Question

In April​ 2010, 47​% of the unemployed had been out of work longer than six months. Policy makers felt that this percentage declined during 2010 as the job market improved. To test this​ theory, a random sample of 300 unemployed people was​ selected, and it was found that 125 had been out of work for more than six months. Using alphaequals0.10​, answer parts a through c below. a. What conclusions can be drawn about the proportion of the unemployed who have been out of work for more than six​ months? Determine the null and alternative hypotheses. Choose the correct answer below. A. Upper H 0​: pgreater than or equals0.47 Upper H 1​: pless than0.47 B. Upper H 0​: pequals0.47 Upper H 1​: pnot equals0.47 C. Upper H 0​: pless than or equals0.47 Upper H 1​: pgreater than0.47 D. Upper H 0​: pgreater than0.47 Upper H 1​: pless than or equals0.47 Determine the critical​ value(s) of the test statistic. z Subscript alphaequals nothing ​(Use a comma to separate answers as needed. Round to two decimal places as​ needed.) Calculate the test statistic. z Subscript pequals nothing ​(Round to two decimal places as​ needed.) Determine the conclusion. Choose the correct answer below. A. Do not reject Upper H 0. There is not sufficient evidence to conclude that the proportion of the unemployed who have been out of work for

Answer 1

The proportion of the unemployed who have been out of work for more than six months is not 0.47

H0: p equals 0.47

H1: p not equals 0.47

Critical values: -1.65 and 1.65

Test statistic: -1.72

Reject H0

Explanation:

The null hypothesis is expressed using the equality sign while the alternate hypothesis is expressed using any of the inequality signs.

Test statistic (z) = (p' - p) ÷ sqrt[p(1 - p) ÷ n]

p' is sample proportion = 125/300 = 0.42

p is population proportion = 0.47

n = 300

z = (0.42 - 0.47) ÷ sqrt[0.47(1 - 0.47) ÷ 300] = -0.05 ÷ sqrt[8.30×10^-4] = -0.05 ÷ 0.029 = -1.72

Significance level = 0.1

Critical values for a two-tailed test using a 0.1 significance level are -1.65 and 1.65

Conclusion:

Reject H0 because the test statistic -1.72 falls outside the region bounded by the critical values -1.65 and 1.65.

The proportion of the unemployed who have been out of work for more than six months is not 0.47.