Respuesta :
Answer:
The 90% confidence interval for the difference between means is (4.189, 8.011).
The point estimate is the difference between sample means and has a value of Md=6.1.
Step-by-step explanation:
We have to calculate a 90% confidence interval for the difference between means.
The sample 1 (American students), of size n1=12 has a mean of 69.4 and a standard deviation of 2.79.
The sample 2 (non-American students), of size n2=17 has a mean of 63.3 and a standard deviation of 3.22.
The difference between sample means is Md=6.1.
[tex]M_d=M_1-M_2=69.4-63.3=6.1[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{2.79^2}{12}+\dfrac{3.22^2}{17}}\\\\\\s_{M_d}=\sqrt{0.649+0.61}=\sqrt{1.259}=1.12[/tex]
The critical t-value for a 90% confidence interval is t=1.703.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_{M_d}=1.703 \cdot 1.12=1.911[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M_d-t \cdot s_{M_d} = 6.1-1.911=4.189\\\\UL=M_d+t \cdot s_{M_d} = 6.1+1.911=8.011[/tex]
The 90% confidence interval for the difference between means is (4.189, 8.011).
