14\ntype the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction…

14\ntype the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar(s).\nthe mean score on a biology exam taken by all undergraduate students in a college in a particular year is 67.8 with a standard deviation of 11.5\nthe standard error of the mean for a sample of 70 students is , and the margin of error of the mean is (round off your answers to the nearest hundredth.)

14\ntype the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar(s).\nthe mean score on a biology exam taken by all undergraduate students in a college in a particular year is 67.8 with a standard deviation of 11.5\nthe standard error of the mean for a sample of 70 students is , and the margin of error of the mean is (round off your answers to the nearest hundredth.)

Answer

Answer:

Standard error of the mean: 1.37, Margin of error of the mean: 2.69

Explanation:

Step1: Recall standard - error formula

The formula for the standard error of the mean ($SE$) is $SE=\frac{\sigma}{\sqrt{n}}$, where $\sigma$ is the population standard deviation and $n$ is the sample size. Given $\sigma = 11.5$ and $n = 70$. $SE=\frac{11.5}{\sqrt{70}}\approx\frac{11.5}{8.37}\approx1.37$

Step2: Recall margin - of - error formula

For a 95% confidence interval (common in statistics when no confidence level is specified), the margin of error ($ME$) for the mean is $ME = z\times SE$, where the $z$ - score for a 95% confidence interval is approximately $z = 1.96$. $ME=1.96\times1.37\approx2.69$