Asurvey 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.

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".

represent the sample mean  

population mean (variable of interest)

s=18.9 represent the sample standard deviation

n=997 represent the sample size  

2) Calculate the confidence interval

The confidence interval for the mean is given by the following formula:

  (1)

In order to calculate the critical value we need to find first the degrees of freedom, given by:

Since the confidence is 0.95 or 95%, the value of and , 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 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):

So on this case the 95% confidence interval would be given by (12.03;14.37)    

49%

step-by-step explanation:

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