Exam 10: B: Inference From Small Samples

Coffee Vending Machines Narrative An automatic coffee vending machine dispenses a different amount of coffee in millilitres (mL) for each cup. Assume the following nine measurements were taken from a population with a normal distribution: 185, 170, 196, 176, 173, 187, 193, 170 and 173 mL. -Refer to Coffee Vending Machines Narrative. Construct an 80% confidence interval for the mean amount of coffee that is dispensed for all cups of coffee from this machine.

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. Interpret the interval in the previous question.

Hourly Wages Narrative A random sample of 15 hourly wages for waitresses (including tips) was drawn from a normal population. The sample mean and sample standard deviation were computed as = $14.9 and s = $6.75. -Refer to Hourly Wages Narrative. Can we infer at the 5% significance level that the population mean is greater than 12, assuming that you know the population standard deviation is equal to 6.75? Give reasons for your answer.

Test Scores Narrative The test scores on a 100-point test were recorded for 20 students: 73, 95, 93, 83, 77, 75, 83, 84, 78, 59, 86, 91, 69, 64, 74, 79, 70, 67, 77, and 86. -Refer to Test Scores Narrative Calculate the mean and standard deviation of the scores.

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. Is it reasonable to assume equality of variances in this ? Justify your answer.

Children Narrative Two random samples of 3-year-old children, each of size 25, are taken from independent populations. The populations are distributed with equal variances. The first sample has a mean of 35.5 and a standard deviation of 3.0 while the second sample has a mean 33.0 and standard deviation of 4.0. A test for the difference between the two population means is conducted on this data. -Refer to Children Narrative. Between which two values does the p-value for a one-tailed test whose computed statistic is 2.50 (in the hypothesized direction) lie?

Employees Test Scores Narrative A random sample of 35 employees who completed two years of college were asked to take a basic mathematics test. The mean and standard deviation of their scores were 75.1 and 12.8, respectively. In a random sample of 50 employees who completed only high school, the mean and standard deviation of the test scores were 72.1 and 14.6, respectively. -Refer to Employees Test Scores Narrative. Can we infer at the 10% significance level that a difference exists between the two groups?

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. Is it reasonable to assume equality of variances in this ? Justify your answer.

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. Use = 0.05 to test the hypothesis that the two population variances are equal.

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. State the appropriate null and alternative hypotheses to test whether there is a significant difference between the two companies in average time a customer is on hold.

Manufacturing Garment Average Narrative A garment manufacturing company recorded the amount of time that it took to make a pair of jeans on eight different occasions. The times in minutes are as follows: 12.5, 13.0, 11.9, 10.2, 13.1, 13.6, 13.8, and 14.0. Assume these measurements were taken from a population with a normal distribution. Do the sample data suggest that the average time it takes this company to make a pair of jeans is less than 13.5 minutes? -Refer to Manufacturing Garment Average Narrative. Construct a 95% confidence interval for the mean amount of time it takes this company to make a pair of jeans.

Earthquake Analysis Narrative The length of duration, in minutes, of earthquakes in British Columbia has been recorded for future analysis and information. The length of duration of a random sample of six earthquakes is as follows: 1.1, 0.9, 1.5, 0.7, 1.4, and 1.3. -Refer to Earthquake Analysis Narrative. Interpret the interval in the previous question.

A child psychologist was interested in the difference in age (in years) between a boy and girl when they first learn to ride a two-wheeled bicycle. The psychologist developed a 99% confidence interval for the difference in average ages to be (-0.58, 0.73). What conclusion, if any, can be drawn from this interval? Justify your answer.

Bottling Productivity Narrative Five soft drink bottling companies have agreed to implement a time management program in hopes of increasing productivity (measured in cases of soft drinks bottled per hour). The number of cases of soft drinks bottled per hour before and after the implementation of the program are listed below: Company -Refer to Bottling Productivity Narrative. State the appropriate null and alternative hypotheses to test whether the time management has been effective in increasing productivity.

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. Use = 0.05 to test the hypothesis that the two population variances are equal.

Average Battery Life Narrative The average life of a certain type and brand of battery is 75 weeks. The average life of each of nine randomly selected batteries is as follows: 74.5, 75.0, 72.3, 76.0, 75.2, 75.1, 75.3, 74.9, and 74.8. Assume the battery life distribution is normal. Do the sample data suggest the average life is smaller than 75 weeks? -Refer to Average Battery Life Narrative. Compute the approximate p-value associated with the test statistic in question 54. Do the sample data support the alternative hypothesis at the = 0.05 level? Justify your conclusion.

Studying Time Narrative A faculty advisor was interested in determining whether there is a difference between male and female students in the amount of time (in hours) spent studying on weeknights (Monday through Thursday). The advisor selected a random sample of 12 female students and a second random, but independent, sample of 10 male students and asked each student to indicate the average amount of time spent studying on a weeknight. The following summary statistics are obtained. -Refer to Studying Time Narrative. Approximate the p-value for the test in the above question.

Employees Test Scores Narrative A random sample of 35 employees who completed two years of college were asked to take a basic mathematics test. The mean and standard deviation of their scores were 75.1 and 12.8, respectively. In a random sample of 50 employees who completed only high school, the mean and standard deviation of the test scores were 72.1 and 14.6, respectively. -Refer to Employees Test Scores Narrative. Estimate with 90% confidence the difference in mean scores between the two groups of employees.

Assume that the population distributions of times (in minutes) for two different skiers to race the same course are normal with equal variances. Two random samples, drawn independently from the populations, showed the following statistics: = 4, = 7.52, = 0.25; = 5, = 8.37, and = 0.09. Construct and interpret a 95% confidence interval for the true difference in average time of skiers to race the same course.

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. Use = 0.10 to test the hypotheses that the two population variances are equal.