MATH1P98 - Winter 2021 - Assignment #3: Due: Tue March 31 @ 11:59 pm EST
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1. A study asked students to report their height and then compare to the actual measured
height. Assume that the paired sample data are simple random samples and the differences
have a distribution that is approximately normal.
Reported Height 68 71 63 70 71 60 65 64 54 63 66 72
Measured Height 67.9 69.9 64.9 68.3 70.3 60.6 64.5 67 55.6 74.2 65 70.8
a) State the null and alternative hypotheses.
b) Use EXCEL to construct a 99% confidence interval estimate of the difference of means
between reported heights and measured heights. Attach your printout to this question,
where the reported height is column A, measured height in column B, and the difference
in column C.
i) Open Excel and click DATA on the ribbon of the Excel.
ii) Click Data Analysis. If Data Analysis is not available, please follow the instructions
in Assignment 1.
iii) Select Descriptive Statistics and click OK.
iv) Enter the range of the heights including the label (A1:A13).
v) Select Labels in First Row.
vi) Select Summary statistics.
vii) Select Confidence Level for Mean and type in 99 and click OK.
Calculate and write down the 99% confidence interval by hand based on the result you get
from the Excel (keep four decimal places in your final answer).
c) Interpret the resulting confidence interval.
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2. 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 1 1 2 2 2 3 3 3 10
y 1 2 3 1 2 3 1 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 Excel with α = 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 Excel with α = 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?
3. 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 Excel with α = 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.
(d) Which feature of the data would be missed if part (a) was completed without constructing
a scatterplot?
4. 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.
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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?
5. In the following data x = size of a park in acres and y = number of park employees
x 39334 324 17315 8244 620231 43501 8625 31572 14276 21094
y 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. Write the equation of the regression line. Do you think the line gives accurate
predictions? Why?
(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.