SOLUTION: Hello, i am having a bit of a problem that i am struggling with. I was wondering can you please break the problem down? A survey was conducted that asked 1004 people how many book

Question 1139503: Hello, i am having a bit of a problem that i am struggling with. I was wondering can you please break the problem down? A survey was conducted that asked
1004 people how many books they had read in the past year. Results indicated that
x overbar
x
equals
=
12.5
12.5 books and s
equals
=
16.6
16.6 books. Construct a
99
99% confidence interval for the mean number of books people read. Interpret the interval.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Given info:

is the sample size

is the sample mean

is the sample standard deviation

At 99% confidence, the z critical value is approximately z = 2.576
This can be found either through a table or a calculator. I used this table to get the value (Go to the bottom of the table, look at the row that starts with Z and the column that has 99% at the bottom; you should see 2.576 just above the "99%".)

note: we don't know the population standard deviation (sigma) so we should use the T distribution; however, since n = 1004 is so large, this means we can use an approximation of the normal Z distribution instead. For more info, check out the Central Limit Theorem. So this is why I'm using Z instead of T. For large values of n, computing the critical T value is often not possible with a table (though a calculator can handle it just fine). Often anything over n = 30 is considered "large".

-----------------------------------

Using the values mentioned, the lower boundary of the confidence interval is:

And the upper boundary is:

--------------------------------------------------------------------------------------
Answer:

The 99% confidence interval is (11.2, 13.8) which can be written as

Interpretation: We are 99% confident that the population parameter is in this interval. So we are 99% confident that the population mean of the number of books read is somewhere between 11.2 and 13.8 books. If you took 100 repeated samples and created confidence intervals from them, then about 99 of them should contain the true parameter mu.

Be careful not to say that "there is a 99% chance that the parameter mu is in the interval (11.2, 13.8)" as this is misleading and often a trick/trap that your teacher may set up to make sure the student is paying attention.

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