Question

Based on a sample of 20 people, the sample mean GPA was 3.25 with a standard deviation of 0.02

The test statistic is:
(to 2 decimals)

The critical value is:
(to 2 decimals)

Answer 1

Using the t-distribution, it is found that:

• The test statistic is t = -11.18.

• The critical value is $t^{\ast} = \pm 2.093$.

What are the hypotheses tested?

At the null hypothesis, it is tested if the mean GPA of the students is of 3.3, that is:

$H_0: \mu = 3.3$

At the alternative hypothesis, it is tested if the mean GPA is different than 3.3, hence:

$H_1: \mu \neq 3.3$.

What is the test statistic?

The test statistic is given by:

$t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}$

The parameters are:

• $\overline{x}$ is the sample mean.

• $\mu$ is the value tested at the null hypothesis.

• s is the standard deviation of the sample.

• n is the sample size.

The values of the parameters are given as follows:

$\overline{x} = 3.25, \mu = 3.3, s = 0.02, n = 20$

Hence, the test statistic is given by:

$t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}$

$t = \frac{3.25 - 3.3}{\frac{0.02}{\sqrt{20}}}$

t = -11.18.

We are testing if the mean is different of a value, hence we have a two-tailed test, with 20 - 1 = 19 df and a standard significance level of 0.05, hence, using a t-distribution calculator, the critical value is $t^{\ast} = \pm 2.093$.

More can be learned about the t-distribution at https://brainly.com/question/16162795

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