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[answered] MATH1P98 - Assignment #5 - Section #1,2 Due: Monday, Decemb


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MATH1P98 - Assignment #5 - Section #1,2

 

Due: Monday, December 5 @ 11:59 pm

 

Students are expected to complete all questions on the assignment. However, only a subset of

 

questions will be considered for marking. Marks will be deducted for incomplete assignments.

 

Assignment submissions must be neat, legible, written on one side of the page only, and questions must be submitted in order. A cover page must be attached to the front of the assignment

 

(see sample cover page on Sakai). Staple all pages on the top left corner.

 

Please submit answers to the following questions to your assignment drop box by 11:59pm

 

of the due date. The text is Elementary Statistics using Excel (5th Edition), by M. Triola.

 

Correction: Data set in Question 4 has been replaced

 

1. For this question use the following set of data points. Use Excel?s CORREL function to

 

find the value of the correlation coefficient.

 

x 1

 

y 1 1 1 2 2 2 3

 

2 3 1 2 3 1 3 3 10

 

2 3 10 (a) Obtain a scatter plot of the 10 data points.

 

(b) Find the value of the correlation coefficient for the 10 data points.

 

(c) Use Table A-6 on page 778 and ? = 0.05 to determine if there is a linear correlation.

 

Now remove the point with coordinates (10, 10) so there are 9 pairs of points.

 

(d) Obtain a scatter plot of the 9 data points.

 

(e) Find the value of the correlation coefficient for the 9 data points.

 

(f) Use Table A-6 on page 778 and ? = 0.05 to determine if there is a linear correlation.

 

(g) What conclusion do you make about the possible effect of a single pair of values?

 

2. For this question use the following set of data points.

 

x 10

 

8

 

13

 

9

 

11

 

14

 

6

 

4

 

12

 

7

 

5

 

y 9.14 8.14 8.74 8.77 9.26 8.1 6.13 3.10 9.13 7.26 4.74

 

(a) Find the value of the linear correlation coefficient r.

 

(b) Use Table A-6 on page 778 and ? = 0.05 to determine if there is evidence to support

 

the claim of a linear correlation between the two variables.

 

(c) Obtain a scatterplot and add a trendline. Display the equation of the line on the

 

plot. 1 (d) Which feature of the data would be missed if part (a) was completed without constructing a scatterplot?

 

3. It has been said that one can use cricket chirps to estimate temperature. For this question

 

use the following set of data points.

 

Chirps in 1 minute 882 1188 1104 864 1200 1032 960 900

 

Temperature (F )

 

69.7 93.3 84.3 76.3 88.6 82.6 71.6 79.6

 

(a) Obtain a scatterplot of the data.

 

(b) Find the correlation coefficient.

 

(c) Follow the steps below to perform a hypothesis test to determine if the linear correlation is significantly different from 0 at the 5% level.

 

i. State the null and alternate hypothesis.

 

ii. Use the r value from your Excel output to compute the t test statistic as described

 

on page 543.

 

iii. State the appropriate degrees of freedom.

 

iv. Use Excel to find the p?value for determining whether the correlation coefficient

 

is significantly different from 0.

 

v. Based on the p?value, do we to reject or not reject the null hypothesis? What

 

can you say about the existence of a linear relationship between cricket chirps

 

per minute and temperature (F )?

 

(d) Use Excels Data Analysis to obtain the regression analysis.

 

(e) State the regression equation. Provide a brief sentence that interprets the value of

 

the slope.

 

(f) Find the best predicted value when a cricket chirps 3000 times in 1 minute. What is

 

wrong with this predicted value?

 

4. In the following data x = size of a park in acres and y = number of park employees

 

x

 

y 39334 324 17315 8244 620231 43501 8625 31572 14276 21094

 

95

 

95

 

102

 

69

 

67

 

77

 

81

 

116

 

51

 

36 x 103289 130023 16068 3286 24089 6309 14502 62595 23666 35833

 

y

 

96

 

71

 

76

 

112

 

43

 

87

 

131

 

136

 

80

 

52

 

(a) Use Excels Data Analysis to find the equation of the regression line and a Line Fit

 

Plot (Refer to page 555 for Excel directions). Write the equation of the regression

 

line. Do you think the line gives accurate predictions? Why? 2 (b) Delete the observation with largest x value from the data set. Redo the Data Analysis

 

to obtain the new equation of the regression line and the new Line Fit Plot calculations

 

for the new data set. Write the equation of the regression line. Does this observation

 

greatly affect the equation of the line? Compare the signs of the slopes of the two

 

regression lines.

 

5. The data in the file Weight of football players (on Sakai) represent weights (pounds) of a

 

random sample of professional football players on the following teams.

 

X1

 

X2

 

X3

 

X4

 

X5 = weights of players for the Dallas Cowboys

 

= weights of players for the Green Bay Packers

 

= weights of players for the Denver Broncos

 

= weights of players for the Miami Dolphins

 

= weights of players for the San Francisco Forty Niners Reference: The Sports Encyclopedia Pro Football

 

Follow the steps below to test whether the mean weight of football players is the same for

 

all 5 teams. Use a significance level of 5%.

 

(a) Write the null and alternate hypothesis

 

(b) Use Excel to perform an ANOVA analysis. (Refer to page 641 for Excel directions).

 

(c) Write the value of the test statistic. (Copy it from the Excel printout.)

 

(d) What is the p?value associated with this test statistic? (Copy it from the Excel

 

printout.)

 

(e) Based on the p?value from the ANOVA table, do we reject or not reject the null

 

hypothesis? What can be concluded about the mean weights of the players on the 5

 

different teams? 3

 


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