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

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

Step-by-step 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.

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.

a.

step-by-step explanation:

step 1 distribute 2 to every term in the parentheses

step 2 add 10 on both sides of the equal sign