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5.3 Population Variances Are Not Kn ssumptions: Populations are normal and small samples deviations are assumed to be equal. est statistic: (x- ) - D II

5.3 Population Variances Are Not Kn ssumptions: Populations are normal and small samples deviations are assumed to be equal. est statistic: (x- ) - D II

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 25PPS
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4.5.3 Population Variances Are Not Known, of = oź Populations are normal and small samples Assumptions: deviations are assumed to be equal. (x- x2) - D t = Test statistic: 1 Sp 21 n2. df = n1 + n2-2 (n,-1)s;+(n2-1)s Sp n1+n2-2 Example 4.18 An insurance company wants to know if the average speed at which men drive cars is greater than that of women drivers. The company took a random sample of 26 cars driven by men on a highway and found the mean speed to be 72 miles per hour with a standard deviation of 2.2 miles per hour. Another sample of 16 cars driven by women on the same highway gave a mean speed of 68 miles per hour with a standard deviation of 2.5 miles per hour. Assume that the speeds at which all men and all women drive cars on this highway are both normally distributed with the same population standard deviation. Test at 2.5% significance level whether the average speed at which men drive cars is greater than that of women drivers. (Ans: Test Stat = 5.433, reject Ho) Solution:
Transcribed Image Text:4.5.3 Population Variances Are Not Known, of = oź Populations are normal and small samples Assumptions: deviations are assumed to be equal. (x- x2) - D t = Test statistic: 1 Sp 21 n2. df = n1 + n2-2 (n,-1)s;+(n2-1)s Sp n1+n2-2 Example 4.18 An insurance company wants to know if the average speed at which men drive cars is greater than that of women drivers. The company took a random sample of 26 cars driven by men on a highway and found the mean speed to be 72 miles per hour with a standard deviation of 2.2 miles per hour. Another sample of 16 cars driven by women on the same highway gave a mean speed of 68 miles per hour with a standard deviation of 2.5 miles per hour. Assume that the speeds at which all men and all women drive cars on this highway are both normally distributed with the same population standard deviation. Test at 2.5% significance level whether the average speed at which men drive cars is greater than that of women drivers. (Ans: Test Stat = 5.433, reject Ho) Solution:
Example 4.17 A set of facilitation tools to help with data analysis for problem solving is being developed by a group of statisticians at UITM. In order to test effectiveness of these tools, a group of research officers were asked to analyze and produce a built-in report for a set of data on the computer. Twelve equally capable research officers were randomly selected and six were randomly assigned a standard procedure to complete the task. The other six were asked to do the task using the developed facilitation tools. The response measured was the time to completion (in minutes): The data collected are shown below: Group1 (standard procedure) Group 2 (facilitation tool) 61 69 68 74 58 63 32 42 40 34 38 33 Assume that the population variances of the two procedures are different. Two sample T test Minitab output are given below. Two-Sample T-Test and CI: group 1; group 2 different which ne better? Two-sample T for group 1 vs group 2 Mean StDev SE Mean 1 6. 65.50 5.89 2.4 group group 2 6. 36.50 4.09 1.7 > b TT better becau g Difference = mu (group 1) - mu (group 2) Estimate for difference: dees not ins kde o. so there N a diffent 29.0000 98% CI for difference: (20.5224; 37.4776) P-Value = 0.000 DF = 8 T-Test of difference = 0 (vs not =): T-Value = 9.91 Based on the output, answer the following questions: a) State the null and alternative hypothesis. b) Show that the test statistics 9.91. c) Can we conclude that there is difference in the average completion times for the two procedures? Sinie 9= 0 Solution:
Transcribed Image Text:Example 4.17 A set of facilitation tools to help with data analysis for problem solving is being developed by a group of statisticians at UITM. In order to test effectiveness of these tools, a group of research officers were asked to analyze and produce a built-in report for a set of data on the computer. Twelve equally capable research officers were randomly selected and six were randomly assigned a standard procedure to complete the task. The other six were asked to do the task using the developed facilitation tools. The response measured was the time to completion (in minutes): The data collected are shown below: Group1 (standard procedure) Group 2 (facilitation tool) 61 69 68 74 58 63 32 42 40 34 38 33 Assume that the population variances of the two procedures are different. Two sample T test Minitab output are given below. Two-Sample T-Test and CI: group 1; group 2 different which ne better? Two-sample T for group 1 vs group 2 Mean StDev SE Mean 1 6. 65.50 5.89 2.4 group group 2 6. 36.50 4.09 1.7 > b TT better becau g Difference = mu (group 1) - mu (group 2) Estimate for difference: dees not ins kde o. so there N a diffent 29.0000 98% CI for difference: (20.5224; 37.4776) P-Value = 0.000 DF = 8 T-Test of difference = 0 (vs not =): T-Value = 9.91 Based on the output, answer the following questions: a) State the null and alternative hypothesis. b) Show that the test statistics 9.91. c) Can we conclude that there is difference in the average completion times for the two procedures? Sinie 9= 0 Solution:
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