STATS Assignment – Assigned any numbers for x and y in the first two columns

| August 30, 2017

Question
Assigned any numbers for x and y in the first two columns.

.09px;=”” 12px=””>
x y x2 y2 xy
?x ?y ?x2 ?y2 ?(xy)
Complete the table and calculate sums in the last row.
We will use these sums to calculate Coefficient of Correlation
and Equation of Linear Regression.

Part 1. Use following formula to calculate Coefficient of Linear Correlation:

After you have your r value (called a Pearson Coefficient) compare it to
the critical value in the Table A-6 Pearson Correlation Coefficient.
Use line with n=6 and significance level ? = 0.05.
If your calculated r is greater than the table value there is a linear correlation between x and y in your data.

Part 2. Find an Equation of Regression Line in a form: y = b0 + b1x
Parameters: b1 (slope) and b0(y-intercept) can be calculated by formulas:

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1. Consider a trial where a person is charged with a murder.
The Null Hypothesis is that the defendant is not guilty.
State possible Type I and Type II errors in this case.

2. Imagine performing a hypothesis test if an average age of college graduates is 31 years.
Will it be Left-Tailed, Right-Tailed or Two-Tailed test?

3. Use attached Table A-2 for Normal Distribution to find the critical z value for Right-Tailed test with significance level ? = 0.10.

4. Use attached Table A-3 for t-Distribution to find the critical t value for Left-Tailed test with sample size = 15 significance level ? = 0.01.

5. Use attached Table A-2for Normal Distribution to find p-value for a Left-Tailed test
with test statistics z = – 1.24.

6. 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.

7. 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.

H0– population proportion p = 0.26
H1– population proportion p > 0.26

Calculate z-value for test statistics

Use attached Table A-2 for Normal Distribution to find p-value.
At the significance level 0.05 make decision: reject or do not reject H0.

8. Hypothesis test of a single population mean.
Null Hypothesis Ho: ? = 500

Alternative Hypothesis H1: ? ? 500 (Two-Tailed test)

In a random sample of 81 subjects, the sample mean found to be .
Population standard deviation is ?.

Calculate test statistics and find P-value for this test (use attached table A-2).
With significance level ? = 0.02 (remember, this is two-tailed test) make the decision:
accept or reject Ho. Explain your decision

For # 9, 10, 11, 12 use data from the table below:

.09px;=”” 12px=””>
x

y

x2

y2

xy

2

11

4

16

6

14

8

18

10

25

?x=

?y=

?x2=

?y2=

?(xy)=

9. Complete the table. Fill in all columns and calculate sums in the last row.

10. Use results from #9 and calculate Pearson Coefficient of Linear Correlation.

11. Use results from #9 and calculate slope of Linear Regression Line.

12. Use results from #9 and calculate y-intercept of Linear Regression Line.

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