Mathematics, 14.05.2021 17:00, wickedskatboarder

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

Answers: 2

Show answers

Answers

answered: vavio3287

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:

H_0: p = 0.25

At the alternate hypothesis, we test that the proportion is above 25%, that is:

H_a: p 0.25

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

0.25 is tested at the null hypothesis:

This means that $\mu = 0.25, \sigma = \sqrt{0.25*0.75}$

Sample of 85 schools, 32 need a waiver:

This means that $n = 85, p = \frac{32}{85} = 0.3765$

Value of the test statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{0.3765 - 0.25}{\frac{\sqrt{0.25*0.75}}{\sqrt{85}}}$

z = 2.69

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%.

answered: Guest

My name is jeff bbdsbbsnnsnsnnsnsnsnsndndnndndnndnsns
For which rational expression is -2 an excluded value of x

answered: Guest

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

$4/2 = 2\\7/3.5=2\\8/4=2\\10/5=2$

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

$y=\frac{x}{2}$

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.