Mathematics, 17.10.2019 16:30 poolwaterisgross

Several years ago, 39% of parents who had children in grades k-12 were satisfied with the quality of education the students receive. a recent poll asked 1 055 parents who have children in grades k-12 if they were satisfied with the quality of education the students receive. of the 1 055 surveyed, 466 indicated that they were satisfied. construct a 95% confidence interval to assess whether this represents evidence that parents' attitudes toward the quality of education have changed.

Answers: 2

Show answers

Answers

We can say that 95% confidence interval represents evidence that parents attitudes toward the quality of education have changed.

Step-by-step explanation:

Given :

39% of parents who had children in grades K-12 were satisfied with the quality of education the students receive.

The 1055 surveyed, 466 indicated that they were satisfied with the quality of education the students receive.

95% confidence interval.

Sample Size, n = 1055

Solution :

Hypothesis -

$\rm H_0 : p = 0.39$

$\rm H_a : p \neq 0.39$

Now sample proportion,

$\hat{p} = \dfrac{466}{1055}$

$\hat{p} \approx 0.44$

For 95% confidence critical value is

$z_\frac{\alpha}{2} = 1.96$

Now Confidence interval is

$\hat{p} \pm z_\frac{\alpha }{2}\sqrt{\dfrac{p(1-p)}{n}} = 0.44 \pm (1.96)\sqrt{\dfrac{0.39(1-0.39)}{1055}}$

$= 0.44 \pm (1.96)\sqrt{\dfrac{0.39\times(0.61)}{1055}} = 0.44 \pm 0.03$

$\rm = 0.44-0.03 \; \; ,\; \; 0.44+0.03$

= (0.41 , 0.47)

Since confidence interval does not contain 0.39 hence we reject the null hypothesis.

Therefore we can say that 95% confidence interval represents evidence that parents attitudes toward the quality of education have changed.

For more information, refer the link given below

link

Answer from: jenm345

Answer with explanation:

Let p be the population proportion of parents who had children in grades K-12 were satisfied with the quality of education the students receive.

Given : Several years ago, 39% of parents who had children in grades K-12 were satisfied with the quality of education the students receive.

Set hypothesis to test :

$H_0: p=0.39\\\\H_a :p\neq0.39$

Sample size : n= 1055

Sample proportion : $\hat{p}=\dfrac{466}{1055}=0.441706161137\approx0.44$

Critical value for 95% confidence : $z_{\alpha/2}=1.96$

Confidence interval : $\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{p(1-p)}{n}}$

$0.44\pm (1.96)\sqrt{\dfrac{0.39(1-0.39)}{1055}}\\\\0.44\pm0.0299536805135\\\\0.44\pm0.03\\\\=(0.44-0.03, 0.44+0.03)\\\\=(0.41,\ 0.47)$

Since , Confidence interval does not contain 0.39.

It means we reject the null hypothesis.

We conclude that 95% confidence interval represents evidence that parents' attitudes toward the quality of education have changed.

Answer from: Quest

If you need an equation, it would be y=2x+8, y would be how long it grew, x being weeks.if you need how long he was asleep, it would be 4 weeks if he started with no beard, the equation would be x=8÷2if he did have a beard before hand, the equation would be 2w+x=8

Answer from: Quest

option 3 . (5x + 1) - (-10x + 6)

step-by-step explanation:

option 1 :

(4x + 3) + (-9x + 4)

or 4x+3 -9x + 4

or -5x + 7

option 2

(x - 2) - (6x - 9)

or x-2-6x + 9

or -5x + 7

option 3