The heights of a random sample of 50 college students showed a mean of 167.4 centimeters and a standard deviation of 6.9 centimeters. ​(a) Construct a 98​% confidence interval for the mean height of all college students. ​(b) What can we assert with 98​% confidence about the possible size of our error if we estimate the mean height of all college students to be 167.4 ​centimeters?

Accepted Solution

Answer: a) (165.13, 169.67), b) Error = 2.274.Step-by-step explanation:Since we have given thatMean = 167.4 cmStandard deviation = 6.9 cmN = 50we need to construct 98% confidence interval.So, Interval would be [tex]\bar{x}\pm2.33\dfrac{\sigma}{\sqrt{n}}\\\\=167.4\pm 2.33\times \dfrac{6.9}{\sqrt{50}}\\\\=167.4\pm 2.274\\\\=(167.4-2.274,167.4+2.274)\\\\=(165.13,169.67)[/tex]b) Margin of error would be [tex]z\times \dfrac{\sigma}{\sqrt{n}}\\\\=2.33\times \dfrac{6.9}{\sqrt{50}}\\\\=2.274[/tex]Hence, a) (165.13, 169.67), b) Error = 2.274.