Homework answers / question archive / Name ______________________ Business Statistics Free Response Questions #7: for Chapter 11 Worth 10 points

Name ______________________ Business Statistics Free Response Questions #7: for Chapter 11 Worth 10 points

Statistics

Share With

Name ______________________ Business Statistics Free Response Questions #7: for Chapter 11 Worth 10 points. You should be using the t-score on this assignment. Not the z-score, since population standard deviation, s, is unknown. Directions: You can either type out answers to these questions then submit a word document or pdf (please no GoogleDoc sharing links or Apple pages files) or you can write out your answer by hand and take a photo (try to avoid HEIC image format, please) or scan the sheet of paper. PLEASE make sure you hand in something that is aligned correctly (not sideways) and clear enough for me to read. 1. A random sample of 28 purchases showed the following amounts (in $). The mean was $45.26 and the standard deviation was $20.67. (you could verify this if you want to, but it is not required). a) What is the standard error of the mean? Show the calculation. b) How would the standard error change if the sample size had been 7 instead of 28? (Assume that the sample standard deviation did not change.) Show work or justify your answer. 2. For the price of E-85 gasoline from a random sample of 25 gas stations in a region gives the following statistics: ??? = $4.79 and s = $0.33. Give the StatCrunch output for this. **Make sure you provide images or screenshots of your StatCrunch output, you will lose points if you don’t. a) Find a 90% confidence interval for the mean price of E-85 gasoline in that region. b) Find the 95% confidence interval for the mean. c) If we had the same statistics from a sample of 50 stations, what would the 90% confidence interval be now? 3. What are the chances your flight will leave on time? The U.S. Bureau of Transportation Statistics of the Department of Transportation publishes information about airline performance. Here are summary statistics for the percentage of flights departing on time each month from July 2004 through July 2019: n = 251 ??? = 75.65 s = 3.91 a) Find a 95% confidence interval for the mean percentage of flights that depart on time. Give the StatCrunch output for this. **Make sure you provide images or screenshots of your StatCrunch output, you will lose points if you don’t b) Interpret this interval for a traveler planning to fly. 4. The Major League Baseball (MLB) sets manufacturing standards for baseballs. For example, the weight of the baseball needs to be on average 145 grams. In other words, if it is different than 145 grams, MLB will reject the set of baseballs. Suppose a manufacturer introduces a new kind of baseball and provides a randomly selected sample of them for testing. Based on the mean weight in the sample, the MLB comes up with a P-value of 0.25. Explain in this context what the 25% represents. 5. A company with a large fleet of cars hopes to keep gasoline costs down and sets a goal of attaining a fleet average of more than 35 miles per gallon. To see if the goal is being met, they check the gasoline usage for 100 company trips chosen at random, finding a mean of 37.2 mpg and a standard deviation of 3.5 mpg. Is this strong evidence that they have failed to attain their fuel economy goal? Let α = 0.05 for this. Make sure you show work and justify your answers. Give the StatCrunch output for this. **Make sure you provide images or screenshots of your StatCrunch output, you will lose points if you don’t a) Write appropriate hypotheses. b) Are the necessary assumptions to perform inference satisfied? c) Test the hypothesis and find the test statistic and P-value. d) State your conclusion in the context of the original goal