In the year 2000, the state of Indiana began a $40-million renovation of its state fairgrounds, which included the building of a miniature golf course and a state-of-the-art livestock building. Now, Indiana officials are interested in learning what sorts of people are visiting the new attractions. In a survey done at this years state fair, it was found that, among a random sample of 78 couples at the fair with their children, 51 had visited the new miniature golf course, and among an independently chosen, random sample of 65 couples at the fair on a date (without children), 38 had visited the miniature golf course. Based on these samples, can we conclude, at the .05 level of significance, that the proportion p1 of all couples attending the fair with their children who visited the miniature golf course is different from the proportion p2 of all couples attending the fair on a date who visited the miniature golf course? Perform a two-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. 1. null 2. alternative 3. test statistic 4. value of test stat (round 3 dec) 5. p-value 6. can we conclude that the proportion of couples visiting the miniature course is different between the two groups?2) Medical researchers interested in determining the relative effectiveness of two different drug treatments on people with a chronic mental illness established two independent test groups. The first group consisted of 9 people with the illness, and the second group consisted of 14 people with the illness. The first group received treatment 1 and had a mean time until remission of 163 days, with a standard deviation of 6 days. The second group received treatment 2 and had a mean time until remission of 162 days, with a standard deviation of 9 days. Assume that the populations of times until remission for each of the two treatments are normally distributed with equal variance. Can we conclude, at the 0.1 level of significance, that the mean number of days before remission after treatment 1, 1, is greater than the mean number of days before remission after treatment 2,2?
Perform a one-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. 1. Null 2. Alternative 3. Test statistic 4. value of test statistic 5. P-value 6.can we conclude that the mean number of days before remission after treatment 1 is is greater than the mean numb of days after treatment 2?
3) At LLD Records, some of the market research of college students is done during promotions on college campuses, while other market research of college students is done through anonymous mail, phone, internet, and record store questionnaires. In all cases, for each new CD the company solicits an intent-to-purchase score from the student, with 0 being the lowest score (no intent to purchase) and 100 being the highest score (full intent to purchase).
The manager finds the following information for 145 intent-to-purchase scores for a soon-to-be-released CD: Group sample size sample mean sample var On campus 29 63.6 85.1 By mail 29 67.4 140.9 By phone 29 64.7 72.5 By internet 29 64 85.4 By store 29 60.8 50.8 The managers next step is to conduct a one-way, independent-samples ANOVA test to decide if there is a difference in the mean intent-to-purchase score for this CD depending on the method of collecting the scores. Answer the following, carrying your intermediate computations to at least three decimal places and rounding your responses to at least one decimal place. 1.What is the value of the mean square for error that would be reported in the ANOVA test? 2.What is the value of the mean square for treatments that would be reported in ANOVA test?
4) The General Social Survey is an annual survey given to a random selection of about 1500 adults in the United States. Among the many questions asked are What is the highest level of education youve completed? and If youre employed full-time, how many hours do you spend working at your job during a typical week?In a recent year, 1104 respondents answered both questions. The summary statistics are given in the chart below. (The sample data consist of the times, in hours per week, that were given by the respondents.) Group sample size sample mean sample var Less than hs 291 41.5 85.6 High school 277 42.9 118.2 Bachelors 271 43.1 103.1 Graduate 265 42.7 102.1 To decide if there are any differences in the mean hours per week worked by these different groups, we can perform a one-way, independent-samples ANOVA test. Such a test uses the statistic F= Variation between the samples/Variation within the samples For the data from the survey, F=1.45 1. Give the P-value corresponding to this value of the f statistic. (round to 3 dec) 2. From the survey data, can we conclude that at least one of the groups differs significantly from the others in mean hours worked in a typical week? Use .01 level of significance.5) The following time series data represent the quarterly amounts spent on advertising (in millions of dollars) by a large toy company (read across):
Quarter 1 Quarter 2 Quarter 3 Quarter 4 22.1 20.2 22.1 23.4 23.1 22.6 23.8 20.6 23.5 21.8 24.0 23.1 22.1 23.1 26.6 22.5 27.9 29.1 25.1 24.2 28.9 28.7 27.1 23.0 30.7 26.1 30.9 24.0 29.7 28.8 24.4 25.7 24.5 28.7 29.4 25.1 32.1 This series of data begins in Quarter 1 of 1992 (i.e.,t=1 time period corresponds to the first quarter of ). Using regression analysis, a linear trend line of the form Tt = 21.57 + .020t was fit to the data. Using this information, generate a forecast for the total yearly amount of money that will be spent on advertising in 2006.
6) The Cadet is a popular model of sport utility vehicle, known for its relatively high resale value. The bivariate data given below were taken from a sample of sixteen Cadets, each bought new two years ago and each sold used within the past month. For each Cadet in the sample, we have listed both the mileage, x (in thousands of miles), that the Cadet had on its odometer at the time it was sold used, and the price, y (in thousands of dollars), at which the Cadet was sold used.
x y mileage selling price 23.8 28.1 22.7 30.2 34.1 25.5 25.8 27 38.8 21.3 23 32.3 24.3 30.6 24.5 28 26.7 29.9 20.9 31 29.6 27.6 20.6 31.3 27.8 26.6 37.4 22.8 15.6 33.7 28 30 The least-squares regression line for these data has a slope of approximately -0.50. What is the value of the y-intercept of the least-squares regression line of these data. Round at least 2 dec places. What is the value of the sample correlation coefficient for these data. Round answer to at least 3 dec places.
7) The professor of an introductory statistics course has found something interesting: there is a small correlation between scores on his first midterm and the number of years the test-takers have spent at the university. For the 61 students taking the course, the professor found that the two variables number of years spent by the student at the university and score on the first midterm have a sample correlation coefficient r of about -0.17.Test for a significant linear relationship between the two variables by doing a hypothesis test regarding the population correlation coefficient p. (Assume that the two variables have a bivariate normal distribution.) Use the .05 level of significance, and perform a two-tailed test. 1. null 2. alternative 3. type of test statistic 4. value of test statistic (round 3 places) 5. the two critical values at .05 level of sig. 6. Based on the data, can the prof conclude that there is a significant linear relationship between the number of years and score of midterm8) The finance department of an automobile insurance company uses a multiple regression model to estimate the total number of accident claims that will be filed each month. Based on the most recent 30 months of claims data, the company has selected 4 independent variables that it believes are related to accident claims. Let B1,B2B4 denote the coefficients of the 4 variables in this model. When this data is entered into a regression software program, the error sum of squares (SSE) associated with the model is reported to be 72.16 and the corresponding regression sum of squares (SSR) is 19.63. Using a significance level of .05, can you conclude that at least one of the independent variables in the model provides useful (i.e., statistically significant) information for predicting monthly accident claims?Perform a one-tailed test. 1.null 2.alternative 3.type of test statistic 4.value of test statistic (round 2 places) 5.the p-value (round 3 places) 6. can you conclude that at least one of the independent variables provides useful info for predicting accident claims?9) Using 11 observations on each variable, a computer program generated the following multiple regression model. y = 80.5 6.291 +9.532 + 7.133If the standard errors of the coefficients of the independent variables are, respectively 2.03, 5.18, and 6.25. Can you conclude that the independent variable x2 is needed in the regression model? Let B1, B2, and B3 denote the coefficients of the 3 variables in this model, and use a two-sided hypothesis test and significance level of .01 to determine your answer 1.null 2.alternative 3.type of test stat 4.value of test stat (2 dec places) 5.two critical values at .01 level (2 dec places) 6.can you conclude that the indep variable x is needed in the regression model?10)