Answer:
c) there is 95% confidence that the population mean number of books read is between 13.77 and 15.83.
Step-by-step explanation:
We have to calculate a 95% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=14.8.
The sample size is N=1003.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
The degrees of freedom for this sample size are:
The t-value for a 95% confidence interval and 1002 degrees of freedom is t=1.96.
The margin of error (MOE) can be calculated as:
Then, the lower and upper bounds of the confidence interval are:
The 95% confidence interval for the mean number of books read is (13.77, 15.83).
This indicates that there is 95% confidence that the true mean is within 13.77 and 15.83. Also, that if we take multiples samples, it is expected that 95% of the sample means will fall within this interval.