task 4\ndetermining whether a difference is statistically significant\nyou calculated the standard deviation…
task 4\ndetermining whether a difference is statistically significant\nyou calculated the standard deviation of the sample mean differences to be 0.69. you also calculated the sample mean difference to be 1.74. 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.\npart a\nquestion\ndetermine the 95% confidence interval for the difference of the sample means. then complete the statements.\nthe 95% confidence interval is to.\nthe value of the sample mean difference is 1.74, which falls the 95% confidence interval.
Answer
Explanation:
Step1: Recall the z - value for 95% confidence interval
For a 95% confidence interval, the z - value $z = 1.96$.
Step2: Calculate the margin of error
The margin of error $E=z\times\sigma_{\bar{x}_1 - \bar{x}2}$, where $\sigma{\bar{x}_1 - \bar{x}_2}=0.69$ is the standard deviation of the sample - mean differences. So $E = 1.96\times0.69=1.96\times\frac{69}{100}=1.3524$.
Step3: Calculate the lower and upper bounds of the confidence interval
The lower bound $L=\bar{x}_1-\bar{x}_2 - E$ and the upper bound $U=\bar{x}_1-\bar{x}_2 + E$. Since $\bar{x}_1-\bar{x}_2 = 1.74$, the lower bound $L=1.74 - 1.3524 = 0.3876$ and the upper bound $U=1.74+1.3524 = 3.0924$.
Answer:
The 95% confidence interval is $0.39$ to $3.09$. The value of the sample mean difference is 1.74, which falls within the 95% confidence interval.