![314180](/avatars/7488.jpg)
314180
14.05.2021 •
Mathematics
In Texas, state law requires that for regular classroom settings in elementary grades K-4, the student-to-teacher ratio can be no more than 22:1. Schools may request a waiver to exceed this ratio. A hypothesis test is performed to determine if the proportion of schools needing such a waiver is above 25% using a random sample of 85 schools and a significance level of 5%. What conclusion should be drawn if 32 of the schools surveyed need a waiver to exceed the required student-to-teacher ratio
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Ответ:
Step-by-step explanation:
A hypothesis test is performed to determine if the proportion of schools needing such a waiver is above 25%
At the null hypothesis, we test that the proportion is of 25%, that is:
At the alternate hypothesis, we test that the proportion is above 25%, that is:
The test statistic is:
In which X is the sample mean,
is the value tested at the null hypothesis,
is the standard deviation and n is the size of the sample.
0.25 is tested at the null hypothesis:
This means that![\mu = 0.25, \sigma = \sqrt{0.25*0.75}](/tpl/images/1324/0567/fd34a.png)
Sample of 85 schools, 32 need a waiver:
This means that![n = 85, p = \frac{32}{85} = 0.3765](/tpl/images/1324/0567/96442.png)
Value of the test statistic:
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion above 0.3765, which is 1 subtracted by the p-value of z = 2.69.
Looking at the z-table, z = 2.69 has a p-value of 0.9964
1 - 0.9964 = 0.0036
The p-value of the test is 0.0036 < 0.05, thus we reject the null hypothesis that the proportion is 25%, and accept the alternate hypothesis that the proportion of schools needing such a waiver is above 25%.
Ответ:
Answer is in the photo. I couldn't attach it here, but uploaded it to a file hosting. link below! Good Luck!
cutt.ly/4zZs6GM