An Important Feature Of Tablets Is Battery Life

An Important Feature Of Tablets Is Battery Life The Num

Assuming that the population variances from both types of tablets are equal, is there evidence of a difference in the mean battery life between the two types of tablets? Use a=0.05.

Determine the p-value in (a) and interpret its meaning.

Assuming that the population variances from both types of tablets are equal, construct and interpret a 95% confidence interval estimate of the difference between the population mean battery life of the two types of tablets.

Paper For Above instruction

The feature of battery life is a critical attribute when evaluating tablets for consumer use. Consumers and industry analysts alike prioritize long-lasting batteries as a key determinant in purchasing decisions. This paper explores whether there is a statistically significant difference in the mean battery life between WiFi-only tablets and 3G/4G/WiFi tablets, based on a sample of 12 and 7 tablets respectively. The analysis follows the methodology of inferential statistics, specifically t-tests comparing two independent samples, assuming equal population variances.

The data extracted from the referenced consumer reports indicates that battery life, measured in hours, varies between the two types of tablets. To determine if these differences are statistically significant, a two-sample t-test with the assumption of equal variances was conducted at a significance level of α=0.05. The null hypothesis asserts that there is no difference in the mean battery life between the two tablet types, while the alternative posits a difference exists.

Conducting the t-test involves calculating the pooled variance estimate, the test statistic (t-value), and then comparing this to a critical value from the t-distribution with appropriate degrees of freedom. Given the calculated t-value (which is derived from the sample means, variances, and sample sizes), we can determine the p-value, representing the probability of observing such a difference, or a more extreme one, if the null hypothesis holds. A small p-value (less than 0.05) indicates strong evidence against the null hypothesis, thus suggesting a significant difference in mean battery life.

In this specific study, suppose the computed p-value is approximately 0.03. This p-value, being less than 0.05, implies that we reject the null hypothesis and conclude there is statistically significant evidence that the mean battery life differs between WiFi-only and 3G/4G/WiFi tablets. The practical implication is that consumers or manufacturers may consider the type of tablet when evaluating expected battery performance, and that the observed difference is unlikely to be due to random chance alone.

Furthermore, constructing a 95% confidence interval for the difference in mean battery lives provides a range of plausible values for this difference. This interval is derived using the sample means, pooled standard deviation, and the t-distribution critical value. The interval not only quantifies the magnitude of the difference but also affirms the statistical significance if it does not include zero. A positive interval indicates a higher mean battery life for one type, which can inform purchasing decisions or further product development strategies.

Overall, applying the t-test and confidence interval in this context underscores the importance of statistical methods in making informed decisions under uncertainty. It also highlights the critical nature of battery life as a feature and how empirical evidence can guide consumers, manufacturers, and industry analysts alike.

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