The Following Problems Are to Be Written up in Polished Form , Showing All Relevant Work

Problems W6

The following problems are to be written up in polished form, showing all relevant work

1. A nationwide study of American homeowners revealed that 64% have one or more lawn mowers. A lawn equipment manufacturer, located in Omaha, claims the estimate is too low for households in Omaha.

a. Can the value 0.64 be rejected if a survey of 496 homes in Omaha yields 350 with one or more lawn mowers? Use the p-value approach and  = 0.05 to make your decision.

b. Suppose a second sample is collected one month after the first with the results indicating 367 out of 504 homes in Omaha have one or more lawn mowers. Would this be enough to show at least 70% of homeowners in Omahaown one of more lawnmowers? Use the p-value approach and  = 0.05 to make your decision.

2. It is generally accepted that convicted burglars spend an average of 18.7 months in jail. To check this claim a researcher takes a random sample of 50 such cases from court files and finds that x-bar = 20.5 months. Assuming  is known to be 7.9 months; does the sample evidence support the belief that the average stay is 18.7 months at the 0.025 level of significance?

3. As a part of contract negotiations, management claims that the mean annual salary for clerical workers is $30,000. The union would like to show the mean is lower. A random sample of 17 annual clerical salaries is collected and yields a sample mean of $28,157 and standard deviation of $3500. Is this sufficient evidence to support the Union’s position? Use a significance level of  = 0.05. You may assume the mean annual salaries are normally distributed.

4. A light-bulb manufacturer advertises that the average life for its light bulbs is 900 hours. A random sample of 15 of its light bulbs resulted in the following lives in hours.

a. Find x-bar and s for this data set.

1. At the 10% significance level, do the data provide evidence that the mean life for the company’s light bulbs differs from the advertised mean? You may assume the values for bulb life are normally distributed. Use the traditional method to make your decision.

5. A public bus company official claims that the mean waiting time for bus number 14 during peak hours is less than 10 minutes. Karen took bus number 14 during peak hours on 18 different occasions. Her mean waiting time was 7.2 minutes with a standard deviation of 1.6 minutes. At the 0.01 significance level, test the claim that the mean is less than 10 minutes. You may assume that the time spent waiting for bus 14 is normally distributed.

6. Various temperature measurements are recorded at different times for a particular city. The mean of 23°C is obtained for 45 temperatures on 45 different days. Assuming that σ = 1.5°C, test the claim that the population mean is 22°C. Use a 0.05 significance level.