Exam 10: B: Inference From Small Samples

Motorcycle Fuel Consumption Narrative A Harley Davidson dealer wants to know the average fuel consumption (in litres per 100 km) of a 1992 XLT. A random sample of 17 was taken from a normally distributed population and produced a mean of 4.5 L/100 km and a standard deviation of 0.36 L/100 km. -Refer to Motorcycle Fuel Consumption Narrative. The dealer claims that the average fuel consumption of a Harley Davidson 1992 XLT is 4.2 L/100 km. At a 95% level of confidence, can this claim be rejected? Justify your answer.

The mean playing times (in hours) for five different co-ed volleyball games for two different teams are listed below. Is there sufficient evidence to conclude the mean playing time for the two teams differ? Justify your answer. Assume the population distributions are normal and . Use a 0.05 significance level.

Vertical Blinds Installation Narrative A drapery store manager was interested in determining whether a new employee can install vertical blinds faster than an employee who has been with the company for two years. The manager takes independent samples of ten vertical blind installations of each of the two employees and computes the following information. -Refer to Vertical Blinds Installation Narrative. Calculate the pooled estimate of the common variance

Vertical Blinds Installation Narrative A drapery store manager was interested in determining whether a new employee can install vertical blinds faster than an employee who has been with the company for two years. The manager takes independent samples of ten vertical blind installations of each of the two employees and computes the following information. -Refer to Vertical Blinds Installation Narrative. Use = 0.05 to test the hypothesis that the two population variances are equal.

Grocery Receipts Narrative A simple random sample of 100 grocery receipts was drawn from a normal population. The mean and standard deviation of the sample were $120 and $25, respectively. -Refer to Grocery Receipts Narrative. Test the hypothesis vs. at the 10% significance level.

Motorcycle Fuel Consumption Narrative A Harley Davidson dealer wants to know the average fuel consumption (in litres per 100 km) of a 1992 XLT. A random sample of 17 was taken from a normally distributed population and produced a mean of 4.5 L/100 km and a standard deviation of 0.36 L/100 km. -Refer to Motorcycle Fuel Consumption Narrative. Construct a 95 percent confidence interval for the mean fuel consumption of any 1992 Harley Davidson XLT.

What is the appropriate t critical value for each of the following confidence levels and sample sizes when testing the two-sided alternative hypothesis? a. 80% confidence, n = 17 b. 90% confidence, n = 7 c. 99% confidence, n = 4 d. 95% confidence, n = 14

The following data were drawn from a normal population: 15, 4, 24, 8, 16, 13, 9, 15, 7, and 22. Estimate the population mean with 90% confidence.

Laptop Battery Charge Time Narrative A computer laboratory manager was in charge of purchasing new battery packs for her lab of laptop computers. She narrowed her choices to two models that were available for her machines. Since the models cost about the same, she was interested in determining whether there was a difference in the average time the battery packs would function before needing to be recharged. She took two independent random samples and computed the following summary information: -Refer to Laptop Battery Charge Time Narrative. Perform the appropriate test of hypotheses to determine whether there is a significant difference in average functioning time before recharging between the two models of battery packs. Test using = 0.05.

Coffee Breaks Narrative Do government employees take longer coffee breaks than private sector workers? That is a question that interested a management consultant. To examine the issue, he took a random sample of ten government employees and another random sample of ten private sector workers and measured the amount of time (in minutes) they spent in coffee breaks during the day. The results are listed below. -Refer to Coffee Breaks Narrative. Do these data provide sufficient evidence at the 5% significance level to support the consultant's question Justify your conclusion.

Laptop Battery Average Narrative The manufacturer of a particular battery pack for laptop computers claims its battery pack can function for 8 hours, on average, before having to be recharged. A random sample of 16 battery packs was selected and tested. The mean functioning time before having to be recharged was 7.2 hours with a standard deviation of 1.9 hours. -Refer to Laptop Battery Average Narrative. Assuming the distribution of functioning times is approximately normal, find a 95% confidence interval for the true average functioning time before needing to be recharged.

Vertical Blinds Installation Narrative A drapery store manager was interested in determining whether a new employee can install vertical blinds faster than an employee who has been with the company for two years. The manager takes independent samples of ten vertical blind installations of each of the two employees and computes the following information. -Refer to Vertical Blinds Installation Narrative. What is the appropriate conclusion? Give reasons for your answer.

Average Telephone Time on Hold Narrative A customer service representative was interested in comparing the average time (in minutes) customers are placed on hold when calling Gaz Metropolitain and Hydro-Quebec, both in Quebec. The representative obtained two independent random samples and calculated the following summary information: Assume the distributions of time a customer is on hold are approximately normal. -Refer to Average Telephone Time on Hold Narrative. What is the appropriate conclusion? Justify your answer.

Given a random variable that has a t distribution with the specified degrees of freedom, what percentage of the time will its value fall into the indicated region? a. 15 degrees of freedom, between -2.131 and 2.131 b. 19 degrees of freedom, between -2.539 and 2.539 c. 23 degrees of freedom, between -1.319 and 1.319 d. 10 degrees of freedom, between -3.169 and 3.169

Snowmobile Speeds Narrative A customer was interested in comparing the top speed (in kilometres per hour) of two models of snowmobiles. The customer selected two independent random samples of the snowmobiles and calculated the following summary information: Assume the distribution of top speeds is approximately normal. -Refer to Snowmobile Speeds Narrative. Is it reasonable to assume equality of variances in this ? Justify your answer.

What is the appropriate t critical value for each of the following confidence levels and sample sizes when testing the two-sided alternative hypothesis? a. 80% confidence, n = 17 b. 90% confidence, n = 7 c. 99% confidence, n = 4 d. 95% confidence, n = 14

Interest Rates Narrative The following 10 observations are interest rates on unpaid balances on credit cards for a department store: 10.4, 10.1, 9.5, 10.5, 10.6, 9.3, 9.9, 10.7, 9.5, and 10.0. -Here are the red blood cell counts (in cells per microlitre) of a healthy person measured on each of 15 days: 5.6, 5.4, 5.2, 5.4, 5.7, 5.5, 5.6, 5.4, 5.3, 5.5, 5.5, 5.1, 5.6, 5.4, and 5.4. Find a 95% confidence interval estimate of the true mean red blood cell count for this person during the period of testing.

Grocery Receipts Narrative A simple random sample of 100 grocery receipts was drawn from a normal population. The mean and standard deviation of the sample were $120 and $25, respectively. -Refer to Grocery Receipts Narrative. Estimate the population mean with 90% confidence.

In an effort to raise ratings, a television network president decides to reduce the number of commercials. A random sample of eight one-hour programs was monitored from each of two major networks. The data below reflect the time in minutes of commercials for each of the 16 shows. Suppose denotes the mean commercial time for network 1 and denotes the mean commercial time for network 2. Estimate - using a 95% confidence interval. Assume both population distributions are normal and have equal variances.

Childcare Costs Narrative The public relations officer for a particular city claims the average monthly cost for childcare outside the home for a single child is $600. A potential resident is interested in whether the claim is correct. She obtains a random sample of 14 records and computes the average monthly cost of this type of childcare to be $589 with a standard deviation of $40. -Refer to Childcare Costs Narrative. Approximate the p-value for the test in the previous question.