26 Jul IS THERE STATISTICAL SUPPORT FOR THE MANUFACTURERS CLAIM?
Exercise ProblemsFor this assignment complete the exercises below. Show enough of your work so that your instructor can follow your logic.#1 (Pg 417) The file P09_01.xlsx contains a random sample of 100 lightbulb lifetimes. The company that produces these lightbulbs wants to know whether it can claim that its lightbulbs typically last more than 1000 burning hours.a. Identify the null and alternative hypotheses for this situation.b. Can this lightbulb manufacturer claim that its lightbulbs typically last more than 1000 hours at the 5% significance level? What about at the 1% significance level? Explain your answers.#2 (Pg 417) A manufacturer is interested in determining whether it can claim that the boxes of detergent it sells contain on average more than 500 grams of detergent. The firm selects a random sample of 100 boxes and records the amount of detergent (in grams) in each box. The data are provided in the file P09_02.xlsx.a. Identify the null and alternative hypotheses for this situation.b. Is there statistical support for the manufacturers claim? Explain. #9 (Pg 435) In the past 60% of all undergraduate students enrolled at State University earned their degrees within four years of matriculation. A random sample of 95 students from the class that matriculated in the fall of 2008 was recently selected to test whether there has been a change in the proportion of students who graduate within four years. Administrators found that 40 of these 95 students graduated in the spring of 2012 (i.e. four academic years after matriculation).a. Given the sample outcome find a 95% confidence interval for the relevant population proportion. Does this interval estimate suggest that there has been a change in the proportion of students who graduate within four years? Why or why not?b. Suppose now that State University administrators want to test the claim made by faculty that the proportion of students who graduate within four years at State University has fallen below the historical value of 60% this year. Use this sample proportion to test their claim. Report a p-value and interpret it. #12 (Pg 436) A market research consultant hired by a leading softdrink company wants to determine the proportion of consumers who favor its low-calorie drink over the leading competitors low-calorie drink in a particular urban location. A random sample of 250 consumers from the market under investigation is provided in the file P08_18.xlsx. a. Find a 95% confidence interval for the proportion of all consumers in this market who prefer this companys drink over the competitors. What does this confidence interval tell us?b. Does the confidence interval in part a support the claim made by one of the companys marketing managers that more than half of the consumers in this urban location favor its drink over the competitors? Explain your answer.c. Comment on the sample size used in this study. Specifically is the sample unnecessarily large? Is it too small? Explain your reasoning. #47 (Pg 450) The file P08_49.xlsx contains data on 400 orders placed to ElecMart company over a period of several months. For each order the file lists the time of day the type of credit card used the region of the country where the customer resides and others. (This is the same data set used in Example 3.4 of Chapter 3.) Use a chi-square test for independence to see whether the following variables are independent. If the variables appear to be related discuss the form of dependence you see.a. Time and Regionb. Region and Buy Categoryc. Gender and Card Type
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