Math 1342 Test 5 Question 1 25 points A random sample of data was obtained 47 80 68 29 95 67 70 35 54 13 15 28 79 49 21 64 40 52 40 44 60 80 79 78 57 80 102 90 48 40 80 16 50 a. Use StatCrunch, Excel or Hand Calculate to generate Summary Statistics b. Use StatCrunch, Excel or Hand Calculate to create a Box Plot c. Based on your summary statistics, IQR and Box Plot does the Data Contain Outliers? d. Use StatCrunch, Excel or Hand Calculate to generate a 95% confidence interval for the mean e. Use StatCrunch, Excel or Hand Calculate and Hypothesis Testing (P-Value Method) for the claim that the mean is different from 50 at a 95% confidence level. Question 2 25 points A random sample of data was obtained 23 61 45 12 15 6 26 40 21 27 32 38 44 65 22 5 15 13 45 40 a. Use StatCrunch, Excel or Hand Calculate to generate Summary Statistics b. Use StatCrunch, Excel or Hand Calculate to generate a Stem and Leaf Plot c. Use StatCrunch, Excel or Hand Calculate to generate a 90% confidence interval for the mean d. Use StatCrunch, Excel or Hand Calculate to generate a 95% confidence interval for the variance e. Use StatCrunch, Excel or Hand Calculate and Hypothesis Testing (P-Value Method) for the claim that the mean is less than 35 at a 90% confidence level. Question 3 25 points A random sample of data was obtained 10.1 9.8 9.8 9.4 9.0 9.8 9.6 9.1 9.9 10.0 8.7 9.6 10.0 9.4 a. Use StatCrunch, Excel or Hand Calculate to generate Summary Statistics b. Based on your summary statistics, IQR does the Data Contain Outliers? c. Use StatCrunch, Excel or Hand Calculate to generate a 92% confidence interval for the mean d. Use StatCrunch, Excel or Hand Calculate to generate a 98% confidence interval for the mean e. Use StatCrunch, Excel or Hand Calculate and Hypothesis Testing (P-Value Method) for the claim that the mean is less than 10 at a 90% confidence level. Question 4 25 points A survey was done concerning - Do you favor like strawberry ice-cream? 1 = Yes, 0 = No and the results were as follows 1 0 1 0 1 0 0 1 1 1 1 1 0 1 1 0 0 1 0 1 0 1 1 0 0 1 1 1 1 1 0 1 1 0 0 0 0 1 0 1 a. Use StatCrunch, Excel or Hand Calculate to the 90% confidence interval for the proportion of people that FAVOR strawberry ice-cream. b. Use StatCrunch, Excel or Hand Calculate to the 90% confidence interval for the proportion of people that DO NOT FAVOR strawberry ice-cream. c. Use StatCrunch, Excel or Hand Calculate and Hypothesis Testing (P-Value Method) for the claim that the proportion of people that favor strawberry ice-cream is greater than 45% at 90% confidence level. d. Use StatCrunch, Excel or Hand Calculate and Hypothesis Testing (P-Value Method) for the claim that the proportion of people that favor that favor strawberry ice-cream is different from 40% at 90% confidence level. Math 1342 Sample Test 5 Solutions Question 1 25 points A random sample of data was obtained 47 8 68 29 95 90 7 54 3 15 33 49 21 64 4 52 4 44 6 8 79 78 57 80 100 9 48 40 80 16 50 a. Use StatCrunch, Excel or Hand Calculate the Summary Statistics Summary statistics: Column n var1 Mean Variance Std. dev. Median Range Min Max Q1 Q3 IQR 31 43.451613 977.58925 31.266424 47 b. Use StatCrunch, Excel or Hand Calculate to create a Box Plot 106 3 109 9 68 59 c. Based on your summary statistics, IQR and Box Plot does the Data Contain Outliers? Min Max Q1 Q3 IQR 3 109 9 68 59 An outlier lives outside of (q1 - 1.5 IRQ, q3+ 1.5IRQ) = ( 9 - 1.5*59, 68 + 1.5*50) And none of our data lives there. d. Use StatCrunch, Excel or Hand Calculate to generate a 90% confidence interval for the mean 90% confidence interval results: : Mean of variable Standard deviation not specified. Variable n Sample Mean var1 31 Std. Err. L. Limit U. Limit 43.451613 5.6156155 34.214747 52.688478 e. Use StatCrunch, Excel or Hand Calculate and Hypothesis Testing (P-Value Method) for the claim that the mean is different from 40 at a 94% confidence level. Hypothesis test results: : Mean of variable H0 : = 40 HA : 40 Standard deviation not specified. Variable n Sample Mean var1 31 Std. Err. Z-Stat P-value 43.451613 5.6156155 0.61464552 0.5388 Alpha = 1 - Confidence = 1 - 0.94 = 0.06 P-Value > alpha since 0.5388 > 0.06 So do NOT reject the Null Hypothesis Our claim was H1 and we had do NOT REJECT so conclude There is not enough evidence to support the claim that the mean is different from 40. Question 2 25 points A random sample of data was obtained 61 12 6 40 27 38 93 5 13 40 a. Use StatCrunch, Excel or Hand Calculate to generate Summary Statistics Summary statistics: Column n Mean Variance var1 10 Std. dev. Median Range Min Max Q1 Q3 IQR 33.5 766.05556 27.677709 32.5 88 5 93 12 40 28 b. Use StatCrunch, Excel or Hand Calculate to generate a Stem and Leaf Plot 0 : 56 1 : 23 2:7 3:8 4 : 00 5: 6:1 7: 8: 9:3 c. Use StatCrunch, Excel or Hand Calculate to generate a 95% confidence interval for the mean 95% confidence interval results: : Mean of variable Variable Sample Mean Std. Err. DF var1 33.5 8.75246 L. Limit U. Limit 9 13.70056 53.29944 d. Use StatCrunch, Excel or Hand Calculate to generate a 97% confidence interval for the variance 97% confidence interval results: 2 : Variance of variable Variable Sample Var. DF var1 766.05556 L. Limit U. Limit 9 336.11211 2952.8578 e. Use StatCrunch, Excel or Hand Calculate and Hypothesis Testing (P-Value Method) for the claim that the mean is less than 30 at a 96% confidence level. Hypothesis test results: : Mean of variable H0 : = 30 HA : < 30 Variable Sample Mean Std. Err. DF var1 33.5 8.75246 T-Stat P-value 9 0.39988758 0.6507 Alpha = 1 - Confidence = 1 - 0.96 = 0.04 P-Value > alpha since 0.6507 > 0.04 So do NOT reject the Null Hypothesis Our claim was H1 and we had do NOT REJECT so conclude There is not enough evidence to support the claim that the mean is less than 30. Question 3 25 points A random sample of data was obtained 10.8 9.8 9.8 9.4 8.8 9.8 9.6 9.9 10.0 8.4 9.6 10.0 9.4 a. Use StatCrunch, Excel or Hand Calculate to generate Summary Statistics Summary statistics: Column n var1 Mean Variance Std. dev. 13 9.6384615 0.3425641 0.58528976 Min Max Q1 Q3 IQR 8.4 10.8 9.4 9.9 0.5 b. Based on your summary statistics, IQR does the Data Contain Outliers? Min Max Q1 Q3 IQR 8.4 10.8 9.4 9.9 0.5 An outlier would live outside of (q1 - 1.5IRQ, q3 + 1.5IRQ) Or ( 9.4 - 0.75, 9.9 + 0.75) = (8.65, 10.65) So outliers are 8.4 and 10.8 c. Use StatCrunch, Excel or Hand Calculate to generate a 92% confidence interval for the mean 92% confidence interval results: : Mean of variable Variable Sample Mean var1 Std. Err. DF L. Limit U. Limit 9.6384615 0.16233017 12 9.3280354 9.9488877 d. Use StatCrunch, Excel or Hand Calculate to generate a 98% confidence interval for the mean 98% confidence interval results: : Mean of variable Variable Sample Mean var1 Std. Err. DF L. Limit U. Limit 9.6384615 0.16233017 12 9.2032547 10.073668 e. Use StatCrunch, Excel or Hand Calculate and Hypothesis Testing (P-Value Method) for the claim that the mean is less than 10 at a 99% confidence level. Hypothesis test results: : Mean of variable H0 : = 10 HA : < 10 Variable Sample Mean var1 Std. Err. DF T-Stat 9.6384615 0.16233017 12 -2.2271797 P-value 0.0229 Alpha = 1 - Confidence = 1 - 0.99 = 0.01 P-Value > alpha since 0.0229 > 0.01 So do NOT reject the Null Hypothesis Our claim was H1 and we had do NOT REJECT so conclude There is not enough evidence to support the claim that the mean is less than 10. Question 4 25 points A survey was done concerning - Do you favor saving the Astrodome? 1 = Yes, 0 = No and the results were as follows 1 1 1 0 1 0 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 1 0 1 1 0 0 0 0 1 0 1 a. Use StatCrunch, Excel or Hand Calculate to the 93% confidence interval for the proportion of people that FAVOR saving the Astrodome. Number of responses = 40, Number of Yes = 22, Number of No = 18 93% confidence interval results: p : Proportion of successes Method: Standard-Wald Proportion Count Total Sample Prop. p 22 40 Std. Err. L. Limit U. Limit 0.55 0.078660664 0.4074739 0.6925261 b. Use StatCrunch, Excel or Hand Calculate to the 97% confidence interval for the proportion of people that DO NOT FAVOR saving the Astrodome. In this case \"success\" is the number of NO 97% confidence interval results: p : Proportion of successes Method: Standard-Wald Proportion Count Total Sample Prop. p 18 40 Std. Err. L. Limit U. Limit 0.45 0.078660664 0.27929925 0.62070075 c. Use StatCrunch, Excel or Hand Calculate and Hypothesis Testing (P-Value Method) for the claim that the proportion of people that favor saving the Astrodome is greater than 50% at 90% confidence level. Hypothesis test results: p : Proportion of successes H0 : p = 0.5 HA : p > 0.5 Proportion Count Total Sample Prop. p 22 40 Std. Err. Z-Stat 0.55 0.079056942 0.63245553 P-value 0.2635 Alpha = 1 - Confidence = 1 - 0.90 = 0.1 P-Value > alpha since 0.2635 > 0.1 So do NOT reject the Null Hypothesis Our claim was H1 and we had do NOT REJECT so conclude There is not enough evidence to support the claim that proportion is greater than 50%. d. Use StatCrunch, Excel or Hand Calculate and Hypothesis Testing (P-Value Method) for the claim that the proportion of people that favor saving the Astrodome is different from 50% at 90% confidence level. Hypothesis test results: p : Proportion of successes H0 : p = 0.5 HA : p 0.5 Proportion Count Total Sample Prop. p 22 40 Std. Err. Z-Stat 0.55 0.079056942 0.63245553 P-value 0.5271 Alpha = 1 - Confidence = 1 - 0.90 = 0.1 P-Value > alpha since 0.5271 > 0.1 So do NOT reject the Null Hypothesis Our claim was H1 and we had do NOT REJECT so conclude There is not enough evidence to support the claim that proportion is different from 50%. Math 1342 Final Exam 1. 25 pts Stock Prices A random sample of stock prices per share (in dollars) is shown. Use Stat Crunch to find the Summary Statistics (include IQR, exclude Std. Error) and paste in the results. a) Use Stat Crunch to create and paste in the Box Plot b) Comment on the Box Plot in terms of median being shifted left or right and if there any outliers. c) Use Stat Crunch to form the \"correct\" 97% confidence interval for the mean paste in the results and then make a type the interval form. d) From previous data the mean was 35. Is there enough evidence at alpha = 0.05 to conclude that the mean has increased. Use Stat Crunch, paste in the results. Use the P Value Method to conclude to make a conclusion. 2. 25 pts Triples and Home Runs The number of triples and the number of home runs obtained by a selected sample of MLB players are shown. a) Use Stat Crunch to create a scatter plot and paste in your results. b) Use Stat Crunch to calculate the correlation coefficient and paste in your results. c) Use Stat Crunch to find the equation of the regression line, predict for x= 37, paste in the results as well as the graph of the best line and then type in your equation. 3. 25 pts Goodness of Fit Ages of Head Start Program Students The Head Start Program provides a wide range of services to low-income children up to the age of 5 and their families. Its goals are to provide services to improve social and learning skills and to improve health and nutrition status so that the participants can begin school on an equal footing with their more advantaged peers. The distribution of ages for participating children is as follows: 4% five-yearolds, 52% four-year-olds, 34% three-year-olds, and 10% under 3 years. When the program was assessed in a particular region, it was found that of the 200 participants, 20 were 5 years old, 120 were 4 years old, 40 were 3 years old, and 20 were under 3 years. Is there sufficient evidence at = 0.05 that the proportions differ from the program's? a) Enter the data into Stat Crunch and paste in your data table. b) Use Stat Crunch for Goodness of Fit and paste in your results. c) Use the P Value Method to conclude to make a conclusion. 4. 25 pts - Calories in Fast-Food Sandwiches Three popular fast-food restaurant franchises specializing in burgers were surveyed to find out the number of calories in their frequently ordered sandwiches. At the 0.05 level of significance, can it be concluded that a difference in mean number of calories per burger exists? a) Enter the data into Stat Crunch and paste in your data table. b) Use Stat Crunch for ANOVA and paste in your results. c) Use the P Value Method to conclude to make a conclusion. Math 1342 Sample Final Exam 1. 25 pts State Gasoline Taxes A random sample of state gasoline taxes (in cents) is shown here for 12 states. a) Use Stat Crunch to find the Summary Statistics (include IQR, exclude Std. Error) and paste in the results. b) Use Stat Crunch to create and paste in the Box Plot c) Comment on the Box Plot in terms of median being shifted left or right and if there any outliers. d) Use Stat Crunch to form the \"correct\" 92% confidence interval for the mean paste in the results and then make a type the interval form. e) From previous data the mean was 47. Is there enough evidence at alpha = 0.05 to conclude that the mean has decreased. Use Stat Crunch, paste in the results. Use the P Value Method to conclude to make a conclusion. 2. 25 pts Forest Fires and Acres Burned Number of fires and number of acres burned are as follows: a) Use Stat Crunch to create a scatter plot and paste in your results. b) Use Stat Crunch to calculate the correlation coefficient and paste in your results. c) Use Stat Crunch to find the equation of the regression line, predict for x= 60, paste in the results as well as the graph of the best line and then type in your equation. 3. 25 pts Goodness of Fit - Truck Colors In a recent year, the most popular colors for light trucks were white, 30%; black, 17%; red, 14%; silver, 12%; gray, 11%; blue, 8%; and other, 8%. A survey of light truck owners in a particular area revealed the following. At = 0.05, do the proportions differ from those stated? a) Enter the data into Stat Crunch and paste in your data table. b) Use Stat Crunch for Goodness of Fit and paste in your results. c) Use the P Value Method to conclude to make a conclusion. 4. 25 pts -Number of Farms The numbers (in thousands) of farms per state found in three sections of the country are listed next. Test the claim at = 0.05 that the mean number of farms is the same across these three geographic divisions. a) Enter the data into Stat Crunch and paste in your data table. b) Use Stat Crunch for ANOVA and paste in your results. c) Use the P Value Method to conclude to make a conclusion