Answer:
The minimum sample size required to estimate the required proportion is 176 students.
Step-by-step explanation:
We are given the following data:
Guessed sample proportion = p = 0.34
Margin of Error = m = 0.07
Confidence Interval = 95%
We need to calculate the minimum sample size required. Since we are dealing with proportions, we will use the formulas of one-sample z-test for population proportions, according to which:
[tex]m=z \times \sqrt{\frac{p(1-p)}{n} }[/tex]
The value of z can be seen from the z-tables or z-calculators. The z value for 95% confidence interval comes out to be 1.96
Substituting the values in the above formula gives us:
[tex]0.07=1.96 \times \sqrt{\frac{0.34(1-034)}{n} } \\\\ 0.07=1.96 \times \frac{\sqrt{0.34(0.66)}}{\sqrt{n}}\\\\\sqrt{n} =\frac{1.96}{0.07} \times \sqrt{0.34 \times 0.66}\\\\ n=(\frac{1.96}{0.07})^{2} \times 0.34 \times 0.66\\\\ n=175.93[/tex]
Thus, the minimum sample size required to estimate the required proportion is 176 students.
