Question

A decade-old study found that the proportion, p, of high school seniors who believed that "getting rich" was an important personal goal was 70%. A researcher decides to test whether or not that percentage still stands. He finds that, among the 230 high school seniors in his random sample, 141 believe that "getting rich" is an important goal. Can he conclude, at the 0.01 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. a Р The null hypothesis: H < X S The alternative hypothesis: 8 D=0 OSO DO The type of test statistic: (Choose one) D# O<O O> The value of the test statistic: (Round to at least three decimal places.) X 5 ? The p-value: (Round to at least three decimal places.) Can we conclude that the proportion of high school seniors who believe that getting rich" is an important goal has changed? Yes No

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.7
Alternative Hypothesis, Ha: p ≠ 0.7

single roortion z test

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.613 - 0.7)/sqrt(0.7*(1-0.7)/230)
z = -2.879

P-value Approach
P-value = 0.004
As P-value < 0.01, reject the null hypothesis.

yes, we can conclude