Question

Please help with all 4 of these problems. If you know how to do them with a TI 84 Calculator that would be amazing if you could list the steps for that as well. Thank you next.

1. Find the critical value the tat2 for a sample size of 43 and 99% confidence level (1 point) 2. Find the critical value the Zaz for a sam ple size of 64 and 80% confidence level. (1 point) 3. In a poll of 800 randomly selected subjects, 320 answered "yes" when asked if they planned to vote in a state election. Construct a 98% confidence interval estimate of the proportion of all who plan to vote in that election. (2 points) Find the sample size required to estimate the mean age of registered drivers in the United States. Assume that we want 90% confidence that the sample mean is within 0.25 year of the true population mean age. Also assume that the standard deviation for the population is known to be 8 years. (2 points) 4.

Answer 1

1.
Degree of freedom = n - 1 = 43 - 1 = 42

For 99% confidence level, $\alpha$ = 1 - 0.99 = 0.01

Critical value of t at $\alpha$ = 0.01/2 = 0.005, and df = 42 is -2.698

2.

$\alpha$ = 1 - 0.8 = 0.2

Critical value of z at $\alpha$ = 0.2/2 = 0.1 is -1.281552

3.
Sample proportion, p = 320 / 800 = 0.4

Standard error of proportion,= $\sqrt{p(1-p)/n} = \sqrt{0.4*(1-0.4)/800}$ = 0.01732051

$\alpha$ = 1 - 0.98 = 0.02

Critical value of z at $\alpha$ = 0.02/2 = 0.01 is $\pm$ 2.326348

98% confidence interval is,

(0.4 - 2.326348 * 0.01732051, 0.4 + 2.326348 * 0.01732051)

= (0.3597, 0.4403)

4.

Margin of error, E = 0.25

$\alpha$ = 1 - 0.9 = 0.1

Critical value of z at $\alpha$ = 0.1/2 = 0.05 = 1.644854

Sample size, n = (z $\sigma$ / E)²

= (1.644854 * 8 / 0.25)²

= 2770.478

$\approx$ 2770 (Rounding to nearest integer)