Ignore this section: Statistics STA 1103 - W17 Assignment 2 (Part C) Due Wed March 15 In person, or on Moodle Student Name: ______________________ Student Number: _____________________ 2017 LAMBTON COLLEGE IN TORONTO Statistics STA 1103 - W17 In Class Quiz #2 - Two Sample Hypothesis Test & ANOVA 2.5% of your final mark 1. If the null hypothesis that 2 means are equal is true, 97% of the computed z-values will be between what 2 values? a. b. c. d. +/- 2.58 +/- 2.22 +/- 2.17 None of the above 2. Using 2 independent samples, 2 population means are compared to see if a difference exists. In the 1st sample there are 15 observations and 12 in the 2 nd sample. How many degrees of freedom are associated with the critical value? a. b. c. d. 24 25 26 None of the above 3. What is the critical value for a one-tailed hypothesis test in which a null hypothesis is tested at the 5% level of significance based on 2 samples, where both sample sizes are 13? a. b. c. d. 2.064 2.060 1.711 None of the above 4. Here are results of a math exam at Lambton College for Toronto (1) & Sarnia (2) campuses Campus Toronto Sarnia Students 90 110 Average Score 33 31 Std Dev 8 7 sp2 55.75 At the 95% level of confidence for a one sided test, what is the t statistic? a. b. c. d. 1.89 3.44 2.00 2.67 5. If the alternative hypothesis is that Toronto students scored better, what is the critical value and conclusion? a. b. c. d. 1.645, we can reject the null hypothesis and conclude Toronto scored higher 1.972, there is not enough evidence to conclude that Toronto scored higher 2.576, the t statistic is less than the critical value, so Toronto scored higher 1.653, Toronto students are no better than Sarnia students in math 2017 LAMBTON COLLEGE IN TORONTO Statistics STA 1103 - W17 2017 LAMBTON COLLEGE IN TORONTO Statistics STA 1103 - W17 6. Which of the following is NOT a characteristic of the F distribution? a. b. c. d. It is based on two sets of degrees of freedom It is positively skewed As the values of X increases, the F curve approaches the X-axis & eventually equals zero It is asymptotic 7. (i) The test statistic used in ANOVA is F (ii) The calculated F value must be equal to or greater than zero (0) (iii) The shape of the F distribution is symmetrical. a. All 3 statements are true b. None of the 3 statements are true c. (i) & (iii) are true but not (ii) d. (i) & (ii) are true but not (iii) 8. Analysis of Variance (ANOVA) can be used to: a. Compare nominal data b. Compute t test c. Compare population proportions d. Simultaneously compare several population means 9. The F test statistic is the ratio of the: a. Estimate of the population mean based on the differences among the sample standard deviations to the estimate of the population variance based on the variation within the samples b. Estimate of the population variance based on the differences among the sample means to the estimate of the population variance based on the variation within the samples c. Estimate of the population variance based on the sums of the sample means to the estimate of the population variance based on the variation within the samples. d. None of the above 10. A random sample of 30 company executives was selected and asked for their annual income and level of education. The following table summarized the results 2017 LAMBTON COLLEGE IN TORONTO Statistics STA 1103 - W17 10. (cont) Using these results and output, what conclusions can you draw? a. Since the calculated F-value is smaller than the F-critical value, there is a significant difference in the incomes of these 3 groups b. Since the calculated F-value is smaller than the F-critical value, there is no significant difference in the incomes of these three groups c. Since the P-value is about 0.001, there is an 10% chance of these results happening when there is no significant difference in the incomes of these three groups d. Since the calculated F-value is larger than the F-critical value, and the P-value is so small, there is strong evidence to suggest that the three groups with different levels of education do not all have the same incomes e. Since the calculated F-value is larger than the F-critical value, and the P-value is so small, there is strong evidence to suggest that all three groups with different levels of education have the same incomes 11. A large department store examined a sample of the 18 credit card sales and recorded the amounts charged for each of 3 types of credit cards: MasterCard, Visa and American Express. 6 MasterCard sales, 7 Visa and 5 American Express sales were recorded. The store used ANOVA to test if the mean sales for each credit card were equal. What are the degrees of freedom for the F statistic? a. b. c. d. e. 18 in the numerator, 3 in the denominator 3 in the numerator, 18 in the denominator 2 in the numerator, 15 in the denominator 0 in the numerator, 15 in the denominator None of these statements are true 12. Suppose that an automobile manufacturer designed a radically new lightweight engine and wants to recommend the grade of gasoline to use. The four grades are: Light, Regular, Premium, and Super Premium. The test car made 3 trial runs on the test track using each of the 4 grades. What is the critical value of F using 0.05 level of significance? a. b. c. d. 1.96 4.07 2.33 None of the above 2017 LAMBTON COLLEGE IN TORONTO Ch 10- 2 Sample HypTest.w17 Question 2 (pg 297) a. One tailed test. b. Reject H0 if critical value= 1.405 z= c. 2.672.59 2 0.75 0.66 + 65 50 2 = 0.60707 d. Since 0.60707<1.405, Fail to Reject Ho e. P-value=0.272 This is the probability that H0 Is true. It is the probability that mean in population one is not greater than mean in population 2. Since this P-value>0.08, we cannot reject H0. Question 7 (pg 301) Question 23 (pg 316), p`1=70/100=0.7 p`2=90/150=0.6 This is a one tailed test. Decision Rule: Reject test statistics >critical value 1.645 Test statistics Z= 0.70.6 = 0.70.3 0.60.4 1.644 + 100 150 Since 1.644<1.645, Ho is not rejected. Conclude that there is no enough evidence that the two population proportions are not equal. last file Ch11.ANOVA.exercises.w17 answer Self Review 11-1 (pg 327) X`1=9, S1=2, x`2=8.5, S2=1.5, n1=n1=10 Ho: 2 1 2 2 2 2 Ho : 1> 2 =0.05, S 12 22 F= = 2 2 Test statistics= S 2 1. 5 =1.78 P-value= 0.202 Since P-value>0.05 Ho is not rejected. There is no enough evidence to conclude that there is more variation in number of rejects per day attributed by marks. a. H0: Ha: All means are equal At least one mean is different b. Reject H0 if P-value<0.05 c. Anova TSS=yij2 - (yij)2/n 254 2 2 2 2 TSS= (20 +21 +... 17 +16 ) 14 2 SS-between= Ti SSWithin=123.7143- ANOVA Source of Variation Between Groups Within Groups SS 14.16429 109.55 Total 123.7143 2 =123.7143 ( yij )2 952 752 84 2 254 2 = + + =109.55 n 5 4 5 14 ( ) 109.55 =109.55 df MS F 2 7.082143 0.711123 11 9.959091 13 d. Since P-value>0.05, do not reject Ho. e. N0 there is no difference. 95% CI for difference: =19-16.7 2.306 = 2.3 5.3288 =(-3.0288, 7.6288) 26 0.7 + 5 5 P-value 0.5123 F crit 3.982 Statistics STA 1103 - W17 Assignment 2 (Part C) Due Wed March 15 In person, or on Moodle Student Name: ______________________ Student Number: _____________________ 2017 LAMBTON COLLEGE IN TORONTO Statistics STA 1103 - W17 In Class Quiz #2 - Two Sample Hypothesis Test & ANOVA 2.5% of your final mark 1. If the null hypothesis that 2 means are equal is true, 97% of the computed z-values will be between what 2 values? a. b. c. d. +/- 2.58 +/- 2.22 +/- 2.17 None of the above Z0.015=2.17 2. Using 2 independent samples, 2 population means are compared to see if a difference exists. In the 1st sample there are 15 observations and 12 in the 2 nd sample. How many degrees of freedom are associated with the critical value? a. b. c. d. 24 25 D.F=n1+n2-2=12+15-2=25 26 None of the above 3. What is the critical value for a one-tailed hypothesis test in which a null hypothesis is tested at the 5% level of significance based on 2 samples, where both sample sizes are 13? a. b. c. d. 2.064 2.060 1.711 t 0.025, 14=1.711 None of the above 4. Here are results of a math exam at Lambton College for Toronto (1) & Sarnia (2) campuses Campus Toronto Sarnia Students 90 110 Average Score 33 31 Std Dev 8 7 sp2 55.75 At the 95% level of confidence for a one sided test, what is the t statistic? a. 1.89 b. c. d. 3.44 2.00 2.67 t= 3331 ( 55.75 1 1 + 90 110 ) =1.89 5. If the alternative hypothesis is that Toronto students scored better, what is the critical value and conclusion? 2017 LAMBTON COLLEGE IN TORONTO Statistics STA 1103 - W17 a. b. c. d. 1.645, we can reject the null hypothesis and conclude Toronto scored higher 1.972, there is not enough evidence to conclude that Toronto scored higher 2.576, the t statistic is less than the critical value, so Toronto scored higher 1.653, Toronto students are no better than Sarnia students in math T0.5,198=1.653 6. Which of the following is NOT a characteristic of the F distribution? a. b. c. d. It is based on two sets of degrees of freedom It is positively skewed As the values of X increases, the F curve approaches the X-axis & eventually equals zero It is asymptotic 7. (i) The test statistic used in ANOVA is F (ii) The calculated F value must be equal to or greater than zero (0) (iii) The shape of the F distribution is symmetrical. a. All 3 statements are true b. None of the 3 statements are true c. (i) & (iii) are true but not (ii) d. (i) & (ii) are true but not (iii) 8. Analysis of Variance (ANOVA) can be used to: a. Compare nominal data b. Compute t test c. Compare population proportions d. Simultaneously compare several population means 9. The F test statistic is the ratio of the: a. Estimate of the population mean based on the differences among the sample standard deviations to the estimate of the population variance based on the variation within the samples b. Estimate of the population variance based on the differences among the sample means to the estimate of the population variance based on the variation within the samples c. Estimate of the population variance based on the sums of the sample means to the estimate of the population variance based on the variation within the samples. d. None of the above 10. A random sample of 30 company executives was selected and asked for their annual income and level of education. The following table summarized the results 2017 LAMBTON COLLEGE IN TORONTO Statistics STA 1103 - W17 10. (cont) Using these results and output, what conclusions can you draw? a. Since the calculated F-value is smaller than the F-critical value, there is a significant difference in the incomes of these 3 groups b. Since the calculated F-value is smaller than the F-critical value, there is no significant difference in the incomes of these three groups c. Since the P-value is about 0.001, there is an 10% chance of these results happening when there is no significant difference in the incomes of these three groups d. Since the calculated F-value is larger than the F-critical value, and the P-value is so small, there is strong evidence to suggest that the three groups with different levels of education do not all have the same incomes e. Since the calculated F-value is larger than the F-critical value, and the P-value is so small, there is strong evidence to suggest that all three groups with different levels of education have the same incomes 11. A large department store examined a sample of the 18 credit card sales and recorded the amounts charged for each of 3 types of credit cards: MasterCard, Visa and American Express. 6 MasterCard sales, 7 Visa and 5 American Express sales were recorded. The store used ANOVA to test if the mean sales for each credit card were equal. What are the degrees of freedom for the F statistic? a. b. c. d. e. 18 in the numerator, 3 in the denominator 3 in the numerator, 18 in the denominator 2 in the numerator, 15 in the denominator 0 in the numerator, 15 in the denominator None of these statements are true (3-1, 18-3) 12. Suppose that an automobile manufacturer designed a radically new lightweight engine and wants to recommend the grade of gasoline to use. The four grades are: Light, Regular, Premium, and Super Premium. The test car made 3 trial runs on the test track using each of the 4 grades. What is the critical value of F using 0.05 level of significance? a. 1.96 2017 LAMBTON COLLEGE IN TORONTO Statistics STA 1103 - W17 b. c. d. 4.07 2.33 None of the above 2017 LAMBTON COLLEGE IN TORONTO Ch 10- 2 Sample HypTest.w17 Question 2 (pg 297) a. One tailed test. b. Reject H0 if critical value= 1.405 z= c. 2.672.59 2 0.75 0.66 + 65 50 2 = 0.60707 d. Since 0.60707<1.405, Fail to Reject Ho e. P-value=0.272 This is the probability that H0 Is true. It is the probability that mean in population one is not greater than mean in population 2. Since this P-value>0.08, we cannot reject H0. Question 7 (pg 301) Question 23 (pg 316), p`1=70/100=0.7 p`2=90/150=0.6 This is a one tailed test. Decision Rule: Reject test statistics >critical value 1.645 Test statistics Z= 0.70.6 = 0.70.3 0.60.4 1.644 + 100 150 Since 1.644<1.645, Ho is not rejected. Conclude that there is no enough evidence that the two population proportions are not equal. last file Ch11.ANOVA.exercises.w17 answer Self Review 11-1 (pg 327) X`1=9, S1=2, x`2=8.5, S2=1.5, n1=n1=10 Ho: 2 1 2 2 2 2 Ho : 1> 2 =0.05, S 12 22 F= = 2 2 Test statistics= S 2 1. 5 =1.78 P-value= 0.202 Since P-value>0.05 Ho is not rejected. There is no enough evidence to conclude that there is more variation in number of rejects per day attributed by marks. a. H0: Ha: All means are equal At least one mean is different b. Reject H0 if P-value<0.05 c. Anova TSS=yij2 - (yij)2/n 254 2 2 2 2 TSS= (20 +21 +... 17 +16 ) 14 2 SS-between= Ti SSWithin=123.7143- ANOVA Source of Variation Between Groups Within Groups SS 14.16429 109.55 Total 123.7143 2 =123.7143 ( yij )2 952 752 84 2 254 2 = + + =109.55 n 5 4 5 14 ( ) 109.55 =109.55 df MS F 2 7.082143 0.711123 11 9.959091 13 d. Since P-value>0.05, do not reject Ho. e. N0 there is no difference. 95% CI for difference: =19-16.7 2.306 = 2.3 5.3288 =(-3.0288, 7.6288) 26 0.7 + 5 5 P-value 0.5123 F crit 3.982 Statistics STA 1103 - W17 Assignment 2 (Part C) Due Wed March 15 In person, or on Moodle Student Name: ______________________ Student Number: _____________________ 2017 LAMBTON COLLEGE IN TORONTO Statistics STA 1103 - W17 In Class Quiz #2 - Two Sample Hypothesis Test & ANOVA 2.5% of your final mark 1. If the null hypothesis that 2 means are equal is true, 97% of the computed z-values will be between what 2 values? a. b. c. d. +/- 2.58 +/- 2.22 +/- 2.17 None of the above Z0.015=2.17 2. Using 2 independent samples, 2 population means are compared to see if a difference exists. In the 1st sample there are 15 observations and 12 in the 2 nd sample. How many degrees of freedom are associated with the critical value? a. b. c. d. 24 25 D.F=n1+n2-2=12+15-2=25 26 None of the above 3. What is the critical value for a one-tailed hypothesis test in which a null hypothesis is tested at the 5% level of significance based on 2 samples, where both sample sizes are 13? a. b. c. d. 2.064 2.060 1.711 t 0.025, 14=1.711 None of the above 4. Here are results of a math exam at Lambton College for Toronto (1) & Sarnia (2) campuses Campus Toronto Sarnia Students 90 110 Average Score 33 31 Std Dev 8 7 sp2 55.75 At the 95% level of confidence for a one sided test, what is the t statistic? a. 1.89 b. c. d. 3.44 2.00 2.67 t= 3331 ( 55.75 1 1 + 90 110 ) =1.89 5. If the alternative hypothesis is that Toronto students scored better, what is the critical value and conclusion? 2017 LAMBTON COLLEGE IN TORONTO Statistics STA 1103 - W17 a. b. c. d. 1.645, we can reject the null hypothesis and conclude Toronto scored higher 1.972, there is not enough evidence to conclude that Toronto scored higher 2.576, the t statistic is less than the critical value, so Toronto scored higher 1.653, Toronto students are no better than Sarnia students in math T0.5,198=1.653 6. Which of the following is NOT a characteristic of the F distribution? a. b. c. d. It is based on two sets of degrees of freedom It is positively skewed As the values of X increases, the F curve approaches the X-axis & eventually equals zero It is asymptotic 7. (i) The test statistic used in ANOVA is F (ii) The calculated F value must be equal to or greater than zero (0) (iii) The shape of the F distribution is symmetrical. a. All 3 statements are true b. None of the 3 statements are true c. (i) & (iii) are true but not (ii) d. (i) & (ii) are true but not (iii) 8. Analysis of Variance (ANOVA) can be used to: a. Compare nominal data b. Compute t test c. Compare population proportions d. Simultaneously compare several population means 9. The F test statistic is the ratio of the: a. Estimate of the population mean based on the differences among the sample standard deviations to the estimate of the population variance based on the variation within the samples b. Estimate of the population variance based on the differences among the sample means to the estimate of the population variance based on the variation within the samples c. Estimate of the population variance based on the sums of the sample means to the estimate of the population variance based on the variation within the samples. d. None of the above 10. A random sample of 30 company executives was selected and asked for their annual income and level of education. The following table summarized the results 2017 LAMBTON COLLEGE IN TORONTO Statistics STA 1103 - W17 10. (cont) Using these results and output, what conclusions can you draw? a. Since the calculated F-value is smaller than the F-critical value, there is a significant difference in the incomes of these 3 groups b. Since the calculated F-value is smaller than the F-critical value, there is no significant difference in the incomes of these three groups c. Since the P-value is about 0.001, there is an 10% chance of these results happening when there is no significant difference in the incomes of these three groups d. Since the calculated F-value is larger than the F-critical value, and the P-value is so small, there is strong evidence to suggest that the three groups with different levels of education do not all have the same incomes e. Since the calculated F-value is larger than the F-critical value, and the P-value is so small, there is strong evidence to suggest that all three groups with different levels of education have the same incomes 11. A large department store examined a sample of the 18 credit card sales and recorded the amounts charged for each of 3 types of credit cards: MasterCard, Visa and American Express. 6 MasterCard sales, 7 Visa and 5 American Express sales were recorded. The store used ANOVA to test if the mean sales for each credit card were equal. What are the degrees of freedom for the F statistic? a. b. c. d. e. 18 in the numerator, 3 in the denominator 3 in the numerator, 18 in the denominator 2 in the numerator, 15 in the denominator 0 in the numerator, 15 in the denominator None of these statements are true (3-1, 18-3) 12. Suppose that an automobile manufacturer designed a radically new lightweight engine and wants to recommend the grade of gasoline to use. The four grades are: Light, Regular, Premium, and Super Premium. The test car made 3 trial runs on the test track using each of the 4 grades. What is the critical value of F using 0.05 level of significance? a. 1.96 2017 LAMBTON COLLEGE IN TORONTO Statistics STA 1103 - W17 b. c. d. 4.07 2.33 None of the above 2017 LAMBTON COLLEGE IN TORONTO