To appeal to customers that are trying to cut calories, a company that sells orange juice decides to market a premium juice, "OJ 50", which has half as many calories as traditional orange juice. The ingredient listing reveals that OJ 50 consists of 50% water and 50% orange juice. Besides misleading customers to pay more for less orange juice, a consumer group believes that the product actually consists of greater than 50% water. To test this claim they select a random sample of 50 bottles of their 52-ounce ÕJ 50 and detemine the proportion of each that is water. They decide to use a=0.05. (a) State appropriate hypotheses for performing a significance test. (b) Describe what a Type I error would be in this context. (c) What is the probability of making a Type I error when perfoming this test? (4) Describe what a Type II error would be in this context. (e) Which error (Type I or Type II) is more serious for the company that produces OJ 50? Explain.

A researcher working at Hershey's is interested in comparing two new chocolate bars: Chocolate Bar A versus Chocolate Bar B. The researcher expects the bars to be different in how much customers will eat per month. The researcher believes the more candy bars someone eats will indicate which one tastes the best. An experiment is designed to compare the two new bars. The number of candy bars eaten by one group of 8 people in a month is measured with Candy Bar A and then the number of candy bars eaten in the same month by another group of 8 participants is measured with Candy Bar B. Use the data below to determine if there is a difference in the consumption of the two candy bars. Candy Bar A Candy Bar B Number of Candy Bars eaten within a month 10, 30, 5, 35, 60, 3, 20, 30, 28, 27, 26, 27, 17, 25 12, 20 With a = .05, determine the critical value of t* that needs to be employed here. The value of the appropriate of t* is: 2.145 O 1.717 2.064 2.819 2.074 O The correct answer is not listed.

A consumer-testing agency wants to evaluate the claim made by a manufacturer of discount tires. The manufacturer claims that its tires can be driven at least 35,000 miles before wearing out. To determine the average number of miles that can be obtained from the manufacturer’s tires, the agency randomly selects 60 tires from the manufacturer’s warehouse and places the tires on 15 cars driven by test drivers on a 2-mile oval track. The number of miles driven (in thousands of miles) until the tires are determined to be worn out is given in the following table. Car Miles Driven 1 25 2 27 3 35 4 42 5 28 6 37 7 40 8 31 9 29 10 33 11 30 12 26 13 31 14 28 15 30 Average 31.47 Standard  5.04 Agency would like to know if the manufacturer’s claim is false.  Carryout an appropriate hypothesis test (use 1% significance level). Check any assumptions you think are relevant before doing the text.

An interdepartmental task force is being formed to investigate an increase in violent crimes. 1/5 of the task force will be police officers from the local precinct. 1/4 will be ATF agents, and the remaining 22 will be from the FBI. How many people are participating in the task force?

Based on a survey, more than  1  in  4  American children have cholesterol levels of  180  milligrams or higher.

A sample of ore is found to be 0.0022% gold and 0.059% silver. What is the percentage of matter in the ore that is neither gold or silver?