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We've seen how to compare the means of two samples with known population variances (refer, for instance, to Example 4 in Recitation 11), but when we need to compare the means of two samples with unknown (but assumed to be equal) population variances, a method called 'variance pooling' needs to be used to find the 'pooled sample variance' that should be used when calculating the confidence interval. The pooled variance is given by n, +n2 -2 with v=n, +n, -2 degrees of freedom (see page 308 of your e-book). Now look at the example below. Production engineers need to compare the average efficiencies of two production processes. Process 1 and Process 2 are sampled 14 and 11 times and they yielded average efficiencies of 90 and 83 (out of 100), respectively. The sample standard deviations are 6 and 5, again, respectively. Help them construct a 90% confidence interval, assuming that efficiency values are Normally distributed with equal variances. Click here to view page 1 of the table of critical values of the t-distribution. Click here to view page 2 of the table of critical values of the t-distribution. With 90%, confidence, the difference between population mean efficiencies u, -H2 will be between (Round to two decimal places including any zeros.) and

We've seen how to compare the means of two samples with known population variances (refer, for instance, to Example 4 in Recitation 11), but when we need to compare the means of two samples with unknown (but assumed to be equal) population variances, a method called 'variance pooling' needs to be used to find the 'pooled sample variance' that should be used when calculating the confidence interval. The pooled variance is given by n, +n2 -2 with v=n, +n, -2 degrees of freedom (see page 308 of your e-book). Now look at the example below. Production engineers need to compare the average efficiencies of two production processes. Process 1 and Process 2 are sampled 14 and 11 times and they yielded average efficiencies of 90 and 83 (out of 100), respectively. The sample standard deviations are 6 and 5, again, respectively. Help them construct a 90% confidence interval, assuming that efficiency values are Normally distributed with equal variances. Click here to view page 1 of the table of critical values of the t-distribution. Click here to view page 2 of the table of critical values of the t-distribution. With 90%, confidence, the difference between population mean efficiencies u, -H2 will be between (Round to two decimal places including any zeros.) and

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 58E: What is meant by the sample space of an experiment?
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We've seen how to compare the means of two samples with known population variances (refer, for instance, to Example 4 in Recitation 11), but when we need to compare the means of two samples with unknown (but assumed to be equal) population variances, a method called 'variance pooling' needs to be used to find the 'pooled sample variance' that should be used when calculating the confidence interval. The pooled variance is given by Spool = n, +n2 -2 with v=n, +n, -2 degrees of freedom (see page 308 of your e-book). Now look at the example below. Production engineers need to compare the average efficiencies of two production processes. Process 1 and Process 2 are sampled 14 and 11 times and they yielded average efficiencies of 90 and 83 (out of 100), respectively. The sample standard deviations are 6 and 5, again, respectively. Help them construct a 90% confidence interval, assuming that efficiency values are Normally distributed with equal variances. Click here to view page 1 of the table of critical values of the t-distribution. Click here to view page 2 of the table of critical values of the t-distribution. With 90%, confidence, the difference between population mean efficiencies u, - H, will be between and (Round to two decimal places including any zeros.)
Transcribed Image Text:We've seen how to compare the means of two samples with known population variances (refer, for instance, to Example 4 in Recitation 11), but when we need to compare the means of two samples with unknown (but assumed to be equal) population variances, a method called 'variance pooling' needs to be used to find the 'pooled sample variance' that should be used when calculating the confidence interval. The pooled variance is given by Spool = n, +n2 -2 with v=n, +n, -2 degrees of freedom (see page 308 of your e-book). Now look at the example below. Production engineers need to compare the average efficiencies of two production processes. Process 1 and Process 2 are sampled 14 and 11 times and they yielded average efficiencies of 90 and 83 (out of 100), respectively. The sample standard deviations are 6 and 5, again, respectively. Help them construct a 90% confidence interval, assuming that efficiency values are Normally distributed with equal variances. Click here to view page 1 of the table of critical values of the t-distribution. Click here to view page 2 of the table of critical values of the t-distribution. With 90%, confidence, the difference between population mean efficiencies u, - H, will be between and (Round to two decimal places including any zeros.)
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