STAT 200 Week 6 Homework
NAME__________________ Score ______ / 50
STAT 200: Introduction to Statistics
Homework #6: Lesson9, Sections 3-6
Clearly Indicate Your Final Answer
Total Points Earned:
1. ______ out of 8
2. ______ out of 14
3. ______ out of 12
4. ______ out of 16
Score ______ / 50
1. (8 points) Listed below (and in the available Excel Data Set file) are the PSAT and SAT scores from prospective college applicants. The scores were reported by subjects who responded to a request posted by the web site talk.collegconfidential.com.
PSAT | 183 | 207 | 167 | 206 | 197 | 142 | 193 | 176 |
SAT | 2200 | 2040 | 1890 | 2380 | 2290 | 2070 | 2370 | 1980 |
a. (2 points) What is the regression equation that predicts the SAT scores given the PSAT scores as input?
b. (2 points) One student not included in the table above had a PSAT score of 229. What is the best predicted SAT score for this student?
c. (2 points) Is the result close to the student’s actual score of 2400?
d. (2 points) Are these valid results? Why or why not?
2. (14 points) The association between the temperature and the number of times a cricket chirps in 1 minute was studied by really bored statistics students. Listed below (and in the available Excel Data Set file) are the numbers of chirps in 1 minute and the corresponding temperatures in degrees Fahrenheit.
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. (2 points) What is the regression equation that predicts the temperature given the number of cricket chirps in 1 minute as an input?
b. (2 points) Find the best predicted temperature at a time when a cricket chirps 3000 times in 1 minute.
c. (2 points) What is wrong or a potential problem with the prediction in part a?
Now, assume we want to test to determine if there is sufficient evidence to conclude that there is an association or relationship between the number of chirps in 1 minute and the temperature.
d. (2 points) What is the hypothesis test associated with this claim?
e. (2 points) What is the rank correlation coefficient associated with this comparison?
f. (2 points) What is/are the critical values?
g. (2 points) What is the result of the hypothesis test (i.e. “Reject the Null Hypothesis” or “Fail to Reject the Null Hypothesis)? Why did you respond with this answer, and what does it mean?
3. (12 points) The Mars Candy Company claim that its M&M plain candies are distributed with the following color percentages: 16% green, 20% orange, 14% yellow, 24% blue, 13% red, and 13 % brown. The data set below contains data from a simple random sample of 100 M&Ms, 8 of which are brown (i.e. 8% or the proportion of 8 out of 100 are brown). Use a 0.05 significance level to test the claim of the Mars Candy Company.
Count | Red | Orange | Yellow | Brown | Blue | Green |
1 | 0.751 | 0.735 | 0.883 | 0.696 | 0.881 | 0.925 |
2 | 0.841 | 0.895 | 0.769 | 0.876 | 0.863 | 0.914 |
3 | 0.856 | 0.865 | 0.859 | 0.855 | 0.775 | 0.881 |
4 | 0.799 | 0.864 | 0.784 | 0.806 | 0.854 | 0.865 |
5 | 0.966 | 0.852 | 0.824 | 0.840 | 0.810 | 0.865 |
6 | 0.859 | 0.866 | 0.858 | 0.868 | 0.858 | 1.015 |
7 | 0.857 | 0.859 | 0.848 | 0.859 | 0.818 | 0.876 |
8 | 0.942 | 0.838 | 0.851 | 0.982 | 0.868 | 0.809 |
9 | 0.873 | 0.863 |
|
| 0.803 | 0.865 |
10 | 0.809 | 0.888 |
|
| 0.932 | 0.848 |
11 | 0.890 | 0.925 |
|
| 0.842 | 0.940 |
12 | 0.878 | 0.793 |
|
| 0.832 | 0.833 |
13 | 0.905 | 0.977 |
|
| 0.807 | 0.845 |
14 |
| 0.850 |
|
| 0.841 | 0.852 |
15 |
| 0.830 |
|
| 0.932 | 0.778 |
16 |
| 0.856 |
|
| 0.833 | 0.814 |
17 |
| 0.842 |
|
| 0.881 | 0.791 |
18 |
| 0.778 |
|
| 0.818 | 0.810 |
19 |
| 0.786 |
|
| 0.864 | 0.881 |
20 |
| 0.853 |
|
| 0.825 |
|
21 |
| 0.864 |
|
| 0.855 |
|
22 |
| 0.873 |
|
| 0.942 |
|
23 |
| 0.880 |
|
| 0.825 |
|
24 |
| 0.882 |
|
| 0.869 |
|
25 |
| 0.931 |
|
| 0.912 |
|
26 |
|
|
|
| 0.887 |
|
27 |
|
|
|
| 0.886 |
|
a. (2 points) Identify the null and alternative hypothesis associated with this claim.
b. (4 points) What is the value of the test statistic?
c. (2 points) What is the P-value?
d. (2 points) What is the critical value?
e. (2 points) What is the area of the critical region?
f. (2 points) What is the result of the hypothesis test (i.e. “Reject the Null Hypothesis” or “Fail to Reject the Null Hypothesis)? Why did you respond with this answer, and what does it mean?
4. (16 points) The table below lists the chest deceleration measurements of crash test dummies (in g, where g is the force of gravity) of a standard crash test from samples of small, midsize, and large cars.
Small | 44 | 39 | 37 | 54 | 39 | 44 | 42 |
Medium | 36 | 53 | 43 | 42 | 52 | 49 | 41 |
Large | 32 | 45 | 41 | 38 | 37 | 38 | 33 |
a. (2 points) What characteristics of the data above indicates that we should use one-way analysis of variance?
b. (2 points) If the objective is to test the claim that the three size categories have the same mean chest deceleration, why is the method referred to as analysis of variance?
c. (2 points) If we want to test for the equality of three means, why do we not use three separate hypothesis tests for ,
, and
?
d. (2 points) Perform an analysis of variance on the data set. Provide the table of results (hint: use Excel’s Dana Analysis add-in to complete this step without having to do the work by hand).
e. (2 points) What is the value of the test statistic you found in part d?
f. (2 points) What kind of distribution is used with the test statistic from part e?
g. (2 points) If we use a 0.05 significance level in analysis of variance with this data set, what is the P-value?
h. (2 points) What would we conclude about the data set from this analysis of variance?
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