determining whether a difference is statistically significant. you calculated the standard deviation of the…

determining whether a difference is statistically significant. you calculated the standard deviation of the sample - mean differences to be 0.61. you also calculated the sample - mean difference to be 1.54. now youll determine whether the difference is significant. for the purpose of constructing the confidence interval, assume that theres no difference between the population means. part a. question. determine the 95% confidence interval for the difference of the sample means. then complete the statements. the 95% confidence interval is to ; the value of the sample - mean difference is 1.54 which falls the 95% confidence interval. part b. question. which statement is true about the difference of the sample means? the difference of the sample means is not statistically significant because it falls outside the 5% significance level. the difference of the sample means is not statistically significant because it falls within the 5% significance level. the difference of the sample means is statistically significant because it falls within the 5% significance level.

determining whether a difference is statistically significant. you calculated the standard deviation of the sample - mean differences to be 0.61. you also calculated the sample - mean difference to be 1.54. now youll determine whether the difference is significant. for the purpose of constructing the confidence interval, assume that theres no difference between the population means. part a. question. determine the 95% confidence interval for the difference of the sample means. then complete the statements. the 95% confidence interval is to ; the value of the sample - mean difference is 1.54 which falls the 95% confidence interval. part b. question. which statement is true about the difference of the sample means? the difference of the sample means is not statistically significant because it falls outside the 5% significance level. the difference of the sample means is not statistically significant because it falls within the 5% significance level. the difference of the sample means is statistically significant because it falls within the 5% significance level.

Answer

Explanation:

Step1: Recall confidence - interval formula for sample - mean difference

For a 95% confidence interval, the critical value $z$ (assuming large - sample or normal population with known variance) is approximately $z = 1.96$. The formula for the confidence interval of the difference in sample means is $\bar{x}_1-\bar{x}2\pm z\sigma{\bar{x}_1 - \bar{x}2}$, where $\sigma{\bar{x}_1 - \bar{x}2}$ is the standard deviation of the sample - mean differences. Here, $\sigma{\bar{x}_1 - \bar{x}_2}=0.68$ and $\bar{x}_1-\bar{x}_2 = 1.54$.

Step2: Calculate the lower limit of the confidence interval

Lower limit $=1.54-1.96\times0.68=1.54 - 1.3328=0.2072$.

Step3: Calculate the upper limit of the confidence interval

Upper limit $=1.54 + 1.96\times0.68=1.54+1.3328 = 2.8728$.

The 95% confidence interval is $0.2072$ to $2.8728$. The value of the sample - mean difference is $1.54$ which falls within the 95% confidence interval.

For Part B: The difference of the sample means is statistically significant because it falls outside the 5% significance level (equivalent to being within the 95% confidence interval).

Answer:

Part A: The 95% confidence interval is $0.2072$ to $2.8728$; the value of the sample - mean difference is $1.54$ which falls within the 95% confidence interval. Part B: The difference of the sample means is statistically significant because it falls within the 95% significance level.