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.

Accepted Solution

Answer:Interval=170±7.068Option D is Correct which says "None of these is Correct"Step-by-step explanation:In order to find the interval we will use the following formula:Interval=X±[tex]\frac{Z*S}{\sqrt{n} }[/tex]Where:X is the average numberZ is the distributionS is the Standard Deviationn is the sample sizeIn our case:X=$170, S=$25.50, CI=0.95 or 95%In order to find Z we will find alpha/2alpha=1-0.95alpha=0.05alpha/2=0.025 or 2.5%From Cumulative Standard distribution table:Z at alpha/2 i.e 2.5%=1.960Now:Interval=170±[tex]\frac{1.960*25.50}{\sqrt{50} }[/tex]Interval=170±7.068Option D is Correct which says "None of these is Correct"