Question

Steve wants to estimate the average ACT scores of students graduated from his high school. He randomly selected 30 students from an email list and ask them to provide the information. Of them 15 students replied and the summary of the ACT score is as below: Mean STD Min Max 21.6 8.4 14 32 (1) (2pts) In this study, what is the sample of the study? What is the population of the study? (2) (5pts) Steve is told that the population standard deviation for ACT score is 7.0 for his high school, and suppose we can apply Central Limit Theorem for the study, estimate the average ACT score of all his high school graduates with 98% confidence level. (No points will be given without necessary steps).

Answer 1

Answer:

I this study the sample is 30 students from an email list

and population is 15 students whos graduated from his school.

2)

Standard deiation =7.0 n=15

alpha=1-0.98

=0.02

critical z value(two tailed) for 98% confidence level is: z=2.326

Margin of error= z*(s.d/SQRT(n))

=2.326 (7.0/sqrt(15)) = 4.203

98% confidence interval for population mean =21.6+/-4.203

=(25.803, 17.397)

3)

if population standard deviation is not known,we will use t distribution.

df=15-1=14 alpha = 0.01

t=tinv(0.05,14)=2.977

Margin of error=2.977*(8.4/sqrt(15))

= 6.456

99%confidence interval for population mean =21.6+/-6.456

=(28.056, 15.144)