### stats 2

**1**. *(Chapter 7: Estimating a Population Proportion)
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}, required for calculation, in small table given in our textbook on page 329 Edition 12 or page 332 in Edition 11.

2. *(Chapter 7: Estimating a Population Mean).
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%. Round the answer up to the whole numbers.*

**3. ***(Chapter 7) Find the critical value t _{a/2} for estimate procedure when population standard deviation is not known. Sample size is n=24, Confidence Level 98%.
Tip: Use column with Area in Two Tails in t-Distribution table.*

**4. ***(Chapter 7) 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. This is the case where population standard deviation is not known and you have to use Appendix table A-3 for t-value.
Round the answer up to the whole numbers.*

**
5**.

*(Chapter 8) Use Appendix Table A-2 to find the critical z value for right-tail test with significance level*

*α*

*= 0.10.*

**6**. *(Chapter 8) Show on the z number line critical/rejection region for the Two-Tailed Hypothesis testing with significance level **α** = 0.08 (use highlight or shading like in Conference for week 6).*

**
7**.

*(Chapter 8) Use Appendix Table A-2 to find p-value for a left-tail test*

with test statistics z = – 1.24.

with test statistics z = – 1.24.

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**8**. *Chapter 8: 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.*

*Chapter 8: Testing Claim about a Proportion.*

* For questions 9, 10, 11 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. *

*H _{0} – population proportion p = 0.26
H_{1} – population proportion p > 0.26*

**9**.* Calculate z-value for test statistics*

**10. ***Use Table A-2 to find p-value.
*

**11.**

*At significance level 0.05 reject or do not reject H*

_{0}. Explain your decision.

*Chapter 8: Testing Claim for Population Mean, population standard deviation is known
For questions 12, 13 use following data*

*Consider the hypothesis test with
Null Hypothesis Ho: *

*μ*

*= 500*

*Alternative Hypothesis H _{1}: *

*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.*

**12**. *Calculate test statistics and find P-value for this test (use Appendix table A-2).
*

**13**.

*With significance level*

*α*

*= 0.02 (remember, this is two-tailed test) make the decision:*

accept or reject Ho. Explain your decision

accept or reject Ho. Explain your decision

*Chapter 8: Testing Hypothesis for Population Mean, population standard deviation not known.*

Instead, sample standard deviation is given.

For questions 14 use the following data.

Instead, sample standard deviation is given.

For questions 14 use the following data.

*With sample size n=36, sample mean 710 and sample standard deviation s = 30
Null Hypothesis Ho: *

*μ*

*= 700*

*Alternative Hypothesis H _{1}: *

*μ*

*> 700 (this is right-tailed test)*

*Significance level **α** = 0.05*

**14**.* Calculate t-value for the test statistics.*

*In Table A-3 for t-distribution find critical value. Use column with Area in One Tail 0.05.
Identify rejection region as area to the right of critical value from Table A-3.
Is value of test statistics falls in the rejection region?
Will you reject or do not reject the Null Hypothesis?*

**15**. Let’s practice in finding Critical Value and defining Critical/Rejection Region in three possible cases:

Case 1: Left-Tailed test (Rejection Region on the left side)

Case 2: Right-Tailed test (Rejection Region on the right side)

Case 3: Two-Tailed test (Rejection Region on both sides)

Critical value and position of Rejection Region is defined by the given Significance Level.
There is a simple relation between Significance Level (α) and Confidence Level (CL):
α = 1 – CL (in decimal form).
For example, if Confidence Level 82% then Significance Level α = 1 – 0.82 = 0.18

Here is what you should do:
1. Select Significance Level assigned for you from the table below.
2. Use Appendix Table A-2 to find critical z value in case-1, case-2 and case-3.
3. Show Critical/Rejection Region on z-scale in case-1, case-2 and case-3:
…….-3…….-2…….-1…….0…….1…….2…….3…..

Use Highlight tools (in our Text Editor it has name Background Color) to show Critical Region.
For example, if you want to show region to the left of (-1.28) it should look like:

…….-3…….-2…….-1…….0…….1…….2…….3…..

Significance Level α | |

0.22 |

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