Practical Business Analysis sample essay
1. Re-do all problems in Practice Problem Set 1. 2. Dollar Car Rental Co. was originally named Dollar a Day Car Rental because they charged $1.00 per day to rent a car, plus a charge per mile driven. Many customers complained that the odometers on Dollar’s cars recorded more miles than were actually driven. To evaluate these complaints you take a random sample of 6 Dollar’s cars, drive them on a carefully measured 100-mile course, and record the miles driven as registered by the odometers. The results are 100, 105, 109, 102, 107, and 101, with the sample standard deviation around 3.578. a. Using these sample results, construct a 95% confidence interval for the population mean miles recorded by all Dollar cars for a 100-mile trip. b. As a legal consultant hired by the group of the customers who complained about the odometers, do you have enough evidence to support your clients’ claim? State your hypotheses (H0 vs. Ha), rejection region and both statistical and substantive conclusions.
3. The grades on the final examination given in a large organic chemistry class are normally distributed with a mean of 72 and a standard deviation of 8. The instructor of this class wants to assign an “A” grade to the top 10% of the scores, a “B” grade to the next 10% of the scores, a “C” grade to the next 10% of the scores, a “D” grade to the next 10% of the scores, and an “F” grade to all scores below the 60th percentile of this distribution. For each possible letter grade, find the lowest acceptable score within the established range.
4. The weekly demand for General Motors car sales follows a normal distribution with a mean of 40,000 cars and a standard deviation of 12,000 cars.
a. There is a 5% chance that GM will sell more than what number of cars during the next week? b. What is the probability that GM will sell between 20 and 23 thousand cars during the next week?
5. A department store is interested in the average balance that is carried on its store’s credit card. A sample of 40 accounts reveals an average balance of $1,250 and a standard deviation of $350.
a. Find a 95% confidence interval for the mean account balance on this store’s credit card. b. What sample size would be needed to ensure that we could estimate the true mean account balance and have only 5 chances in 100 of being off by more than $100?
6. A marketing research consultant hired by Coca-Cola is interested in determining the proportion of customers who favor Coke over other soft drinks. A random sample of 400 consumers was selected from the market under investigation and showed that 53% favored Coca-Cola over other brands.
a. Compute a 95% confidence interval for the true proportion of people who favor Coke. Do the results of this poll convince you that a majority of people favor Coke? b. Suppose 2,000 (not 400) people were polled and 53% favored Coke. Would you now be convinced that a majority of people favor Coke?
7. BatCo (The Battery Company) produces your typical consumer battery. The company claims that their batteries last at least 100 hours, on average. Your experience with the BatCo battery has been somewhat different, so you decide to conduct a test to see if the companies claim is true. You believe that the mean life is actually less than the 100 hours BatCo claims. You decide to collect data on the average battery life (in hours) of a random sample and the information related to the hypothesis test is presented below. Use this information to answer the following questions.
a. You believe that the mean life is actually less than 100 hours, should you conduct a one-tailed or a two-tailed hypothesis test? State your alternative hypothesis. b. If you use a 5% significance level, would you conclude that the mean life of the batteries is typically more than 100 hours? State the rejection region and calculate the test statistic. c. If you were to use a 1% significance level in this case, would you conclude that the mean life of the batteries is typically more than 100 hours? Explain your answer.
8. Q-Mart is interested in comparing customer who used it own charge card with those who use other types of credit cards. Q-Mart would like to know if customers who use the Q-Mart card spend more money per visit, on average, than customers who use some other type of credit card. They have collected information on a random sample of 38 charge customers and the data is presented below. On average, the person using a Q-Mart card spends $192.81 per visit and customers using another type of card spend $104.47 per visit. Use the information below to answer the following questions.
a. Given the information above, what is [pic] and [pic] for this comparison? Also, does this represent a one-tailed or a two-tailed test? Explain your answer. b. Using a 1% level of significance, is there sufficient evidence for Q-Mart to conclude that customers who use the Q-Mart card charge, on average, more than those who use another charge card? Explain your answer.
9. Suppose that you were asked to test H0: μ = 10 versus Ha: μ > 10 at the [pic] = 0.05 significance level and with a sample of size n = 10. Furthermore, suppose that you observed values of the sample mean and sample standard deviation and concluded that H0 be rejected. Is it true that you might fail to reject H0 if you were to observe the same values of the sample mean and standard deviation from a sample with n > 10? Why or why not?
10. Stock-market analysts are keenly interested in determining what factors influence the price of a stock. After some examination, a statistician hypothesized that a stock price (Y in $) would be affected by its quarterly dividends (X1 in $), its price/earnings ratio (X2), and the interest rate of treasury bills (X3 in %). The values of the relevant variables were observed for a period of 40 quarters. When the data were run on STATGRAPHICS PLUS, the accompanying printout was created.
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