Question

A sample of 50 students was taken from the local university. These students spent an average of $170 on books this semester, with a standard deviation of $25.50. Which of the following could you say with 95% confidence was the average spent on books by these 50 students? A. $170 plus or minus $3.46 B. $170 plus or minus $5.95 C. $170 plus or minus $8.42 D. None of these is correct.

Answer 1

Interval=170±7.068

Option D is Correct which says "None of these is Correct"

Explanation:

In order to find the interval we will use the following formula:

Interval=X±
`(Z*S)/(√(n) )`

Where:

X is the average number

Z is the distribution

S is the Standard Deviation

n is the sample size

In our case:

X=$170, S=$25.50, CI=0.95 or 95%

In order to find Z we will find alpha/2

alpha=1-0.95

alpha=0.05

alpha/2=0.025 or 2.5%

From Cumulative Standard distribution table:

Z at alpha/2 i.e 2.5%=1.960

Now:

Interval=170±
`(1.960*25.50)/(√(50) )`

Interval=170±7.068

Option D is Correct which says "None of these is Correct"