Question

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 s_pool^2 = (s_1^2(n_1 - 1) + s_2^2(n_2 - 1)) / (n_1 + n_2 - 2) with v = n_1 + n_2 - 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 13 and 10 times and they yielded average efficiencies of 78 and 70 (out of 100), respectively. The sample standard deviations are 4 and 5, again, respectively. Help them construct a 99% confidence interval, assuming that efficiency values are Normally distributed with equal variances. With 99% confidence, the difference between population mean efficiencies ?_1 - ?_2 will be between [ ] and [ ]. (Round to two decimal places including any zeros.)

          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
s_pool^2 = (s_1^2(n_1 - 1) + s_2^2(n_2 - 1)) / (n_1 + n_2 - 2)
with v = n_1 + n_2 - 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 13 and 10 times and they yielded average efficiencies of 78 and 70 (out of 100), respectively. The sample standard deviations are 4 and 5, again, respectively. Help them construct a 99% confidence interval, assuming that efficiency values are Normally distributed with equal variances.

With 99% confidence, the difference between population mean efficiencies ?_1 - ?_2 will be between [ ] and [ ].
(Round to two decimal places including any zeros.)

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^2 = (s1^2(n1 - 1) + s2^2(n2 - 1)) / (n1 + n2 - 2)
with v = n1 + n2 - 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 13 and 10 times and they yielded average efficiencies of 78 and 70 (out of 100), respectively. The sample standard deviations are 4 and 5, again, respectively. Help them construct a 99% confidence interval, assuming that efficiency values are Normally distributed with equal variances.

With 99% confidence, the difference between population mean efficiencies ?1 - ?2 will be between [ ] and [ ].
(Round to two decimal places including any zeros.)

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