Respuesta :
Using the z-distribution, it is found that since the test statistic is more than the critical value for the right-tailed test, this is evidence of a change in education level among mothers.
What are the hypothesis tested?
At the null hypothesis, it is tested if the proportion is still the same, that is:
[tex]H_0: p = 0.31[/tex]
At the alternative hypothesis, it is tested if it has increased, that is:
[tex]H_1: p > 0.31[/tex]
What is the test statistic?
It is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
- [tex]\overline{p}[/tex] is the sample proportion.
- p is the proportion tested at the null hypothesis.
- n is the sample size.
In this problem, the parameters are:
[tex]\overline{p} = 0.32, p = 0.31, n = 8368[/tex]
Hence, the value of the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.32 - 0.31}{\sqrt{\frac{0.31(0.69)}{8368}}}[/tex]
[tex]z = 1.98[/tex]
What is the decision?
Considering a right-tailed test, as we are testing if the proportion is greater than a value, and the standard significance level of 0.05, the critical value is of [tex]z^{\ast} = 1.645[/tex].
Since the test statistic is more than the critical value for the right-tailed test, this is evidence of a change in education level among mothers.
More can be learned about the z-distribution at https://brainly.com/question/16313918
