MATH1P98 - Assignment #4 - Section #4 Due: Monday, November 28 @ 11:59 pm Students are expected to complete all questions on the assignment. However, only a subset of questions will be considered for marking. Marks will be deducted for incomplete assignments. Assignment submissions must be neat, legible, written on one side of the page only, and questions must be submitted in order. A cover page must be attached to the front of the assignment (see sample cover page on Sakai). Staple all pages on the top left corner. Please submit answers to the following questions to your assignment drop box by 11:59pm of the due date. The text is Introduction to Probability & Statistics (3rd Edition), by Mendenhall, et. al. For each test of hypothesis, follow these steps to answer the question. i) Write the null and alternate hypothesis. ii) Write the formula for the test statistic and carry out the calculations by hand. iii) Find the p-value or critical value as indicated in the question. iv) What is the decision (i.e. to reject or fail to reject the null hypothesis)? v) What is the final conclusion that addresses the original question? 1. To determine if chocolate milk was effective as a carbohydrate replacement drink, 9 cyclists performed an intense workout followed by a drink and a rest period. At the end of the rest period each cyclist did an endurance trial in which they exercised until exhausted and the time to exhaustion, in minutes, was recorded. Each cyclist completed the entire regimen on two different days. One day the drink provided was chocolate milk and the other day the drink provided was a carbohydrate replacement drink. The data are Cyclist Chocolate milk Carbohydrate Replacement 1 2 3 4 5 6 7 8 9 24.85 50.09 38.30 26.11 36.54 26.14 36.13 47.35 35.08 10.02 29.96 37.40 15.52 9.11 21.58 31.23 22.04 17.02 a) Is there evidence that the mean time to exhaustion is greater after chocolate milk that after carbohydrate replacement drinks? Test at a 5% level of significance; find critical value(s). b) Preform this test on Excel and print your output. Circle the value of the test statistic and the p-value for this test. 1 2. Researchers investigated how the shape of a bowl affect how much ice cream people tend to scoop when serving themselves. At an \"ice cream social\" people were randomly given either a large circular bowl or a large square bowl. Both bowls hold the same amount when filled to capacity. They were then invited to scoop as much ice cream as they liked. a) Did the bowl shape change the selected portion size? Use a 5% level of significance and critical value(s). Here are the summaries Circular bowl n 26 x 5.07oz s 1.84oz Square bowl 22 6.58oz 2.91oz b) Use the same data to find the 90% confidence interval on the difference of means. c) Based on the confidence interval can one conclude that the bowl shape changed the selected portion size? 3. A survey asked respondents how they felt about this statement. \"I try to avoid eating fast foods.\" The random sample of 800 included 411 people 35 years old or younger, and of those 197 agreed with the statement. Of the 389 people over 35 years old, 246 agreed with the statement. At the 5% level is there evidence that the percentage of people avoiding fast food is different in the two age groups? Find the p-value. 4. Students entering a certain university have historically selected the following programs Progam Business Education Engineering Liberal Arts Science % of students 10% 20% 30% 25% 10% Data obtained for the most recent class show that 730 students selected business, 1050 selected Education, 1500 selected engineering, 1240 chose liberal arts, and 470 chose science. At the 10% level is there evidence that the historical percentages have changed? Use critical value(s). 5. A bath soap manufacturing process is designed to produce a mean of 120 bars of soap per batch. A sample of 10 batches show the following numbers of bars of soap: 108, 118, 120, 122, 119, 113, 124, 122, 122, 120, 123 At the 1% level test if the production process meets the standard output of 120 bars per batch. Use critical value(s). 2 6. A study asked students to report their height and then compare to the actual measured height. Assume that the paired sample data are simple random samples and the differences have a distribution that is approximately normal. 68 Reported Height Measured Height 67.9 71 69.9 63 64.9 70 68.3 71 70.3 60 65 60.6 64.5 64 54 67 55.6 63 74.2 66 72 65 70.8 a) State the null and alternative hypotheses. b) Use EXCEL to construct a 99% confidence interval estimate of the difference of means between reported heights and measured heights. Attach your printout to this question, where the reported height is column A, measured height in column B, and the difference in column C. i) Open Excel and click DATA on the ribbon of the Excel. ii) Click Data Analysis. If Data Analysis is not available, please follow the instructions in Assignment 1. iii) Select Descriptive Statistics and click OK. iv) Enter the range of the heights including the label (A1:A13). v) Select Labels in First Row. vi) Select Summary statistics. vii) Select Confidence Level for Mean and type in 99 and click OK. Calculate and write down the 99% confidence interval by hand based on the result you get from the Excel (keep four decimal places in your final answer). c) Interpret the resulting confidence interval. 3