Question

Based on a sample of 55 people, the sample mean GPA was 3.33 with a standard deviation of 0.08

The test statistic is:
(to 2 decimals)

The p-value is: (to 2 decimals)

Answer 1

Using the t-distribution, it is found that the desired measures are given as follows:

• The test statistic is t = 2.78.

• The p-value is of 0.01.

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:

$\overline{x} = 3.33, \mu = 3.3, s = 0.08, n = 55$

Hence, the test statistic is:

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

$t = \frac{3.33 - 3.3}{\frac{0.08}{\sqrt{55}}}$

t = 2.78.

We are testing if the mean is different of a value, hence we have a two-tailed test. Using a t-distribution calculator, with 55 - 1 = 54 df and t = 2.78, the p-value is of 0.01.

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

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