Question

The mayor asks you to determine whether or not most people (over 50%) support a tax on large soft drinks. You poll 500 adults with an average age of 45 years and a standard deviation of 6 years. The number who support the soft drink tax is 255. Based on the 99% confidence interval for the proportion of adults supporting the soft drink tax, match the following:
1. ____ standard error

2. ____error term

3. ____ confidence interval

4. ____ you report to the mayor that

A..02

B..05

C..09

D..12

E..37

F..46 to .56

G..51

H..40 to .62

I..49 to .53

J..50 to .52

K. MOST people (over 50%) support the tax

L. MOST people (over 50%) do NOT support the tax

M. I cannot say whether or not MOST people (over 50%) support the tax.

Answer 1

Answer:

(1) The standard error is 0.0224.

(2) The error term is 0.058.

(3) The 99% confidence interval for the proportion of adults supporting the soft drink tax is (0.45, 0.57).

(4) Approximately 45% to 57% people support the soft drink tax.

Step-by-step explanation:

Let X = number of adults who support the soft drink tax.

The sample size is, n = 500.

The number of people who support the tax is, X = 255.

Compute the sample proportion as follows:

$\hat p=\frac{X}{n}=\frac{255}{500}= 0.51$

(1)

Compute the standard error as follows:

$SE_{\hat p}=\sqrt{\frac{\hat p(1-\hat p)}{n}} \\=\sqrt{\frac{0.51(1-0.51)}{500}}\\=0.0224$

Thus, the standard error is 0.0224.

(2)

The error term (Margin of error) is:

$MOE=z_{\alpha/2}\times SE_{\hat p}$

For 99% confidence interval the critical value of z is:

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

Compute the value of MOE as follows:

$MOE=z_{\alpha/2}\times SE_{\hat p}\\=2.58\times0.0224\\=0.057792\\\approx0.058$

Thus, the error term is 0.058.

(3)

Compute the 99% confidence interval as follows:

$CI=\hat p\pm MOE\\=0.51\pm0.058\\=(0.452, 0.568)\\\approx(0.45, 0.57)$

Thus, the 99% confidence interval for the proportion of adults supporting the soft drink tax is (0.45, 0.57).

(4)

The report to be submitted to the mayor is that approximately 45% to 57% people support the soft drink tax.