Answer:
The 90% confidence interval for the difference in mean number of days meeting the goal is (4.49, 18.11).
Step-by-step explanation:
The (1 - α)% confidence interval for the difference between two means is:
[tex]CI=\bar x_{1}-\bar x_{2}\pm z_{\alpha/2}\times SE_{\text{diff}}[/tex]
It is provided that:
[tex]\bar x_{1}=45\\\bar x_{2}=33.7\\SE_{\text{diff}} =4.14\\\text{Confidence Level}=90\%[/tex]
The critical value of z for 90% confidence level is,
z = 1.645
*Use a z-table.
Compute the 90% confidence interval for the difference in mean number of days meeting the goal as follows:
[tex]CI=\bar x_{1}-\bar x_{2}\pm z_{\alpha/2}\times SE_{\text{diff}}[/tex]
[tex]=45-33.7\pm 1.645\times 4.14\\\\=11.3\pm 6.8103\\\\=(4.4897, 18.1103)\\\\\approx (4.49, 18.11)[/tex]
Thus, the 90% confidence interval for the difference in mean number of days meeting the goal is (4.49, 18.11).