STAT200 Week 7 Homework

STAT200 Week 7 Homework

This is the last homework in our class

Problem 1. For the X,Y data in the table, compute the coefficient of correlation r.

X Y
10 21
12 27
14 25
16 31
20 32

Show work
________________________________________
Problem 2. For the (X, Y) data in the table, compute slope and y-intercept of the regression line.

X Y
2 10
4 12
8 16
10 22

Show work
Problem 3. (2points) Table below shows results for 10 selected students on Test-1 and Test-2:

Test-1 Test-2 Difference
1 66 77
2 85 90
3 78 70
4 100 95
5 92 100
6 80 85
7 55 70
8 95 100
9 82 90
10 70 75

You should use Hypothesis Testing technique to evaluate Null Hypothesis:
Ho: there is no significant differences between mean score on Test-1 and Test-2.
Use significance level α= 0.10.

Here are steps to follow:
a) Calculate difference of scores for each student.
b) Find Mean (M) and Sample Standard Deviation (s) for values in the column Difference.
c) Find Standard Error of Mean sm = s/√N .
d) Calculate t-value as t = M/sm
e) Use Excel function TDIST(t, df,2) to find p-value (df = N-1).
f) Compare p-value with the given significance level 0.10.
If p-value is less than 0.10 then reject Ho.
If p-value is greater than 0.10 accept Ho.

Show work
________________________________________
4. Consider a trial where a person is charged with a crime.
The Null Hypothesis is that the defendant is not guilty.
Identify following verdicts as Type I or Type II Errors:
a) Person committed crime, b court failed to prove it and found him not guilty.
b) Court found the person guilty for the crime that he did not commit. ________________________________________
5. Imagine performing a hypothesis test if an average age of college graduates is 31 years old.
Will it be Left-Tailed, Right-Tailed or Two-Tailed test?
________________________________________
6. Use attached Table A-2 for Normal Distribution to find the critical z value for Right-Tailed test
with significance level α = 0.33.
________________________________________
7. Use attached Table A-2 for Normal Distribution to find p-value for a Left-Tailed test
with test statistics z = – 2.51. ________________________________________
8. Use attached Table A-3 for t-Distribution to find the critical t value for Left-Tailed test with sample size = 15 and significance level α = 0.01.
________________________________________
9. 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.
________________________________________
10. Testing Claim about a Proportion.
Evaluate the claim that percent of small businesses closed last year (population proportion) is greater than 60%.
H0 – population proportion p = 0.6
H1 – population proportion p > 0.6
Sample of N=200 small businesses were checked all over the country and 130 of them were closed last year.

Calculate z-value for the test statistics is case of population proportion:
z = ((p_s-p))/√((p(1-p))/N)
ps is a sample proportion,
p is a population proportion, taken from Ho,
N – sample size.

b) Use attached Table A-2 for Normal Distribution to find p-value.
Keep in mind, table gives you area to the left of z, but this is Right-Tailed test.

c) At the significance level 0.05 make decision: reject or do not reject H0.
________________________________________
11. Hypothesis test of a single population mean.
Null Hypothesis Ho: μ = 300
Alternative Hypothesis H1: μ ≠ 300 (Two-Tailed test)
In a random sample of 100 subjects, the sample mean found to be x̅ =290.
Population standard deviation is σ=50.
Calculate test statistics
find P-value for this test (use attached table A-2)
With significance level α = 0.1 make the decision: reject or do not reject (accept) Ho. ________________________________________
For # 9, 10 use data from the table below:

x y
1 27
3 28
5 28
6 29
10 30

12. Calculate Coefficient of Linear Correlation.

13. Find the equation of Regression Line.
Question 14. Table below shows number of students who failed different math courses
in Spring (Expected Frequency) and in Fall (Observed Frequency) semesters:

Course Spring
Expected (E)
Frequency Fall
Observed (O)
Frequency (E – O)2 (E – O)2/E
College Algebra 12 15
Statistics 18 14
Calculus-I 10 11
Calculus-II 8 6

Null Hypothesis Ho: distribution of failed students is the same in Spring and Fall semesters.
Use Chi-Square test with the significance level 0.10 to check if given data support or do not
support Ho (should we reject or do not reject Ho).

a) Calculate Chi Square (sum of the last column).
b) Use Excel function =CHIDIST(Chi-Square, df) to find p-value for this case.
c) Compare p-value with the significance level 0.10.
If p-value is less than 0.10 then reject Ho.
If p-value is greater than 0.10 then do not reject (accept) Ho.
Show work
Linear Regression
In this week’s Forum we practice with Correlation
and Equation of Regression Line.

Assigned any numbers for x and y in the first two columns.
x y x2 y2 xy

Σx Σy Σx2 Σy2 Σ(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 α = 0.05.
If your calculated r is greater than critical value then you can make the conclusion that there is a linear correlation between x and y in your data. Otherwise, make the conclusion that there is no linear correlation between your sets of x and y.

Part 2. Find an Equation of Regression Line in a form: y = b0 + b1x
where b1 is a slope and b0 is a y-intercept.
Calculate slope of regression line:

Then find y-intercept: bo = y¯ − b1x¯y¯

where x¯x¯is average for x numbers
and y¯y¯is average for y numbers.