1. State the null and alternative hypotheses for each of the following situations (each 0.5 point): a. A guideline for a telemarketing company states the mean time for completed calls should not exceed four minutes. Each month the company's owner selects a random sample of call logs to determine whether the call-time goal is being met. b. General Crunch Corporation distributes Mini-Oats Cereal in boxes with a stated weight of 18 ounces. To determine whether the filling machine should be adjusted, the quality control manager at General Crunch selects and weighs a random sample of boxes one day each week. c. A manufacturer of trash bags claims its new trash bag can hold or support at least 50 pounds, on average. A random sample of new trash bags is selected and tested. d. Your friend claims the battery life of an ipad mini is less than 5 hrs, on average. You survey a random sample of friends who own an ipad mini to test your friend's claim. 2. Environmental Protection Agency (EPA) regulations say that soil used in play areas should not have lead levels that exceed a 350 parts per million (ppm). Before beginning construction at a new site, an agent will take a sample of soil and run a significance test on the mean lead level in the soil. If the mean lead level in the sample is significantly higher than 350 ppm, then the soil is deemed unsafe and construction cannot continue. Here are the hypotheses for this test: Ho: p 350 ppm Define the Type II error in this problem and explain its consequence. (1 point) 3. A large university is curious if they should build another cafeteria. They plan to survey a sample of their students to see if there is strong evidence that the proportion interested in a meal plan is higher than 40%, in which case they will consider building a new cafeteria. Let p represent the proportion of students interested in a meal plan. Here are the hypotheses they'll use: Ho: p = 0.40 Ha: p > 0.40 Define the Type I error and explain its consequence in the problem. (1 point)4. A random sample contains 30 observations. Determine the p-VALUE for each value of the calculated test statistic below and state your decision about the null hypothesis in each part by comparing the p-VALUE to a = 0.10 Ho: H = 38 Ha: u # 38 a. t = 1.311 (0.5 point) b. t = 2.045 (0.5 point) c. t= -1.4421 (0.5 point) 5. The alcohol content of wine depends on numerous factors, including the grape variety, how the wine is produced, and the weather. Suds Bacchus, noted wine enthusiast, collected data on the alcohol content (percent by volume) of wine for one grape variety produced in 2012 by a random sample of 20 winemakers in Italy. Suds used the Microsoft Excel Descriptive Statistics function to produce the following table to summarize the alcohol content of the wines in the sample: ALCOHOL % Mean 13.093 Standard Error 0.1143 Median 13.165 Mode 13.17 Standard Deviation 0.5111 Sample Variance 0.2612 Kurtosis -0.8385 Skewness -0.1747 Range 1.68 Minimum 12.2 Maximum 13.88 Sum 261.86 Count 20 Use the Descriptive Statistics output to test whether the mean alcohol content of all wines produced for that grape in 2012 in Italy was greater than 12.75% at the 0.10 level of significance. a. State the null and alternative hypotheses associated with the test. ('/2 point) b. What is the calculated value of the associated test statistic? (0.25 point) c. What is the critical value of the associated test statistic? (0.25 point) d. State your decision about the null hypothesis by comparing the calculated and critical values of the test statistic (Parts b and c). ('/2 point)e. State your conclusion ( meaning, describe what the decision means in this problem). (/2 point) 6. A random sample of 330 cases or observations reveals 190 successes. Test whether the population proportion of successes is greater than 0.50 (let a = 0.02). a. State the null and alternative hypotheses associated with the test. (0.5 point) b. What is the critical value of the associated test statistic? (0.25 point) c. What is the calculated value of the associated test statistic? (0.25 point) d. What is the p-value of the associated test statistic? (0.5 point) e. State your decision about the null hypothesis by comparing the critical and calculated values of the test statistic or by comparing p-value with a [Parts b), c), and d)] (0.5 point)
