# Problem A: The “cold start ignition time” of an automobile engine

August 30, 2017

Question
Problem A: The “cold start ignition time” of an automobile engine is investigated by a gasoline manufacturer. The following times (in seconds) were obtained for a test vehicle: 1.75, 1.92, 2.62, 2.35, 3.09, 3.15, 2.53, 1.91. a) Calculate the sample mean, sample standard deviation, and sample proportion of times exceeding 2.5 seconds. b) Compute the sample quartiles, sample interquartile range (SIQR), and the sample range. Compare the sample mean and the sample median. c) Find the five number summary and construct a boxplot. Check for outliers. Comment on the shape of the distribution.

Problem B: The 15 measurements that follow are furnace temperatures recorded on successive batches in a semiconductor manufacturing process (units are °F): 953, 950, 948, 955, 951, 949, 957, 954, 955, 949, 969, 950, 951, 950, 965. a) Calculate the sample mean, sample standard deviation, and sample proportion of temperatures below 950. b) Compute the sample quartiles, sample interquartile range (SIQR), and the sample range. c) Find the five number summary and construct a boxplot. Check for outliers. Comment on the shape of the distribution. Compare the sample mean and the sample median.

Problem C: A random sample of 5 cars of Type A that were test driven yielded gas mileages of 29.1, 29.6, 30, 30.5, 30.8, while a random sample of 5 cars of Type B that were test driven under similar conditions yielded gas mileages of 21, 26, 30, 35, 38. a) For each type of car, estimate the population mean gas mileage and the population variance of gas mileage b) Construct a comparative boxplot and rank the two types of car in terms of quality (justify for your answer).

Problem D: Use the data set in Problem A. The Normal Probability Plot indicates the data came from Normal population. a) Construct and interpret the 95% confidence interval for the population mean start ignition time of an automobile engine. STAT 401 Fall 2015 b) Determine the sample size needed to estimate the population mean start ignition time within the margin of error of 0.25 seconds. c) Construct and interpret the 95% upper confidence bound for the population mean start ignition time. d) Test at 0.05 significance level whether the population mean start ignition time is below 2.9 seconds. Include the hypotheses, the test statistic, the rejection region, the p-value, test decision and conclusion in the context of the problem. e) Construct an appropriate interval and use it to test the hypotheses in part d). Interpret the interval.

Problem E: A health magazine conducted a survey on the drinking habits of US young adults (ages 21-35). On the question “Do you drink beer, wine, or hard liquor each week?” 985 of the 1516 adults interviewed said “yes”. a) Test at 0.02 significance level whether the population proportion of US young adults who beer, wine, or hard liquor on a weekly basis is significantly different from 65%. Include the hypotheses, the test statistic, the rejection region, the p-value, test decision and conclusion in the context of the problem. Check appropriate conditions. b) Construct an appropriate interval and use it to test the hypotheses in part a). Interpret the interval. Check appropriate conditions. c) What sample size is required to estimate the population proportion of US young adults who beer, wine, or hard liquor on a weekly basis within 2% at 98% confidence level, using the information from the current sample? d) Without calculations, explain which of the following two intervals population proportion of US young adults who beer, wine, or hard liquor on a weekly basis is going to be wider and why: 98% confidence interval or 95% confidence interval

Problem F: The life (in hours) of 75-watt light bulbs is under study. A random sample of 35 light bulbs produces a mean of 1014 hours and a standard deviation of 25 hours. a) Test whether the population average life of 75-watt light bulbs is above 1000 hours. Include the hypotheses, the test statistic, the rejection region, the p-value, test decision and conclusion in the context of the problem. b) Do you need to make any additional assumptions for the test in a). If yes, what are they? c) Construct an appropriate interval and use it to test the hypotheses in part a). Interpret the interval.

Problem G[BONUS]: All-time Olympic gold medal counts by continent are: Europe – 3521, America – 1359, Asia – 590, Oceania – 188, Africa – 103. (www.games- encyclo.org). Construct the bar graph and the pie chart for this data set.

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