Question

1. A bank randomly selected 242 checking account customers and found that 113 of them also had savings accounts at this same bank. Construct a 90% confidence interval for the true proportion of checking account customers who also have savings accounts. (Give your answers correct to three decimal places.)

2. In a sample of 62 randomly selected students, 29 favored the amount being budgeted for next year's intramural and interscholastic sports. Construct a 90% confidence interval for the proportion of all students who support the proposed budget amount. (Give your answers correct to three decimal places.)

3. Find n for a 99% confidence interval for p with E = 0.037 using an estimate of p = 0.4. (Round up to the nearest whole number.)

4. Consider the following. (Give your answers correct to two decimal places.)

(a) Calculate the test statistic z used in testing H_o: p = 0.70, H_a: p > 0.70; with the sample n = 283 and x = 253.


(b) Calculate the test statistic z used in testing H_o: p = 0.50, H_a: p < 0.50; with the sample n = 469 and x = 210.


(c) Calculate the test statistic z used in testing H_o: p = 0.35, H_a: p ≠ 0.35; with the sample n = 282 and x = 82.


(d) Calculate the test statistic z used in testing H_o: p = 0.90, H_a: p > 0.90; with the sample n = 534 and x = 516.

5. Consider the following hypothesis-testing situations. (Give your answers correct to four decimal places.)

(a) Determine the p-value for H_o: p = 0.5, H_a: p ≠ 0.5, z = 1.4.


(b) Determine the p-value for H_o: p = 0.7, H_a: p ≠ 0.7, z = -2.31.


(c) Determine the p-value for H_o: p = 0.4, H_a: p > 0.4, z = 1.03.


(d) Determine the p-value for H_o: p = 0.2, H_a: p < 0.2, z = -1.67.

Answer 1

Solution:

1)

Solution :

Given that,

n = 242

x = 113

= x / n = 113 / 242 = 0.467

1 - = 1 - 0.467 = 0.533

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.645 * (((0.467 * 0.533) / 242)

= 0.053

A 90% confidence interval for population proportion p is ,

- E < P < + E

0.467 - 0.053 < p < 0.467 + 0.053

0.414 < p < 0.520

(0.414 , 0.520)