A poll conducted in 1972 asked 1003 people, " During the past year, about how many books did you read either all or part of the way through?" Results of the survey indicated that x-bar=18.9 books and s=1

Question

A poll conducted in 1972 asked 1003 people, " During the past year, about how many books did you read either all or part of the way through?" Results of the survey indicated that x-bar=18.9 books and s=1

9.9 books.

A)Construct a 95% confidence interval for the mean number of books read either all or part of during the preceding year. Interpret the interval.

____,_____

Answer 1

This is the same type of problem as your previous post on confidence intervals.

Use the same formula with these values:

n = 1003
mean = 18.9
sd = 19.9

I'll let you take it from here.

Answer 2

MathGuru, how do i determine the z-score for this one?

Answer 3

95% confidence = 1.96

You can determine these values by using a z-table. Make a note of the more commonly used confidence intervals so you don't have to constantly refer to the table. It will help you remember them too.

Answer 4

To construct a confidence interval for the mean number of books read, we can use the formula:

Confidence Interval = x̄ ± (z * (s/√n))

Where:
x̄ = Sample mean (18.9 books)
s = Sample standard deviation (9.9 books)
n = Sample size (1003 people)
z = Z-score for the desired confidence level

Since we want to construct a 95% confidence interval, we need to find the corresponding z-score. We can use a standard normal distribution table or a calculator to find that the z-score for a 95% confidence level is approximately 1.96.

Substituting these values into the formula, we get:

Confidence Interval = 18.9 ± (1.96 * (9.9/√1003))

Calculating this expression, we find the lower and upper limits of the confidence interval for the mean number of books read, which are:

Lower limit = 18.9 - (1.96 * (9.9/√1003))
Upper limit = 18.9 + (1.96 * (9.9/√1003))

Now we can calculate these values:

Lower limit ≈ 18.38
Upper limit ≈ 19.42

Therefore, the 95% confidence interval for the mean number of books read during the preceding year is approximately 18.38 to 19.42 books.

Interpretation:
This means that we can be 95% confident that the true mean number of books read by people during the past year falls within the range of 18.38 to 19.42 books.