Question

Now assume that a larger sample of 64 student scores is taken. The sample has a mean score of 29.5 and a standard deviation of 3.2. If you were to construct a 95% confidence interval for the ACT scores of this high school class, what would the lower boundary of the interval be?

You've constructed your confidence interval. Statistically, what does this confidence interval tell us? Can it be used to tell us the true population value of the mean ACT score for this high school class? Why or why not?

Answer 1

Solution:

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

Xbar = 29.5

S = 3.2

n = 64

df = n – 1 = 63

Confidence level = 95%

Critical t value = 1.9983

(by using t-table)

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 29.5 ± 1.9983*3.2/sqrt(64)

Confidence interval = 29.5 ± 1.9983*0.4

Confidence interval = 29.5 ± 0.7993

Lower limit = 29.5 - 0.7993 = 28.7007

Upper limit = 29.5 + 0.7993 = 30.2993

Confidence interval = (28.7007, 30.2993)

What would the lower boundary of the interval be?

Answer: 28.7007

Statistically, what does this confidence interval tell us?

This confidence interval tells us that the population mean will lies between 28.7007 and 30.2993.

Can it be used to tell us the true population value of the mean ACT score for this high school class?

Yes, it can be used to tell us the true population value of the mean ACT score for this high school class, because sample is adequate and assume to be random such that sampling distribution follows normal distribution.