Question

In a sample of 808 Republicans, 380 answered that they believe that Sarah Palin has the right experience to be President. Assuming the polling was done correctly and that the data is current, is it reasonable to conclude at a significance level of .01 that less than fifty percent of Republicans feel that Sarah Palin has the right experience to be President?

State the following:

1. sample size

2. sample proportion to three decimal places

3. what type of variable is it?

4. The data is collected from an SRS. Is the sample size sufficiently large?

5. state the null hypothesis.

6. state the alternate hypothesis.

7. write the formula for the standard error and compute it to four decimal places.

8. write the formula for the z-value (test statistic) and compute it to two decimal places.

9. critical value(s)

10. p-value table A3

11. p-value table A2

12. p-value calculator

13. can we reject?

14. conclusion

15. (same problem as above but the level of significance is .05 instead of .01) critical value (s)

15b. conclusion with .05 level

Answer 1

1. sample size , n = 808

2. x = 380

Sample proportion, p̄ = x/n = 0.470

3. It is a proportion.

4. Yes, the sample size is sufficiently large.

5. Null hypothesis.

Ho : p = 0.50

6. Alternate hypothesis.

Ha : p < 0.50

7. Standard error, se = √(p *(1- p )/n) = √(0.50 *(1- 0.50)/808) = 0.0176

8. Test statistic:

z = (p̄ -p)/se = (0.4703 - 0.5)/0.0176 = -1.69

9. Critical value, z crit = NORM.S.INV(0.01) = -2.326

Reject Ho if z < -2.326

12. p-value = NORM.S.DIST(-1.6886, 1) = 0.0456

13. No, we can not reject the null hypothesis.

14. conclusion

There is not enough evidence to conclude that less than fifty percent of Republicans feel that Sarah Palin has the right experience to be President at 0.01 significance level.

15.a. Critical value, z crit = NORM.S.INV(0.05) = -1.645

Reject Ho if z < -1.645

15b. Reject the null hypothesis.

There is enough evidence to conclude that less than fifty percent of Republicans feel that Sarah Palin has the right experience to be President at 0.05 significance level.