Question

Steve wants to know what the average ACT scores of students graduated from his high school is. He randomly selected 25 students from an email list and asked them to provide the information. Of them 20 students replied and the summary of the ACT score is as below: Sample size Mean STD Min Max 20 21.5 5.7 15 26 (1) What is the sample of the study and what is the population of the study? (2) Steve is told that the population standard deviation for ACT score is 4.6 for his high school, estimate the population average ACT score of his high school graduates with 86% confidence level. (3) If the population standard deviation is not provided, estimate the population average ACT score of his high school graduates with 95% confidence level.

Answer 1

[a]. sample is 25 randomly selected students

also population is all students

[b]. (20.0, 23.0)

[c]. (8.8, 24.2)

Explanation:

here is a step by step process to solving this, i hope you find this helpful.

1). The population is all students who graduated from his school while the

sample is 25 randomly selected students from the email list

2). given alpha = 1-0.86=0.14

critical z value(two tailed) for 86% confidence level is:

z=normsinv(0.07) or normsinv(0.93)=1.476

Margin of error=1.476*(4.6/SQRT(20))=1.5

86% confidence interval for population mean

=21.5+/-1.5

=(20.0, 23.0)

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

df=20-1=19

t*=tinv(0.05,19)=2.093

Margin of error=2.093*(5.7/sqrt(20))=2.7

95% confidence interval for population mean

=21.5+/-2.7

=(18.8, 24.2)

cheers i hope this helps!!!!