Mathematics, 23.03.2021 06:00 gagehamel

In a Gallup survey of 1,012 randomly selected U. S. adults (age 18 and over), 53% said that they were dissatisfied with the quality of education students receive in kindergarten through grade 12. Use the normal distribution to construct and interpret a 90% confidence interval for the proportion of U. S. adults who are dissatisfied with the education students receive in kindergarten through grade 12. The standard error is SE

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Answer from: Ashtree519

The standard error is 0.0157.

The 90% confidence interval for the proportion of U.S. adults who are dissatisfied with the education students receive in kindergarten through grade 12 is (0.5042, 0.5558). This means that we are 90% sure that the true proportion of U.S. adults who are dissatisfied with the education students receive in kindergarten through grade 12 is between 0.5042 and 0.5558.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm zs$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

$s = \sqrt{\frac{\pi(1-\pi)}{n}}$ is the standard error.

In a Gallup survey of 1,012 randomly selected U.S. adults (age 18 and over), 53% said that they were dissatisfied with the quality of education students receive in kindergarten through grade 12.

This means that $n = 1012, \pi = 0.53$

The standard error is:

$s = \sqrt{\frac{\pi(1-\pi)}{n}} = \sqrt{\frac{0.53*0.47}{1012}} = 0.0157$

The standard error is 0.0157.

90% confidence level

So $\alpha = 0.1$ , z is the value of Z that has a pvalue of $1 - \frac{0.1}{2} = 0.95$ , so Z = 1.645 .

The lower limit of this interval is:

$\pi - zs = 0.53 - 1.645*0.0157 = 0.5042$

The upper limit of this interval is:

$\pi + zs = 0.53 + 1.645*0.0157 = 0.5558$

Answer from: Quest

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Answer from: Quest

step-by-step explanation:

step 1 distribute 2 to every term in the parentheses

step 2 add 10 on both sides of the equal sign