In a recent 1067 randomly selected adults were asked whether they approve of lab

Question

In a recent 1067 randomly selected adults were asked whether they approve of labor unions, 62% said yes. In, about 64% of adults approved of labor unions. All the 10% significance level, do the data provide sufficient evidence to conclude that the percentage of adults who approve labor unions has decreased since 1936? What are the hypothesis for the one-proportion test? H_0: p: H_2: p (Type integers or decimals) what is the test statistic? Z = (Round to two decimal places as needed.) Identify the P-value. The P-value is (Round to four decimal places as needed.)

Explanation / Answer

Solution:

H0: P = 0.64
H1: P < 0.64

Sample proportion phat = 0.62
Variance of proportion = p*(1-p)/n
= 0.64(0.36)/1067
= 0.000216
S.D. of p is sqrt[0.000216] = 0.0147
z = ( 0.62 - 0.64 ) / 0.0147 = -1.3605

P-value = P( |z| < -1.3605) = 0.0869

Since p-value < 0.05( assumed level of significance), we reject the null hypothesis.
The evidence concludes the percentage of adults who approve labor unions have decreased since 1936

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