Mathematics, 21.04.2020 04:25, miami158999

Use the normal distribution to find a confidence interval for a proportion p given the relevant sample results. Give the best point estimate for p, the margin of error, and the confidence interval. Assume the results come from a random sample. A 99% confidence interval for p given that p-hat = 0.34 and n= 500. Point estimate (2 decimal places) Margin of error (3 decimal places) The 99% confidence interval is to (3 decimal places)

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answered: cheermom2000

(a) The point estimate for the population proportion p is 0.34.

(b) The margin of error for the 99% confidence interval of population proportion p is 0.055.

Step-by-step explanation:

A point estimate of a parameter (population) is a distinct value used for the estimation the parameter (population). For instance, the sample mean $\bar x$ is a point estimate of the population mean μ.

Similarly, the the point estimate of the population proportion of a characteristic, p is the sample proportion $\hat p$ .

The (1 - α)% confidence interval for the population proportion p is:

$CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

The margin of error for this interval is:

$MOE= z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

The information provided is:

$\hat p=0.34\\n=500\\(1-\alpha)\%=99\%$

(a)

Compute the point estimate for the population proportion p as follows:

Point estimate of p = $\hat p$ = 0.34

Thus, the point estimate for the population proportion p is 0.34.

(b)

The critical value of z for 99% confidence level is:

$z={\alpha/2}=z_{0.01/2}=z_{0.005}=2.58$

*Use a z-table for the value.

Compute the margin of error for the 99% confidence interval of population proportion p as follows:

$MOE= z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

$=2.58\sqrt{\frac{0.34(1-0.34)}{500}}$

$=2.58\times 0.0212\\=0.055$

Thus, the margin of error for the 99% confidence interval of population proportion p is 0.055.

(c)

Compute the 99% confidence interval of population proportion p as follows:

$CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

$CI=\hat p\pm MOE$

$=0.34\pm 0.055\\=(0.285, 0.395)$

Thus, the 99% confidence interval of population proportion p is (0.285, 0.395).

answered: Guest

answer: the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.

step-by-step explanation:

the given rate of interest i= 85%

in calculating the monthly payment for a loan with an interest rate compounded monthly, the value of the interest rate per period we use in the formula must be in decimal form.

to convert it in decimal, we divide it by 100, we get

$i=\frac{85}{100}=0.85$