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melisa1 [442]
3 years ago
8

A recent Gallup poll asked 1006 Americans, "During the past year, about how many books, either hardcover or paperback, did you r

ead either all or part of the way through?" Results of the survey indicated that x = 13.4 books and s = 16.6 books. Construct a 99% confidence interval for the mean number of books Americans read either all or part of during the preceding year. Interpret that interval.
Mathematics
1 answer:
tekilochka [14]3 years ago
5 0

Answer:

The required interval is [12.0519,14.7481]

Step-by-step explanation:

Consider the provided information.

It is given that:

n = 1006, mean = 13.4 and s = 16.6  

We need to construct a 99% confidence interval.

That means α = 0.01 and α/2 = 0.005

Z_{\alpha/2}=2.5758

First find the standard error as shown:

SE=\frac{16.6}{\sqrt{1006}} =0.5234

Now to calculate confidence interval calculate: Mean \pm Z_{\alpha/2} \times SE

=13.4 \pm 2.5758 \times 0.5234

=13.4 \pm 1.34817372

[12.0519,14.7481]

Hence, the required interval is [12.0519,14.7481]

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