2. Can You Hear Me Now?

2. Can You Hear Me Now? Red Widget Strategies wants to improve its customer service by being more efficient in how phone calls are processed. Toward that end, Red Widget does a statistical analysis of 1,000 outbound phone calls. The length of the calls is normally distributed, with a population mean = 240 seconds, and a population standard deviation = 40 seconds. a. What is the probability that a particular call lasted less than 180 seconds? b. What is the probability that a particular call lasted between 180 and 300 seconds? c. What is the probability that a call lasted between 110 and 180 seconds? d. What is the probability that a call lasted more than 300 seconds?

3. Union Shop, or Not? A confidential labor organizers' poll was recently conducted in a major discount retail chain. Based on a random sample of 1000 rank and file employees, the researchers classified employees by gender and asked them if they planned to support unionization, by responding "Union" or "No Union." Results are shown in the following table. Union No Union Total Male 200 250 450 Female 300 250 550 Total 500 500 1000 a. State the null and alternative hypotheses. b. Calculate the expected counts. c. Calculate the value of the chi-square test statistic; assume a 95% confidence level. d. Develop a conclusion. What can be said about the relationship between employee gender and preference for union representation? e. Comment on the strengths and drawbacks of using the chi square test statistic.

4. Gotta love the Stairmaster Both employers and insurers are on the lookout for ways to control the costs of health insurance. Toward that end, an insurer-led study of workers in the financial services industry concerns the average fat loss between those who only diet, and those who only exercise. Following are the sample results from study participants on the amount of fat lost after one year: Group 1: Diet Only Sample mean: 5.9 kg Sample standard deviation: 4.1 kg Level of significance: .05 Number of participants: 42 Group 2: Exercise Only Sample mean: 4.1 kg Sample standard deviation: 3.7 kg Level of significance: .05 Number of participants: 47 Research question: Is there a significant difference in average fat lost between these two methods? a. Determine the null and alternate hypotheses. b. Calculate the appropriate test statistic. c. Find the p-value. d. What do you conclude? Be specific.