Math 2311 Written Homework 11 (Sections 8.1 - 8.2) Name:__________________________________ PeopleSoft ID:_______________ Instructions: Homework will NOT be accepted through email or in person. Homework must be submitted through CourseWare BEFORE the deadline. Print out this file and complete the problems. Use blue or black ink or a dark pencil. Write your solutions in the space provided. You must show all work for full credit. Submit this assignment at http://www.casa.uh.edu under "Assignments" and choose hw11. 1. Section 8.1, Problem 8 A company claims that the mean weight per apple they ship is 120 grams with a standard deviation of 12 grams. Data generated from a sample of 49 apples randomly selected from a shipment indicated a mean weight of 122.5 grams per apple. Is there sufficient evidence to reject the company's claim? (use0.05) 2. Section 8.1, Problem 11 Bottles of a popular cola drink are supposed to contain 300 ml of cola. There is some variation from bottle to bottle because the filling machinery is not perfectly precise. The distribution of the contents is normal with standard deviation of 3 ml. A student who suspects that the bottler is under-filling measures the contents of six bottles. The results are: Is this convincing evidence that the mean contents of cola bottles is less than the advertised 300 ml? Test at the 5% significance level. 299.4 297.7 301.0 298.9 300.2 297.0 3. Section 8.1, Problem 14 You would like to know how effective a diet program is at helping people lose weight. 18 over-weight people are randomly selected to participate in the program. They are weighed before and after the program and the results are listed below. Do these results give evidence that the diet program is effective at the 1% significance level? Participant 1 2 3 4 5 6 Before 185 220 190 158 227 211 After 175 215 195 155 230 207 Participant 7 8 9 10 11 12 Before 260 156 201 300 180 270 After 258 159 201 290 172 272 Participant 13 14 15 16 17 18 Before 293 183 205 151 291 166 After 290 185 200 146 287 166 4. Section 8.2, Problem 5 A candidate for mayor claims that under the present administration, 45% of complaints about city government are not addressed within two weeks of submission. A watchdog citizens' group claims that the actual percentage is less than 45%. The group conducted a SRS of 100 complaints submitted to the city government in the last year and determined that only 40% of the complaints were not addressed within two weeks of submission. Do these data provide sufficient evidence to reject the candidate's claim at the 5% significance level? 5. Section 8.2, Problem 7 Mars Inc. claims that they produce M&Ms with the following distributions: Brown 30% Red 20% Yellow 20% Orange 10% Green 10% Blue 10% A bag of M&Ms was randomly selected from the grocery store shelf, and the color counts were: Brown 14 Red 14 Yellow 5 Orange 7 Green 6 Blue 10 Conduct an appropriate test of the manufacturer's claim for the proportion of brown M&Ms. 6. Section 8.2, Problem 10 It is fourth down and a yard to go for a first down in an important football game. The football coach must decide whether to go for the first down or punt the ball away. The null hypothesis is that the team will not get the first down if they go for it. The coach will make a Type I error by doing what