggests that the patient may still have a calcium deficiency. O Yes. This confidence interval suggests that the patient no longer has a calcium deficiency. O No. This confidence interval suggests that the patient may still have a calcium deficiency. No. This confidence interval suggests that the patient no longer has a calcium deficiency. Need Help? Read it Master It12. [0.46/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 7.2.020.5. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The following data represent crime rates per 1000 population for a random sample of 46 Denver neighborhoods.+ 63.2 36.3 26.2 53.2 65.3 32.0 65.0 66.3 68.9 35.2 25.1 32.5 54.0 42.4 77.5 123.2 66.3 92.7 56.9 27.5 69.2 73.8 71.5 58.5 67.2 78.6 33.2 74.9 45.1 132.1 104.7 63.2 59.6 75.7 39.2 69.9 87.5 56.0 154.2 85.5 77.5 84.7 24.2 37.5 41.1 LA USE SALT (a) Use a calculator with mean and sample standard deviation keys to find the sample mean x and sample standard deviation s. (Round your answers to four decimal places.) X = crimes per 1000 people crimes per 1000 people (b) Let us say the preceding data are representative of the population crime rates in Denver neighborhoods. Compute an 80% confidence interval for #, the population mean crime rate for all Denver neighborhoods. (Round your answers to one decimal place.) ower limit crimes per 1000 people upper limit crimes per 1000 people (c) Suppose you are advising the police department about police patrol assignments. One neighborhood has a crime rate of 59 crimes per 1000 population. Do you think that this rate is below the average population crime rate and that fewer patrols could safely be assigned to this neighborhood? Use the confidence interval to justify your answer. Yes. The confidence interval indicates that this c e rate is below the ave e population crime rate. Yes. The confidence interval indicates that this c rime rate does not differ from the average population crime rate. No. The confidence interval indicates that this crime rate is below the average population crime rate. No. The confidence interval indicates that this crime rate does not differ from the average population crime rate. (d) Another neighborhood has a crime rate of 73 crimes per 1000 population. Does this crime rate seem to be higher than the population average? Would you recommend assigning more patrols to this neighborhood? Use the confidence interval to justify your answer. O Yes. The confidence interval indicates that this crime rate does not differ from the average population crime rate. Yes. The confidence interval indicates that this crime rate is higher than the average population crime rate. O No. The confidence interval indicates that this crime rate is higher than the average population crime rate. O No. The confidence interval indicates that this crime rate does not differ from the average population crime rate. (e) Compute a 95% confidence interval for A, the population mean crime rate for all Denver neighborhoods. (Round your answers to one decimal place.) lower limit crimes per 1000 people upper limit crimes per 1000 people13. [0.22/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 7.2.022.5. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The home run percentage is the number of home runs per 100 times at bat. A random sample of 43 professional baseball players gave the following data for home run percentages. 2.4 1.2 6.6 2.3 0.0 1.8 2.5 6.5 1.8 2.7 2.0 1.9 1.3 2.7 1.7 1.3 2.1 2.8 1.4 3.8 2.1 3.4 1.3 1.5 2.9 2.6 0.0 4.1 2.9 2.4 0.0 1.8 3.1 3.2 1.6 4.2 0.0 1.8 2.4 LA USE SALT (a) Use a calculator with mean and standard deviation keys to find x and s. (Round your answers to four decimal places.) X = % 1% (b) Compute a 90% confidence interval for the population mean / of home run percentages for all professional baseball players. Hint: If you use the Student's t distribution table, be sure to use the closest d.f. that is smaller. (Round your answers to two decimal places.) lower limit % upper limit (c) Compute a 99% confidence interval for the population mean / of home run percentages for all professional baseball players. (Round your answers to two decimal places.) lower limit upper limit14. [0.08/1.04 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 7.2.023. MY NOTES ASK YOUR TEACHER PRACTICE ANOT When o is unknown and the sample is of size n 2 30, there are two methods for computing confidence intervals for J. Method 1: Use the Student's t distribution with d.f. = n - 1. This is the method used in the text. It is widely employed in statistical studies. Also, most statistical software packages use this method. Method 2: When n 2 30, use the sample standard deviation s as an estimate for , and then use the standard normal distribution. This method is based on the fact that for large samples, s is a fairly good approximation for . Also, for large n, the critical values for the Student's t distribution approach those of the standard normal distribution. Consider a random sample of size n = 41, with sample mean x = 45.5 and sample standard deviation s = 5.5. (a) Compute 90%, 95%, and 99% confidence intervals for A using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal. 90% 95% 99% lower limit upper limit (b) Compute 90%, 95%, and 99% confidence intervals for i using Method 2 with the standard normal distribution. Use s as an estimate for . Round endpoints to two digits after the decimal. 90% 95% 99% lower limit upper limit (c) Compare intervals for the two methods. Would you say that confidence intervals using a Student's t distribution are more conservative in the sense that they tend to be longer than intervals based on the standard normal distribution? O No. The respective intervals based on the t distribution are longer. Yes. The respective intervals based on the & distribution are longer. O No. The respective intervals based on the t distribution are shorter. Yes. The respective intervals based on the t distribution are shorter. (d) Now consider a sample size of 71. Compute 90%, 95%, and 99% confidence intervals for / using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal. 90% 95% 99% lower limit upper limit (e) Compute 90%, 95%, and 99% confidence intervals for / using Method 2 with the standard normal distribution. Use s as an estimate for . Round endpoints to two digits after the decimal. 90% 95% 99% lower limit upper limit1. [-/1 Points] DETAILS BBUNDERSTAT12 7.3.001. MY NOTES ASK YOUR TEACHER For a binomial experiment with r successes out of n trials, what value do we use as a point estimate for the probability of success p on a single trial? Need Help? Read It Submit AnswerSubmitted 5. [0.4/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 7.3.012.MI.S. MY NOTES ASK YOUR TEACHER PRACTICE For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. In a random sample of 536 judges, it was found that 277 were introverts. LA USE SALT (a) Let p represent the proportion of all judges who are introverts. Find a point estimate for p. (Round your answer to four decimal places.) (b) Find a 99% confidence interval for p. (Round your answers to two decimal places.) lower limit upper limitSubmitted 6. [0.4/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 7.3.015.5. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. A random sample of 5724 physicians in Colorado showed that 3089 provided at least some charity care (i.e., treated poor people at no cost). LA USE SALT (a) Let p represent the proportion of all Colorado physicians who provide some charity care. Find a point estimate for p. (Round your answer to four decimal places.) (b) Find a 99% confidence interval for p. (Round your answers to three decimal places.) lower limit upper limitSubmitted 7. [0.4/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 7.3.016.5. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. Case studies showed that out of 10,205 convicts who escaped from certain prisons, only 7629 were recaptured. LA USE SALT (a) Let p represent the proportion of all escaped convicts who will eventually be recaptured. Find a point estimate for p. (Round your answer to four decimal places.) (b) Find a 99% confidence interval for p. (Round your answers to three decimal places.) lower limit upper limit