9. A consumer electronics company is considering sourcing LED lights for their next television model from two different companies, Brand A and Brand B. It is believed that lights from Brand A produce a higher mean brightness (measured in "nits") compared to those from Brand B. To test this claim, a sample of sixty lights is tested from each brand. The results are sum- marized below: Company Sample Size Sample Mean (nits) Sample Standard Deviation (nits) Brand A Brand B 60 60 1432 113 1350 192 Do the data support the claim that lights from Brand A have a higher mean than lights from Brand B? Use a = 0.05. 10. A marathon is a 42.2 kilometre long-distance running race. Four runners wishing to compare their ability tabulated the time (in minutes) it took to run each marathon they participated in within the last two years. Jen Kyle Omar Tia 282 254 279 269 271 271 269 275 271 2581 270 276 269 272 261 276 266 275 268 255 Can one conclude that the average marathon time differs between any of the runners at a level of significance of 5%? Use the values from the following partially completed ANOVA table in your analysis. (Assume that the underlying populations are normal with common standard deviation.) Source df Sum of Squares Mean Squares F Treatments (between) 205.37 Error(within) Total 1074.55 3. The number of companies offering flexible work schedules has increased as companies try to help employees cope with the demands of home and work. An example of a flextime schedule is to work 4 ten-hour shifts in a week. A survey provided the following information for 220 firms located in two large cities in Ontario. Flextime Schedule City Offered Not Offered Total A 44 70 114 B 25 81 106 Total 69 151 220 (a) Find the probability that a randomly selected firm is from City B. (b) Find the probability that a randomly selected firm is from City B and flextime schedule is not offered. (c) Find the probability that a randomly selected firm is from City A, given that flextime schedule is not offered. (d) Are the events City A and flextime Not Offered independent? 4. A farmer uses artificial insemination to impregnate his cows. This method has an 80% success rate. (a) If 10 cows are selected at random to be inseminated, what is the probability that 8 or more cows become pregnant? (b) Suppose 100 cows are selected at random to be inseminated. Find the mean and standard deviation of this binomial distribution. (c) Suppose 100 cows are selected at random to be inseminated. Use the normal approximation to the binomial distribution to find the probability that 75 or more cows become pregnant. 5. Suppose the life span of a car battery is normally distributed with mean 52 months and standard deviation 18 months. (a) Each battery is sold with a one-year warranty which states that if a new battery fails before the end of 12 months from the date of purchase, then the company will replace it with a new one free of charge. What percentage of batteries will need to be replaced assuming all customers with failed batteries will do so? (b) New batteries are shipped in a crate containing 32 batteries. What is the probability that the average life span of the batteries in a crate will be greater than 48 months? 6. The Court of Regina records provided data on sentencing for 19 criminals convicted of negligent homicide. The mean and standard deviation of the sentences were found to be 72.7 and 10.2 months respectively. Determine a 95% confidence interval for the mean sentence for this crime. State any assumptions that were required for your analysis to be valid. 7. According to a 2018 Statistics Canada report, women held 32.6% of all senior management occupations in Canada. To determine if this number is still the same in 2019, a researcher considered a random sample of 850 senior management positions and found that 296 were held by women. (a) Test the reported claim using a = 0.04. Show all work and necessary steps. (b) Calculate the P-value for your test. If a was changed to 0.10, would your answer remain the same? Briefly explain your reasoning. 8. A student association wants to estimate average student debt. A previous survey found a standard deviation for student debt of $11,500. How large a sample size should be used to be 90% confident of finding the current average student debt with a maximum error of $700? 1. The number of building permits issued last month to a sample of 12 construction firms in a large city were: 2 0 3 1 7 5 6 8 3 16 45 (permits) (a) Find the sample mean. (b) Calculate the sample standard deviation. (c) Find the five number summary for the data set. (d) Determine if there are any outliers in the data set. (e) Sketch a box and whisker plot for the data. 2. A study was conducted to determine the effects of sleep deprivation on a person's ability to solve problems without sleep. A total of 10 subjects participated in the study. After his or her specified sleep deprivation period, each subject was administered a set of simple addition problems, and the number of errors was recorded. These results were obtained: Subject 1 2 3 4 5 6 7 8 9 10 Hours without sleep, 8 8 12 12 16 16 20 20 24 24 Number of errors, y 8 6 6 10 8 14 14 12 16 12 Note: Στ = 160 Σy=106 Στο = 2880 Σ y = 1236 Στη = 1848 (a) Find the linear correlation coefficient, r. (b) Calculate the line-of-best-fit (the linear regression line). (c) Use the regression equation to predict the number of errors for a person who has not slept for 10 hours.