Consider the following hypotheses.
Upper H 0: p ≤ 0.11
Upper H 1: p ≠ 0.11
Given that p = 0.16, n =150, and α = 0.01, answer the following questions.
(a) What conclusion should be drawn?
(b) Determine the p-value for this test.
(c) Determine the critical value(s) of the test statistic. zₐ =1.96 (Use a comma to separate answers as needed. Round to two decimal places as needed.)

(a) There is sufficient evidence to conclude that the population proportion equals 0.11.

(b) p-value is 0.0548

(c) Critical values are -2.58, 2.58

Step-by-step explanation:

(a) Conclusion:

Fail to reject H0 because the p-value 0.0548 is greater than the significance level 0.01.

(b) The test is a two-tailed test because the alternate hypothesis is expressed using not equal to.

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

p' is sample proportion = 0.16

p is population proportion = 0.11

n is sample size = 150

z = (0.16 - 0.11) ÷ sqrt[0.11(1-0.11) ÷ 150] = 0.05 ÷ 0.026 = 1.92

Cumulative area of the test statistic is 0.9726

p-value for a two-tailed test = 2(1 - 0.9726) = 2(0.0274) = 0.0548

(c) The critical values of the test statistic are -2.58, 2.58

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.