(Solved): Two-Sample t-Test and Confidence Interval The following data show the results of two random samples ...

Two-Sample t-Test and Confidence Interval The following data show the results of two random samples that measured the average number of minutes per charge for AA Lithium-ion (Li-ion) rechargeable batteries versus Nickel-Metal Hydride (NiMH) rechargeable batteries. Perform a hypothesis test using significance level $(a)=0.09$ to determine if the true average number of minutes per charge for NiMH batteries is different from that for Li-ion batteries. Please add a Legend to the side-by-side boxplots. a. Use Excel to create histogram for each sample and side-by-side boxplots for the two samples of the given data. Based on the graphs you created in Excel and the given information, why the two-sample t-test is valid for this study? (select all that are true). The samples are not independent. We can reasonably assume that each population has a normal distribution because sampled data do not deviate much from a normal distribution. The samples are not random. The sample size is not large enough. The samples are random and independent. The sample data contain at least one outlier. The sample data contain no outliers. We cannot reasonably assume that each population has a normal distribution because samples do not have approximately a normal distributions. b. Use Excel to perform a two-sample $t$ test to test the claim that the true average number of minutes per charge for $\mathrm{Li}$-ion batteries is different from that for NiMH batteries. Based on your Excel work, answer the following questions. The observed difference in mean number of minutes per charge between Li-ion and NiMH batteries is (rounded to 4 decimal places) The $\mathrm{p}$-value for this test is (rounded to 4 decimal places) At 0.09 significance level, the correct conclusion for this test is There is enough evidence that the true average number of minutes per charge for $\mathrm{NiMH}$ batteries is different from that for Li-ion batteries. There is $\mathrm{NO}$ enough evidence that the true average number of minutes per charge for NiMH batteries is different from that for Li-ion batteries. None of these. c. Use the Excel Two Means Calculator in the course to obtain the margin of error to compute a $91\%$ confidence interval for difference in true average number of minutes per charge between $\mathrm{Li}$-ion and $\mathrm{NiMH}$ batteries. Using the result, fill in the blanks of the following statements rounded properly to 2 decimal places. Show your calculation of Lower and Upper limits on the Excel file The lower limit of $91\%$ confidence interval for difference in true average number of minutes per charge is The upper limit of $91\%$ confidence interval for difference in true average number of minutes per charge is Based on your lower and upper limits of a $91\%$ confidence interval for difference in true average number of minutes per charge, select the correct answer. Since the above confidence interval gives only positive values, we have $91\%$ confident that the true average number of minutes per charge for the Li-ion batteries is higher than that for the NiMH batteries. Since the above confidence interval gives only negative values, we have $91\%$ confident that the true average number of minutes per charge for the Li-ion batteries is smaller than that for the NiMH batteries. Since the above confidence interval contains zero, with $91\%$ confident, it is plausible that the true average number of minutes per charge for the Li-ion batteries is same as that for the NiMH batteries.