a manufacturer of cell phones would like to estimate how much longer the battery lasts in their model 10…

a manufacturer of cell phones would like to estimate how much longer the battery lasts in their model 10 phone than in their model 9 phone. to estimate this difference, they randomly select 40 cell phones of each model from the production line. they subject each phone to a standard battery life test. the 40 model 10 phones have a mean battery life of 14.4 hours with a standard deviation of 2.1 hours. the 40 model 9 phones have a mean battery life of 12.8 hours with a standard deviation of 2.3 hours. a 95% confidence interval for the difference in the population means is (0.594, 2.606). what is the interpretation of this interval?\nwe can be 95% confident that the interval from 0.594 to 2.606 captures $mu_1-mu_2$ = the true difference in the mean battery life for all model 9 and model 10 cell phones.\nwe can be 95% confident that the interval from 0.594 to 2.606 captures $p_1 - p_2$ = the true difference in the proportion of battery life for all model 9 and model 10 cell phones.\nwe can be 95% confident that the interval from 0.594 to 2.606 captures $\bar{x}_1-\bar{x}_2$ = the difference in the mean battery life for the two samples of model 9 and model 10 cell phones.\nwe can be 95% confident that the interval from 0.594 to 2.606 captures $hat{p}_1-hat{p}_2$ = the difference in the proportion of battery life for the two samples of model 9 and model 10 cell phones.

a manufacturer of cell phones would like to estimate how much longer the battery lasts in their model 10 phone than in their model 9 phone. to estimate this difference, they randomly select 40 cell phones of each model from the production line. they subject each phone to a standard battery life test. the 40 model 10 phones have a mean battery life of 14.4 hours with a standard deviation of 2.1 hours. the 40 model 9 phones have a mean battery life of 12.8 hours with a standard deviation of 2.3 hours. a 95% confidence interval for the difference in the population means is (0.594, 2.606). what is the interpretation of this interval?\nwe can be 95% confident that the interval from 0.594 to 2.606 captures $mu_1-mu_2$ = the true difference in the mean battery life for all model 9 and model 10 cell phones.\nwe can be 95% confident that the interval from 0.594 to 2.606 captures $p_1 - p_2$ = the true difference in the proportion of battery life for all model 9 and model 10 cell phones.\nwe can be 95% confident that the interval from 0.594 to 2.606 captures $\bar{x}_1-\bar{x}_2$ = the difference in the mean battery life for the two samples of model 9 and model 10 cell phones.\nwe can be 95% confident that the interval from 0.594 to 2.606 captures $hat{p}_1-hat{p}_2$ = the difference in the proportion of battery life for the two samples of model 9 and model 10 cell phones.

Answer

Brief Explanations:

A confidence interval for the difference in population means gives a range of values within which we are a certain percentage (in this case 95%) confident that the true difference between the population means lies. Here, $\mu_1-\mu_2$ represents the true difference in the mean battery - life for all model 9 and model 10 cell phones. The confidence interval (0.594, 2.606) is for the population parameter, not the sample statistics.

Answer:

A. We can be 95% confident that the interval from 0.594 to 2.606 captures $\mu_1-\mu_2$ = the true difference in the mean battery life for all model 9 and model 10 cell phones.