testing the mean

Question

Based on a sample of 45 people, the sample mean GPA was 2.84 with a standard deviation of 0.08

The critical value is...

Can you demonstrate step by step how to find the critical value?

the test statistic is 3.35

Answer 1

Here's a (more) written out version:

When the sampling distribution of the statistic is normal or nearly normal, the critical value can be expressed as a t score or as a z-score. To find the critical value, follow these steps.

1) Compute alpha (α): α = 1 - (confidence level / 100)

2) Find the critical probability (p*): p* = 1 - α/2

3) To express the critical value as a z-score, find the z-score having a cumulative probability equal to the critical probability (p*).

4) To express the critical value as a t statistic, follow these steps:

Find the degrees of freedom (df). Often, df is equal to the sample size minus one.

The critical t statistic (t*) is the t statistic having degrees of freedom equal to df and a cumulative probability equal to the critical probability (p*).

Answer 2

As the sample size is > 30, we will use a 2-tailed Z-distribution

The critical value depends on the confidence level

At 95% confidence level, you can find the Z-score on a TI-84 as follows

2nd vars

invnorm

area = 0.975 (0.95 + (1-0.95)/2)

mean = 0

sd = 1

paste

giving Z = 1.96 (so critical value = 1.96 and -1.96)