The sample size of the confidence interval test of a proportion is considered appropriately large if np and n(1 - p) > 5.
<span>Given that Arthur is conducting a study on the preferred study options of students from East County College and that 25% of those surveyed preferred studying abroad. Thus, p = 25% = 0.25 and 1 - 0.25 = 0.75
np = 32(0.25) = 8
n(1 - p) = 32(0.75) = 24
Thus, the sample size is appropriately large.
The margin of error is given by:
</span>
<span>
The </span>
for 95% confidence interval is 1.96
Thus, the margin of error is given by:
Therefore, the statement that holds true is "a<span>s the sample size is appropriately large, the margin of error is ±0.15".</span>
<span>Given that Arthur is conducting a study on the preferred study options of students from East County College and that 25% of those surveyed preferred studying abroad. Thus, p = 25% = 0.25 and 1 - 0.25 = 0.75
np = 32(0.25) = 8
n(1 - p) = 32(0.75) = 24
Thus, the sample size is appropriately large.
The margin of error is given by:
</span>
<span>
The </span>
Thus, the margin of error is given by:
Therefore, the statement that holds true is "a<span>s the sample size is appropriately large, the margin of error is ±0.15".</span>