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One sample hypothesis testing homework1. The Los Angeles County Metropolitan Transportation Authority has set a bus mechanical reliability goal of 3,900 bus miles. Bus mechanical reliability is measured specifically as the number of bus miles between mechanical road calls. Suppose a sample of 100 buses resulted in a sample mean of 3,975 bus miles and a sample standard deviation of 275 bus miles. ?ANSWER THIS –Is there evidence that the population mean bus miles is more than 3,900 bus miles ? (use a 0.05 level of significance)USE CRITICAL VALUE METHOD to solve2. You are a manager of a restaurant that delivers pizza to college dormitory rooms. You have just changed your delivery process in an effort to reduce the mean time between the order and the completion of delivery from the current 25 minutes. A sample of 36 orders using the new delivery process yields a sample mean of 22.4 minutes and a sample standard deviation of 6 minutes.Answer this — Using the six-step critical value approach, at the 0.05 level of significance, is there evidence that the population mean delivery time has been reduced below the previous population mean value of 25 minutes?( Use critical value method to solve)The worldwide market share for the mozilla fire fox web browser was 20.3 % in a recent month. (data extracted from netmarketshare.com) Suppose that you decide to select a sample of 100 students at your university and you find that 25 use the Mozilla Firefox web browser.Answer thisUse the five-step p-value approach to try to determine whether there is evidence that the market share for the Mozilla Firefox web browser at your university is greater than the worldwide market share of 20.3% ?(Use the 0.05 level of significance.)Suppose that the sample size is n=400, and you find that 25% of the sample of students at your university (100 out of 400) use the Mozilla Firefox web browser. Use the five-step p-value approach to try to determine whether there is evidence that the market share for the Mozilla Firefox web browser at your university is greater than the worldwide market share of 20.3%. (Use the 0.05 level of significance)Use critical value method for these too.3. A manufacturing company produces electrical insulators. If the insulators break when in use, a short circuit is likely to occur. To test the strength of the insulators, destructive testing is carried out to determine how much force is required to break the insulators. Force is measured by observing the number of pounds of force applied to the insulator before it breaks. The following data force are from 30 insulators subjected to this testing.1,870 1,728 1,656 1,610 1,634 1,784 1,522 1,696 1,592 1,6621,866 1,764 1,734 1,662 1,734 1,774 1,550 1,756 1,762 1,8661,820 1,744 1,788 1,688 1,810 1,752 1,680 1,810 1,652 1,736Answer this – At the 0.05 level of significance, is there evidence that the population mean force required to break the insulator is greater than 1,500 pounds.Use P Value Method.ANOVA And Chi Square Proportion HomeworkA manufacturer of pens has hired an advertising agency to develop an advertising campaign for the upcoming holiday season. To prepare for this project, the research director decides to initiate a study of the effect of advertising on product perception. An experiment is designed to compare five different advertisements. Advertisement A greatly undersells the pen’s characteristics. Advertisement B slightly undersells the pen’s characteristics. Advertisement C slightly oversells the pen’s characteristics. Advertisement D greatly oversells the pen’s characteristics. Advertisement E attempts to correctly state the pen’s characteristics. A sample of 30 adult respondents, taken from a larger focus group, is randomly assigned to the five advertisements ( so that there are 6 respondents to each advertisement.)After reading the advertisement and developing a sense of “product expectation”, all respondents unknowingly receive the same pen to evaluate. The respondents are permitted to test the pen and the plausibility of the advertising copy. The respondents are then asked to rate the pen from 1 to 7 (lowest to highest) on the product characteristic scales of appearance, durability, and writing performance. The combined scores of three ratings (appearance, durability, and writing performance) for the 30 respondents, stored in Pen, are as follows:A B C D E15 16 8 5 1218 17 7 6 1917 21 10 13 1819 16 15 11 1219 19 14 9 1720 17 14 10 14Answer this -At the 0.05 level of significance, is there evidence of a difference in the mean rating of the pens following exposure to five advertisements?If appropriate, determine which advertisements differ in mean ratings.2. A sporting goods manufacturing company wanted to compare the distance traveled by golf balls produced using four different designs. Ten balls were manufactured with each design and were brought to the local golf course for the club professional to test. The order in which the balls were hit with the same club from the first tee was randomized so that the pro did not know which type of ball was being hit. All 40 balls were hit in a short period of time, during which the environmental conditions were essentially the same. The results (distance traveled in yards) for the four designs are stored in Golfball and shown in the followingDesign 1 Design 2 Design 3 Design 4206.32 217.08 226.77 230.55207.94 221.43 224.79 227.95206.19 218.04 229.75 231.84204.45 224.13 228.51 224.87209.65 211.82 221.44 229.49203.81 213.90 223.85 231.10206.75 221.28 223.97 221.53205.68 229.43 234.30 235.45204.49 213.54 219.50 228.35210.86 214.51 233.00 225.09Questions:A)At the 0.05 level of significance, is there evidence of a difference in the mean distance traveled by the golf balls with the different designs?B) If the results in (a) indicate that it is appropriate to do so, use the Turkey-Kramer procedure to determine which designs differ in mean distances?3. Do workers prefer to buy lunch rather than pack their own lunch? A survey of employed Americans found that 75% of the 18 to 24 year olds, 77% of the 25 to 34 year olds, 72% of the 35 to 44 year olds, 58% of the 45 to 54 year olds, 57% of the 54 to 64 year olds, and 55% of the 65 + year olds buy lunch throughout the work week. (Data extracted from bit.ly/z99CeN.) Suppose the survey was based on 200 employed American in each of 6 age groups: 18 to 24, 25 to 34, 35 to 44, 45 to 54, 55 to 64 and 65+Questions:a: At the 0.05 level of significance, is there evidence of a difference among the age groups in the preference for buying lunch?b: Determine the p-value in (a) and interpret its meaning.4. Social media users use a variety of devices to access social networking; mobile phones are increasingly popular. However, is there a difference in the various age groups in the proportion of social media users who use their mobile phone to access social networking? A study showed the following results for the different age groups.USE MOBILE PHONE TO ACCESS SOCIAL NETWORKING? —-AGE 18-34 35-64 65+YES 59% 36% 13% NO 41% 64% 87%Assume that 200 social media users for each age group were surveyed.A: At the 0.05 level of significance, is there evidence of a difference among the age groups with respect to use of mobile phone for accessing social networking?B: Determine the p-value in (a) and interpret its meaning.5. Who uses a cellphone while watching TV? The Pew Research Center’s Internet and American Life Project measured the prevalence of multiscreen viewing experiences by asking American adults who are cellphone owners whether they had used their phone to engage in several activities while watching TV. The study reported that 171 of 316 (54%) of urban American cell-phone owners sampled, and 516 of 993 (52%) of suburban American cellphone owners sampled , 251 of 557 (45%) of rural American cellphone owners used their phone to engage in several activities while watching TV, (Data Extracted from “The rise of the connection viewer”. Pew Research Center’s Internet & American Life Project, July 17, 2012.)Questions:A: Is there evidence of a significant difference among the urban, suburban and rural American cellphone owners with the respect to the proportion who use their phone to engage in several activities while watching TV?B: Determine the p-value and interpret its meaning.
