3 points. Chapter 8. Please answer the following questions on a separate piece of paper. 1. A traffic engineer recently found that the average morning commute time from Los Lunas to Albuquerque was 30 minutes. A previous study conducted in 1990 found the same average morning commute time to be 22 minutes. Does the difference of eight minutes prove that the average morning commute really is longer? Explain. 2. When is it appropriate to use a one-sample t-test? 3. An avid marathon runner believes that today’s runners have a lower average weight compared to runners 25 years ago. Twenty five years ago, the average runner weighed 169 lbs. The weights of 15 runners randomly sampled from this year’s marathon are given below: Runners' Weights in lbs.135167157152161153155141167181159163172164183 a. (A) What is the independent variable and its levels? (B) What is the dependent variable and its scale (i.e., NOIR) of measurement? b. What is the null hypothesis for the problem described above? c. Conduct a test of the null hypothesis using p = .05. Be sure to properly state your statistical conclusion. d. Provide an interpretation of your statistical conclusion from part c. e. What type of statistical error might you have made?f. How could the researcher increase statistical power for this study? g. What is the 95% confidence interval for this study? h. Provide an interpretation for the interval obtained in part g. i. How does the confidence interval obtained in part g compare to your statistical conclusion from part c? (i.e., Where does the value expected by the null hypothesis fall in the confidence interval and how does this support or not support your decision to reject or not reject the null hypothesis?) 4. An inventor believes she has designed a more water efficient evaporative (i.e., “swamp”) cooler. The inventor believes her new design will reduce water usage by up to 15% compared to the traditional cooler. Previous studies have found that the typical evaporative coolers use 15.5 gallons of water per day. The inventor randomly selects 15 homes in the same local area and installs the same size coolers for all homes. The amount of water used per day for the new coolers is given below. Water usage has been adjusted for amount of time the cooler was operated. Gallons Water141612151914131217161411181613 a. (A) What is the independent variable and its levels? (B) What is the dependent variable and its scale (i.e., NOIR) of measurement? b. What is the null hypothesis for the problem described above? c. Conduct a test of the null hypothesis using p = .05. Be sure to properly state your statistical conclusion. d. Provide an interpretation of your statistical conclusion from part c. e. What type of statistical error might you have made? f. How could the researcher increase statistical power for this study? g. What is the 95% confidence interval for this study? h. Provide an interpretation for the interval obtained in part g. i. How does the confidence interval obtained in part g compare to your statistical conclusion from part c? (i.e., Where does the value expected by the null hypothesis fall in the confidence interval and how does this support or not support your decision to reject or not reject the null hypothesis?)5. Questions for #5: a. Explain what Type I and Type II errors are. b. How can a researcher reduce the chance of committing a Type I error? c. How can a researcher reduce the chance of making a Type II error? d. What affect does changing the probability of committing one type of error have on making the other type of error? e. Explain what statistical power is. f. What are the effects of changing the probability of committing both Type I and Type II errors on the likelihood of rejecting the null hypothesis?6. (Changed to Conf Intrvl) A health advocacy group conducted a study to determine if the nicotine content of a particular brand of cigarettes was equal to the advertised amount. The cigarette brand advertised that the average nicotine content per cigarette was 1.4 milligrams. The advocacy group randomly sampled 24 cigarettes. The nicotine level for each of the sampled cigarettes is given below. Nicotine mg. Nicotine mg.1.8 1.91.1 1.61.2 1.91.2 1.91.0 2.02.0 1.61.7 1.12.0 1.82.3 1.91.4 1.40.9 1.82.4 1.5 a. Using Excel, obtain the 95% confidence interval. b. Provide an interpretation of the interval obtained in part A. c. Does the sample support the claim that the average cigarette contains 1.4 milligrams of