Suppose we want a 90% confidence interval for the average amount spent on books by freshmen in their first year at a major unive
rsity. The interval is to have a margin of error of no more than $2. Based on last year's book sales, we estimate that the standard deviation of the amount spent will be close to $30. The number of observations required is closest to: (a) 25.
(b) 30.
(c) 608.
(d) 609.
(e) 865.
Step-by-step explanation: We can construct a (1 - α) % confidence interval for mean by using the formulae below.
u = x + critical value × (standard deviation /√n)
Where x = sample mean and n is the sample size.
The critical value that we are going to use (either z or t critical values) depends on the sample size.
If n > 29 we make use of a z test and if n < 29 we make use of a t test.
Also when using a z test we will (sometimes) make use of the population standard deviation.
And when using a t test, we make use of the sample standard deviation.
"Based on last year's book sales, we estimate that the standard deviation of the amount spent will be close to $30"
Judging by the sentence above, we can see that last year books sales is a fraction of several years of book sales, hence the value of standard deviation given is a sample standard deviation.
Since we are making use of a sample standard deviation, we will be using a t test for our critical value and hence sample size must be less than 29.
According to the Pythagorean theorem, the square of the hypotenuse (the longest side) of a right-angled triangle equals to the sum of the squares of the other two sides. In this case, the ladder is the hypotenuse, which equals to the distance between the bottom of the ladder and the tree + the distance we want to find (x): 5² + x² = 13² 25 + x² = 169 x² = 144 x = √144 = 12. The distance between the ground and the top of the ladder is 12 ft.
