Hypothesis test for a population proportion
A decade-old study found that the proportion, , of high school seniors who believed that "getting rich" was an important personal goal was . A researcher decides to test whether or not that percentage still stands. He finds that, among the high school seniors in his random sample, believe that "getting rich" is an important goal. Can he conclude, at the level of significance, that the proportion has indeed changed?
Perform a two-tailed test. Then fill in the table below.
Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)
The null Hypothesis : Ho : p = 0.70
The alternative hypothesis: H1: p ≠ 0.70
The type of test statistic: Z
The value of the test statistic:
(Round to at least three decimals)
The two critical values at the
0.05 level of significance:
(Round to at least three
Can we conclude that the proportion of high school seniors who yes or no
Believe that “getting rich” is an important goal has changed?
This is what I know so far:
(225) x (0.70) = 157.5 > 5 and n(1-p)=(225) X (1-0.70) = 68.5 > 5
(175) x ((0.70) = 122.5>5 and n(1-p)= (175) X (1-0.70)= 52.5 >5
So now I have
52.5 – 0.70
This is where I am stuck. I can not come up with the value of the test statistic or the two critical values……… Can you please help me; I need step by step instructions.