1. A poll sample of 500 people was conducted if they support new initiative.  200 people said yes. Find the margin of error E and confidence interval for population proportion Apply Confidence Level CL=0.90 (90%). You can find critical value z_a/2.

2. Sample of 100 measurements were taken to analyze concentration of impurities in a product. Calculated sample mean was 65 ppm (parts per million). Assuming that population standard deviation is 20 ppm, estimate margin of error and confidence interval for population mean with confidence level 95%.

3. Sample of 30 people randomly asked in casino shows that average lost per person is $160 with a sample standard deviation s = $40. Based on this data create a 95% confidence interval for population mean.

4. The P-value of a hypothesis test is 0.0345. Which of the following claims is correct?

A) Reject Ho at the 0.05 significance level but not the 0.01 significance level.

B) Reject Ho at the 0.01 significance level but not the 0.05 significance level.

C) Reject Ho at both the 0.01 significance level and the 0.05 significance level.

D) Do not reject Ho at significance level 0.01 and do not reject Ho at the 0.05 significance level.

5. For questions a, b, c use following data:

Evaluate the claim that percent of small businesses closed this year (population proportion) is greater than 26%. Sample of 500 small businesses were taken all over the country and 145 of them were closed this year.   

H₀ - population proportion p = 0.26

H₁ - population proportion p > 0.26

a. Calculate z-value for test statistics

b. Use Table A-2 to find p-value.  

c. At significance level 0.05 reject or do not reject H₀. Explain your decision.

6. For questions a and b use following data

Consider the hypothesis test with 

Null Hypothesis Ho: μ = 500

Alternative Hypothesis H₁: μ ≠ 500   (this is two-tailed test)

In a random sample of 81 subjects, the sample mean found to be x=492.

Population standard deviation is  σ=36. 

a. Calculate test statistics and find P-value for this test.

b. With significance level α = 0.02 (remember, this is two-tailed test) make the decision.