Mathematics, 07.06.2020 02:02 mikecampbellashleyca

In a certain school district, it was observed that 24% of the students in the element schools were classified as only children (no siblings). However, in the special program for talented and gifted children, 119 out of 415 students are only children. The school district administrators want to know if the proportion of only children in the special program is significantly different from the proportion for the school district. Test at the α=0.05 level of significance. What is the hypothesized population proportion for this test?

Answers: 3

Show answers

Answers

We conclude that the proportion of only children in the special program is significantly different from the proportion for the school district.

Step-by-step explanation:

We are given that in a certain school district, it was observed that 24% of the students in the element schools were classified as only children

However, in the special program for talented and gifted children, 119 out of 415 students are only children.

Let p = proportion of only children in the special program.

So, Null Hypothesis, H_0 : p = 24% {means that the proportion of only children in the special program is equal to the proportion for the school district}

Alternate Hypothesis, H_A : p $\neq$ 24% {means that the proportion of only children in the special program is significantly different from the proportion for the school district}

The test statistics that would be used here One-sample z-test for proportions;

T.S. = $\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of only children in the special program = $\frac{119}{415}$ = 0.29

n = sample of students = 415

The hypothesized population proportion for this test is 0.24.

So, the test statistics = $\frac{0.29-0.24}{\sqrt{\frac{0.24(1-0.24)}{415} } }$

= 2.385

The value of z test statistic is 2.385.

Now, at 0.05 significance level the z table gives critical value of -1.96 and 1.96 for two-tailed test.

Since our test statistic doesn't lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the proportion of only children in the special program is significantly different from the proportion for the school district.

Answer from: Quest

5/8 beds for each square yard

Answer from: Quest

just sum

10 + 10 = 20

Another question on Mathematics

Mathematics, 21.06.2019 23:00

The areas of two similar triangles are 72dm2 and 50dm2. the sum of their perimeters is 226dm. what is the perimeter of each of these triangles?

Answers: 1

Answer

Mathematics, 21.06.2019 23:00

Aremote-controlled boat can travel at 4 feet per second in calm water. the boat traveled 48 feet with the current, and then it traveled 16 feet against the current in the same amount of time. how fast is the current?

Answers: 1

Answer

Mathematics, 22.06.2019 02:40

21 type the correct answer in each box. if necessary, round your answers to the nearest hundredth the vertices of abc are a(2,8), b(16, 2), and c(6,2). the perimeter of abc is units, and its area is square units

Answers: 2

Answer

Mathematics, 22.06.2019 03:00

Which is the factored form of the polynomial p(x) shown here?

Answers: 1

Answer

You know the right answer?

In a certain school district, it was observed that 24% of the students in the element schools were c...

Questions