Question

Suppose the class sizes in high schools in a major public school district are normally distributed with an unknown population mean and standard deviation. If a random sample of 28 high school classes is taken to estimate the mean class size, use a calculator to find the t-score that should be used to find a 90% confidence interval estimate for the population mean.

Answer 1

1.703

Explanation:

The reason we try to find t score is because the sample size is below 30, meaning the sample size is small

Hence:

Step 1

We find the degree of freedom

The Degrees of freedom = Number of samples - 1

The random number of samples = 28

= 28 - 1

= 27

Step 2

Using a t score table or t score calculator, we can obtain the t score value for a 90% confidence interval and degree of freedom of 27

90% confidence interval =

10% significance level = 0.10 for two tails or 0.1/2 = 0.05 for one tail

Hence: t90 = 1.703