Question

Use the standard normal distribution or the​ t-distribution to construct a 95​% confidence interval for the population. In a recent​ season, the population standard deviation of the yards per carry for all running backs was 1.27. The yards per carry of 25 randomly selected running backs are shown below. Assume the yards per carry are normally distributed. 1.9 2.7 5.8 4.9 7.4 6.6 6.1 3.4 3.8 1.3 1.6 4.9 2.8 6.8 5.1 6.1 3.1 6.8 4.9 6.6 4.3 7.3 5.6 7.3 3.9

Answer 1

sample : 1.9 2.7 5.8 4.9 7.4 6.6 6.1 3.4 3.8 1.3 1.6 4.9 2.8 6.8 5.1 6.1 3.1 6.8 4.9 6.6 4.3 7.3 5.6 7.3 3.9

95​% confidence interval : [mean-1.96*sd/(n^0.5) , mean+1.96*sd/(n^0.5)]

= [4.84-1.96*1.27/(25^0.5) , 4.84+1.96*1.27/(25^0.5)]

95​% confidence interval for sample mean= [ 4.34216 , 5.33784 ]

(please UPVOTE)