Page 1 of 14 **Excel is not acceptable for this **Part D: All work must be shown step by step in order to receive full credit Part A: Fill in the blank (1-26) 1) 2) 3) 4) 5) Given , H0: = 0, then Ha : ___________________________________ . Given H0: 0, then Ha : ___________________________________ . Given H0: 0, then Ha : ___________________________________ . A statement of what you wish to conclude goes in the ______________. A market analyst believes that more than 30% of the adults in a certain area regularly read a certain magazine. The analyst wishes to conduct a hypothesis test to see whether this belief will be supported. The appropriate statistical hypotheses are: __________________. 6) Given: H0: 50; Ha: < 50; = 0.05. A simple random sample of size 64 is drawn from a non-normally distributed population. X = 45, s2 = 256. The computed value of the test statistic is _________________, which is compared for significance with a value from the ____________________ distribution. 7) Given: H0: = 100; Ha: 100; = 0.03; computed z = 2.25, p = 0.0244. The null hypothesis should reject because __________________________________________. Page 2 of 14 Must show all your work step by step in order to receive the full credit; Excel is not allowed (54-67). 54)Given the following probabilities, find Z0 and please draw the shading the area a. P Show your work ( Z Z 0 ) =0.2090 b. 1.67 Z Z 0 ) =0.8844 P ( c. Z> Z 0 )=0.0455 P ( d. Z Z 3.02 ) =0.0009 P ( 0 e. Z> Z 0 )=0.7224 P ( f. Z Z Z 0 ) =0.1664 P ( 0 Please draw graphs Page 3 of 14 55.The random variable x has a normal distribution with mean 50 and variance 9. Find the value of X, cale is X0, such that: a) P (X x0) = 0.8413 b) P (X > X0) = 0.025 c) P (X > X0) = 0.95 d) P (41 X x0) = 0.8630 56.The random variable x has a normal distribution with - 40 and 2 = 36. Find the value of X, call it X0, such that: b) P ( X < X0 ) = 0.05 a) P ( X X0 ) = 0.10 Page 4 of 14 ) P ( X X0 ) = 0.40 57.A sample of size n = 10 is randomly selected from a normal population with 2 mean = 52 and variance = 22.5. The sample value X is calculated. a) P ( X >55 )=? c) P ( X 55 ) =? b) P ( 50 X 60 )=? Page 5 of 14 58.Consider the following data drawn from a normal distribution population: 4, 8, 12, 11, 14, 6, 12, 8, 9, 5 Construct a 90% confidence interval for the population mean. a) Mean b) Variance c) Standard deviation d) Find a 90% confidence interval for the mean . Interpret this interval Page 6 of 14 59.Please fill in the computer printout and answer the following questions (a-b). Given that =0.05 SUMMARY OUTPUT Regression Statistics Multiple R 0.9037 R Square ______ Adjusted R Square ______ Standard Error ______ Observations ______ ANOVA df SS MS F Significance F Regression 1 4.9 ______ ______ 0.03535 Residual 3 1.1 Total ______ ______ ______ Coefficients Standard Error t Stat P-value Lower95% Upper 95% Lower 95.0% Upper 95.0% Intercept -0.1 ______ -0.15746 0.88488 ______ ______ ______ ______ X1 0.7 ______ 3.65563 ______ ______ ______ ______ ______ a) Predicting Y given that X=5; confidence interval =0.05 b) Estimating mean given that X=5; confidence interval =0.05 Page 7 of 14 60.The following regression equation was obtained using the five independent variables. Given that Intercept Price Advertising =0.05 Coefficients 729.8665 -10.887 0.0465 Std. Error 169.25751 3.4952397 0.0176228 t-Stat 4.3121659 -3.1148078 2.6386297 P-value 0.0010099 0.0089406 0.0216284 F 37.56127994 Significance F 0.00000683 ANOVA Regression Residual Total df 2 12 14 Se =12.86986 SS MS 12442.8 6221.4 1987.6 165.63333 14430.4 R-sq = 0.862263 R-sq(adj) = 0.8393068 a) Write the multiple regression equation b) Interpret the multiple regression equation c) What is the standard error of estimate? Can you use this statistic to assess the model's fit? If so, how? d) Which independent variable appears to be the best predictor of sales? Explain. e) What is the number of observations used in this study? f) What is the coefficient of determination, and what does it tell you about the regression model? g) Assuming that the coefficient on Advertising has Ha: B1 > 0, what statistical decision should be made at 5% level. h) Conduct a global test of hypothesis to determine if any of the regression coefficients are not zero Page 8 of 14 61.Following is a portion of the computer output for a regression analysis relating Y = maintenance expense (dollars per month) to X = usage (hours per week) of a particular brand of computer terminal. The regression equation is: Y = 6.1092 + .8951X Predictor Constant X Analysis of Variance SOURCE Regression Error Total Coef 6.1092 0.8951 Stdev 0.9361 0.1490 DF 1 8 9 SS 1575.76 349.14 1924.90 MS 1575.76 43.64 a) Write the estimated regression equation. b) What is the number of sample in this study? c) Use a t test to determine whether monthly d) Use the estimated regression equation to predict maintenance expense is related to usage at the .05 level of significance. monthly maintenance expense for any terminal that is used 25 hours per week. Page 9 of 14 62. A metropolitan bus system sampler's rider counts on one of its express commuter routes for a week. Use the following data to establish whether the rider ship is evenly balanced by day of the week. Let = 0.05. Day Rider Count Monday 10 Tuesday 34 a) What is you hypothesis testing b) What is your 2 ? c) Is the 2 value significant at the 5 % level of significance? d) Write the conclusion for this question. Wednesday 21 Thursday 57 Friday 44 Page 10 of 14 63. A survey at a ballpark shows this selection of snacks purchased. At 10% significance level, is the snack chosen independent of the gender of the consumer? Snack Gender Male Female Hot Dog 12 13 a) What is your hypothesis testing b) What is your 2 ? c) Is the 2 value significant at the 10 % level of significance? d) Write the conclusion for this question. Peanuts 21 8 Popcorn 19 25 Page 11 of 14 64. Consider the following hypothesis test Ho: 10 Ha: < 10 A sample of 50 provides a sample mean of 9.46 and sample variance of 4. a ) At 5% should the null be rejected? c) What is the p-value? b ) Compute the value of the test statistic 2 d ) What is your conclusion? 65. The calculations undertaken to estimate the model: y = 0 + 1X1 + 2X2 + 50 observations of the variables Y, X1 and X2 produced the following summations: SST = 321.2 SSE = 259.0 a) Find SSR c) Calculate the coefficient of determination b) Calculate the standard error of the estimate. Page 12 of 14 66. Use this data in the table to answer Questions A, B, C, D and E below: Month 1 2 3 4 5 Advertising Expenditure (X) -2 -1 0 1 2 Sales Revenue (Y) 4 3 3 1 -1 a) Compute the sample regression coefficents b0 and b1 b) Compute the estimate variance of the regression c) Compute the estimated variance of b1 c) Compute the standard error of the regression d) Compute the standard error of b1 Page 13 of 14 67. For n = 6 data points, the following quantities have been calculated: xy = 400 x = 40 y = 76 x2 = 346 y2 = 1160 a)Find b1 b)Find b0 c)Write the equation d)Find r e)Find SST f)Find g) Construct the 95% confidence interval for the mean of y when x = 7 h) Construct the 95% confidence interval for the individual value of y when x = 9 2 Se Page 14 of 14