Question

HELP ASAP PLEASE
A teacher wants to compare scores on a geology exam for two classes. The difference between the sample means is 21.4. If the standard deviation of the distribution of the difference between sample means is 16.66, and she is testing the hypothesis at the 68% confidence level, which statement is true?
A.
The difference between the two means is significant, so the null hypothesis must be accepted.
B.
The difference between the two means is not significant, so the alternative hypothesis must be rejected.
C.
The difference between the two means is not significant, so the null hypothesis must be rejected.
D.
The difference between the two means is not significant, so the alternative hypothesis must be accepted.
E.
The difference between the two means is significant, so the alternative hypothesis must be accepted.

Answer 1

Using the z-distribution, it is found that the correct option is:

• E.  The difference between the two means is significant, so the alternative hypothesis must be accepted.

Hypothesis:

At the null hypothesis, it is tested if there is no difference, that is, the mean is of 0, hence:

$H_0: \mu = 0$

At the alternative hypothesis, it is tested if there is a difference, that is, the mean is different of 0, hence:

$H_1: \mu \neq 0$

The test statistic is given by:

$z = \frac{\overline{x} - \mu}{s}$

In which:

• $\overline{x}$ is the sample mean.

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

• s is the standard error.

For this problem, the parameters are: $\overline{x} = 21.4, \mu = 0, s = 16.66$.

Hence, the value of the test statistic is:

$z = \frac{\overline{x} - \mu}{s}$

$z = \frac{21.4 - 0}{16.66}$

$z = 1.28$

Using a z-distribution calculator, the critical value for a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.32, is of $z^{\ast} = 0.9945$.

Since the absolute value of the test statistic is greater than the absolute value of the critical value for the two-tailed test, the difference is significant, so the alternative hypothesis must be accepted, and option E is correct.

You can learn more about the use of the z-distribution to test an hypothesis at  brainly.com/question/16313918