4 points Chapter 6 Answer the following questions on a separate piece of paper. 1. Describe two benefits of using z-scores? 2. Suppose a student finds out that her score on her math test was z = +1.3. How would you explain this score to the student? 3. The average commute to work in a large city is 23 minutes. What is the z-score equivalent for this average? Use the following description to answer question 4. It used to be that American cars were built larger, heavier and with bigger motors compared to cars built by Japanese car maker. Consequently, Japanese cars typically got better gas mileage compared to American cars. To find out if this trend has continued, a consumer advocate researcher randomly selected a group of 2002 model American cars and a group of 2002 model Japanese cars and measured the miles per gallon for each car. The data collected are presented below: American cars: 23 28 18 22 23 16 32 25 22 23 13 15 15 18 Japanese cars: 21 38 17 28 21 33 28 30 22 28 21 18 20 22 4. Using Excel and/or the z-table from your text book, answer the following questions using the data above: a. What are the z scores for the original scores from both car manufacturers’ data on the previous page? b. Provide an interpretation for the first three z scores obtained for the American car makers AND the last three z scores obtained for the Japanese car makers. c. Without do any calculations, what is the mean and standard deviation of the z scores obtained? d. What percentage of z scores are expected to fall in the range of –1.5 to +2.5? e. What percentage of z scores are expected to fall at or below +2.8? f. What percentage of z scores are expected to fall at or below -.50? g. What percentage of z scores are expected to fall at or above +1.7? h. What percentage of z scores are expected to fall in the range of –2.3 to –1.3? i. What percentage of z scores are expected to fall in the range of +1.2 to +3.1?5. (A) Describe what a sampling distribution is and what it contains. (B) What is the mean and SD of any sampling distribution equal to? (Hint: a specific value is not the answer). 6. What happens to the value of the estimated standard error as the shape of a sampling distribution becomes (A) flatter and (B) more peaked? Explain. 7. Provide a general definition/description of what the estimated standard error of the mean (SEM) is. 8. In the long run we can expect the population mean or proportion/percentage to occur. Explain what is mean by the phrase in the long run? 9. A sample of 16 students took the American College Testing (ACT) Program composite college entrance exam and were found to have a mean of 18 and a sample SD equal to 6. (A) What is the value of the estimated standard error of the mean (SEM)? (B) Provide an interpretation of the value obtained in part A. (C) Describe how the researcher might reduce the size of the SEM if the study is repeated. 10. A marketing researcher conducted a survey of 25 shoppers randomly selected at the local mall and found that the average shopper intended to spend an average of $32.00 during their visit to the mall. The researcher also found that, on the average, the sample of shoppers surveyed spent $7.00 different than the mean of $32.00. (A) What is the value of the estimated standard error of the mean (SEM)? (B) Provide an interpretation of the value obtained in part A. (C) Based on the sample surveyed, what is the estimated average amount spent at the mall for all