A survey was conducted that asked 997 people how many books they had read in the past year. Results indicated that x overbar equals 13.2 books and sequels 18.9 books. Construct a 95 ​% confidence interval for the mean number of books people read. Interpret the interval.

Answer:The 95% confidence interval would be given by (12.03;14.37)    Step-by-step explanation:1) Previous concepts A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval". The margin of error is the range of values below and above the sample statistic in a confidence interval. Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean". [tex]\bar X=13.2[/tex] represent the sample mean   [tex]\mu[/tex] population mean (variable of interest) s=18.9 represent the sample standard deviation n=997 represent the sample size  2) Calculate the confidence intervalThe confidence interval for the mean is given by the following formula: [tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1) In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by: [tex]df=n-1=997-1=996[/tex] Since the confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.025,996)".And we see that [tex]t_{\alpha/2}=1.96[/tex] and this value is exactly the same for the normal standard distribution and makes sense since the sample size is large enough to approximate the t distribution with the normal standard distribution. Now we have everything in order to replace into formula (1): [tex]13.2-1.96\frac{18.9}{\sqrt{997}}=12.03[/tex]    [tex]13.2+1.96\frac{18.9}{\sqrt{997}}=14.37[/tex] So on this case the 95% confidence interval would be given by (12.03;14.37)