(Statistics class) HW using Minitab

Fill in the following table by indicating which are the correct decisions, Type I Error, and Type II Error (10 points): Ho is true Ho is false Do no reject Ho Reject Ho A manufacturer of tennis gear has developed a new racquet string that the company claims has a mean breaking strength of 12 kilograms with a standard deviation of 0.7 kilogram. Test the hypothesis that µ = 12 against the alternative that µ ≠ 12 if a random sample of 40 lines is tested and found to have a mean breaking strength of 11.5 kilograms. Use a 0.05 level of significance (15 points). The manufacturer of Vitamix Blenders claims that their blenders use an average of 62 kilowatt hours per year. If a random sample of 15 homes indicates that these blenders use an average of 75 kilowatt hours per year with a standard deviation of 12.2 kilowatt hours, does this suggest at the 0.01 level of significance that Vitamix Blenders, on average, use more than 62 kilowatt hours annually? Assume the population of kilowatt hours to be normal (15 points). A UM researcher claims that the average life span of human males can be extended by as much as 5 years when the calories in their diet are reduced by approximately 30% after the age of 40. Suppose that a random sample of 14 men is fed a normal diet and has an average life span of 76 years with a standard deviation of 3 years, while a random sample of 13 men is fed the restricted diet and has an average life span of 79 years with a standard deviation of 2 years. Test the hypothesis at the 0.01 level of significance, that the average life span of men on this restricted diet is increased by 5 years against the alternative that the increase is less than 5 years. Assume the distributions of life spans for the regular and restricted diets are approximately normal with equal variances (15 points). A builder claims that tankless hot water heaters are installed in 70% of all homes being constructed today in Miami. Would you agree with this claim if a random survey of new homes in Miami showed that 10 out of 20 had tankless hot water heaters installed. Use a 0.10 level of significance and do not use the z-distribution (15 points). Tesla claims that the life of the company’s batteries is approximately normally distributed with a standard deviation equal to 0.95 years. If a random sample of 11 of these batteries has a standard deviation of 1.5 years, do you think that σ > 1.5 years? Use a 0.05 level of significance (15 points). Given the data below, estimate the regression line, find a 95% confidence interval for both β_1 & β_0 in the regression line, and construct a 95% prediction interval for y0 when x0 = 18% (30 points): ∑_(i=1)^25▒〖x_i=409,∑_(i=1)^25▒〖y_i=322,∑_(i=1)^25▒x_i 〗 y_i=7,131,∑_(i=1)^25▒〖x_i^2=9,097,S_xx=2,405.8 ,S_yy=1,522.6,S_xy=1,863.1,x ̅=16.36〗〗 Using Minitab do the following problems: Chapter 11 - 4, 5, 7, 9, 17, 21, 24 Chapter 12 - 2, 4, 8, 12, 17, 20, 23, 25 Write up – You need to do the problems manually first with your calculators and show the results. Then you need to check your results by doing it in minitab. You want to show your results (copy and paste into your word document, don’t do a print screen) for each problem and then you need to state the regression equation and/or draw your conclusions. The assignment should be typed and no handwriting acceptable. Software Procedures Open Minitab. In the Data (i.e., worksheet) window create your columns of data for the problems. Simple Linear Regression Choose Stat  Regression  Regression Fit Best Regression Model In Response, enter C2 (or select C2). In Continuous Predictors, enter C1 (or select C1). Click Storage. Check the Residuals and Fits boxes. Click OK. Click OK (make sure the default here and elsewhere is for a “95%” confidence level). Click Results. Be sure to check Regression equation, coefficients, and analysis of variance. (You can check everything but Durbin-Watson Statistic) Click OK. Click Graphs. Under Residual Plots, click Four in one. Click OK twice. Note that two new columns should appear in the data window: C3 (RESI1) and C4 (FITS1). Print the session window results. What are your conclusions? Multiple Linear Regression: Choose Stat  Regression  Regression Fit Best Regression Model In Response, make sure your “y” is entered. In Continuous Predictors, ensure that your “x” variables are entered. Click Storage. Make sure Residuals and Fits are checked. Click OK. Click Results. Be sure to check Regression equation, coefficients, and analysis of variance. (You can check everything but Durbin-Watson Statistic) Click OK. Click Graphs. Under Residual Plots, make sure Four in one is checked. Click OK twice.