Answer:
A. The value of the sample proportion is 0.4
B. The standard error of the sample proportion is 0.02619
C. 0.3487 ≤ p ≤ 0.4513
Step-by-step explanation:
The value of the sample proportion p' is calculated as:
[tex]p'=\frac{x}{n} = \frac{140}{350}=0.4[/tex]
Where x is the number of success in the sample or the number of students that use a laptop in class to take notes and n is the size of the sample or 350 students.
On the other hand, the standard error SE of the sample proportion is calculated as:
[tex]SEs=\sqrt{\frac{p'(1-p')}{n}}[/tex]
so, replacing the values, we get:
[tex]SE=\sqrt{\frac{0.4(1-0.4)}{350}}=0.02619[/tex]
Finally, an approximate 95% confidence interval for the true proportion p is calculate as:
[tex]p'-z_{\alpha/2} SEs \leq p\leq p'+z_{\alpha/2} SEs[/tex]
Where 1-α is equal to 95%, so [tex]z_{\alpha/2}[/tex] is equal to 1.96. Then, replacing the values we get:
[tex]0.4-1.96(0.02619) \leq p\leq 0.4+1.96(0.02619) [/tex]
0.4 - 0.0513 ≤ p ≤ 0.4 + 0.0513
0.3487 ≤ p ≤ 0.4513
