Question

It costs you S8 to draw a sample of size n = 1 and measure the attribute of interest. You have a budget of $2,000. Complete parts a and b below. a. Do you have sufficient funds to estimate the population mean for the attribute of interest with a 95% confidence interval 4 units in width? Assume ơ: 14. Select the correct choice below and fill in the answer box to complete your choice. O Yes, because the required sample size is O No, because the required sample size is b. If you used a 90% confidence level, would your answer to part a change? Explain. O A. No, because the total cost still exceeds the budget. B. No, because the total cost decreases and the funds are still sufficient. OC. Yes, because the total cost decreases and the funds are now sufficient. D. Yes, because the total cost now exceeds the budget.

Answer 1

Solution:

Given data :

Sample size, n =1

Budget = $ 2000

cost = $8

Now, we have to find out the:

a) Do you have sufficient funds to estimate the population mean:-

Given,

  95% confidence interval width = 4 units

$\sigma$ = 14

  $C.I = Z_{\frac{\alpha }{2}} \frac{\sigma }{\sqrt{n}}$

We already know, the 95% confidence interval value i.e.,1.96

$4 = 1.96 \frac{14 }{\sqrt{n}}* 2 ( For the two tailed ))$

$\sqrt{n} = 1.96 \frac{14 }{4}* 2$

$\sqrt{n} = 1.96 * 3.5*2$

  $\sqrt{n} = 6.86*2$

$n =13.72^{2}$

$n =188.23$

Sample size n = 189

The amount of funds required = n * cost

=189 * 8

= 1512

the amount of funds required = 1512

Hence, we have sufficient funds estimate the population mean

From the question, option A is correct .

Here option A is : yes, because the required sample size is 189