Respuesta :
Answer:
The 98% confidence interval for the true difference between testing averages for students using Method 1 and students using Method 2 is (5.20, 7.60).
Step-by-step explanation:
The (1 - α)% confidence interval for the difference between two population mean when the population standard deviations are known is:
[tex]CI=(\bar x_{1}-\bar x_{2})\pm z_{\alpha/2}\times \sqrt{\frac{\sigma^{2}_{1}}{n_{1}}+\frac{\sigma^{2}_{2}}{n_{2}}}[/tex]
The information provided is:
[tex]\bar x_{1}=82.9\\\sigma_{1}=7.97\\n_{1}=293\\\bar x_{2}=76.5\\\sigma_{2}=6.66\\n_{2}=282[/tex]
The critical value of z for 98% confidence interval is:
[tex]z_{\alpha/2}=z_{0.02/2}=z_{0.0}=2.33[/tex]
*Use a z-table for the critical value.
Compute the 98% confidence interval for the difference between two population means as follows:
[tex]CI=(\bar x_{1}-\bar x_{2})\pm z_{\alpha/2}\times \sqrt{\frac{\sigma^{2}_{1}}{n_{1}}+\frac{\sigma^{2}_{2}}{n_{2}}}[/tex]
[tex]=(82.9-76.5)\pm 1.96\times \sqrt{\frac{7.97^{2}}{293}+\frac{6.66^{2}}{282}}[/tex]
[tex]=6.4\pm 1.199\\=(5.201, 7.599)\\\approx(5.20, 7.60)[/tex]
Thus, the 98% confidence interval for the true difference between testing averages for students using Method 1 and students using Method 2 is (5.20, 7.60).
