Question

In an August 2012 Gallup survey of 1,012 randomly selected U.S. adults (age 18 and over), 53% said that they were dissatisfied with the quality of education students receive in kindergarten through grade 12. Use the standard normal distribution to test if the proportion of U.S. adults who are dissatisfied with the education that students receive in kindergarten through grade 12 differs from 50%. The randomization distribution for this test is approximately normal and the standard error is SE = 0.016. Include all details of the test and use a 5% significance level.

(State your hypotheses, observed statistics, z-test statistic, p-value using statkey, decision and conclusion)

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H0 : p = 0.50

Ha : p 0.50

= 0.53

n = 1012

P0 = 0.50

1 - P0 = 1 -0.50 =0.50

= 0.05

The two tailed test critical value = 1.96

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.53 -0.50/ [0.50*(0.50) /1002 ]

= 1.909

P(z >1.909 ) = 1 - P(z <1.909 ) = 0.0281 *2 = 0.0562

P-value = 0.0562

= 0.05

0.0562 > 0.05

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that Include all details of the test and use a 5% significance level.