How large a sample should be selected to provide a 95% confidence interval with a margin of error of 10? Assume that the population standard deviation is 40. (Round your answer up to the nearest whole number.)
Accepted Solution
A:
Answer:62Step-by-step explanation:Given that in a hypothesis 95% confidence interval had a margin of error of 10.Also given that the population standard deviation is known and equal to 40Since population standard deviation is known, for calculating confidence interval we can use Z critical value.For 95% confidence interval z critical value used is 1.96Margin of error = 1.96* std error = 10Hence standard error = [tex]\frac{10}{1.96} \\=5.102[/tex]Standard error is also equal to [tex]\frac{\sigma}{\sqrt{n} }\\ =\frac{40}{\sqrt{n} } =5.102\\\sqrt{n} =7.84\\n = 61.46=62[/tex]Sample size should be 62