STAT301 Spring 2026 Midterm Exam Name
Please perform the analysis in R for analysis questions. Write your answers on this word file. Turn in
the word file and your R Markdown file to the drop box before due time. Assume all the data follow
the normal distribution unless if otherwise noted.
1. (10pts) A research was designed to study the main effects of practice time (morning vs.
afternoon) and type of shoes (A and B) on athletes’ performance. The researcher recruited 50
athletes in the study and asked all of them wear shoes A and run 1 mile in the morning and then
in the afternoon to record their time to finish. He then asked all of the same individuals wear
shoes B and do the same thing in the morning and then in the afternoon. He compared the time
to finish the 1 mile to test if there is a significant main effect of shoe type and a significant main
effect of practice time.
Answer the questions below:
a) (2pts) What analysis should it be? (Choose from independent t-test, paired t-test, one-way
ANOVA, two-way ANOVA, one-way repeated measure ANOVA, two-way fixed repeated measure
ANOVA, and two-way mixed repeated measure ANOVA).
two way Anova
b) (2pts) What are the independent variables? Practice time and shoe type
c) (2pts) What type of variable are the independent variables? (Choose between categorical and
numeric).
Categorical
d) (1pt) What is the dependent variable? Time to finish the 1 mile
e) (2pts) What type of variable is the dependent variable? (choose from numeric or categorical)
numeric
f) (1pt) What is the possible confounding variable of this case?
The weather of the running time is confounding variable.
2. (8 pts) Listed below are speeds (mi/h) measured from southbound traffic on I-280 near
Cupertino, California. This simple random sample was obtained at 3:30pm on a weekday. Use the
0.05 significance level to test the claim that the population mean speed on that highway for all
the cars is significantly more than the speed limit of 65mi/h.
, STAT301 Spring 2026 Midterm Exam Name
62 61 67 71 74 69 68 69 70
Follow the steps below:
(2pts) Step 1: Formulate the null and alternative hypothesis using the correct notations
H0: mu = 65mi/hr
Ha: mu greater than 65mi/hr
(2pts) Step 2: Choose the one simple t test
(2pts) Step 3: Use R to find the test statistic and p-value (keep 3 decimal places)
T = 2.095, p-value = 0.035
(2pts) Step 5: Conclude to the null hypothesis; AND address the decision in the context
Reject H0. There is evidence to support the claim that the population mean speed on that
highway for all the cars is significantly more than the speed limit of 65mi/h.
3. (8pts) A business analytics project was conducted to compare the performance between three
industry sectors (electronic manufacturing, chemical manufacturing, and food industry). The
analyst found the performance indices of 15 companies with 5 being electronic manufacturing, 5
being chemical manufacturing, and 5 being in food industry. The table below shows the
performance indices of those 15 companies. Use the 0.05 significance level to test the claim that
the average performance was significantly different among the three industry sectors. Enter the
data in R with the correct format first and then follow the steps below for the test.
Electronic Chemical Food industry
manufacturing manufacturing
59 52 79
71 51 51
68 43 82
82 66 93
90 79 60
Step 1: (2pts) Formulate the null and alternative hypotheses
H0: mu of Electronic manufacturing = mu of Chemical manufacturing = mu of Food industry
Ha: at least two mean are different
Step 2: (2pts) Choose the one way anova test
Step 3: (2pts) Find the test statistic and p-value from R (keep 3 decimal places)
F = 1.824, p-value = 0.203
Please perform the analysis in R for analysis questions. Write your answers on this word file. Turn in
the word file and your R Markdown file to the drop box before due time. Assume all the data follow
the normal distribution unless if otherwise noted.
1. (10pts) A research was designed to study the main effects of practice time (morning vs.
afternoon) and type of shoes (A and B) on athletes’ performance. The researcher recruited 50
athletes in the study and asked all of them wear shoes A and run 1 mile in the morning and then
in the afternoon to record their time to finish. He then asked all of the same individuals wear
shoes B and do the same thing in the morning and then in the afternoon. He compared the time
to finish the 1 mile to test if there is a significant main effect of shoe type and a significant main
effect of practice time.
Answer the questions below:
a) (2pts) What analysis should it be? (Choose from independent t-test, paired t-test, one-way
ANOVA, two-way ANOVA, one-way repeated measure ANOVA, two-way fixed repeated measure
ANOVA, and two-way mixed repeated measure ANOVA).
two way Anova
b) (2pts) What are the independent variables? Practice time and shoe type
c) (2pts) What type of variable are the independent variables? (Choose between categorical and
numeric).
Categorical
d) (1pt) What is the dependent variable? Time to finish the 1 mile
e) (2pts) What type of variable is the dependent variable? (choose from numeric or categorical)
numeric
f) (1pt) What is the possible confounding variable of this case?
The weather of the running time is confounding variable.
2. (8 pts) Listed below are speeds (mi/h) measured from southbound traffic on I-280 near
Cupertino, California. This simple random sample was obtained at 3:30pm on a weekday. Use the
0.05 significance level to test the claim that the population mean speed on that highway for all
the cars is significantly more than the speed limit of 65mi/h.
, STAT301 Spring 2026 Midterm Exam Name
62 61 67 71 74 69 68 69 70
Follow the steps below:
(2pts) Step 1: Formulate the null and alternative hypothesis using the correct notations
H0: mu = 65mi/hr
Ha: mu greater than 65mi/hr
(2pts) Step 2: Choose the one simple t test
(2pts) Step 3: Use R to find the test statistic and p-value (keep 3 decimal places)
T = 2.095, p-value = 0.035
(2pts) Step 5: Conclude to the null hypothesis; AND address the decision in the context
Reject H0. There is evidence to support the claim that the population mean speed on that
highway for all the cars is significantly more than the speed limit of 65mi/h.
3. (8pts) A business analytics project was conducted to compare the performance between three
industry sectors (electronic manufacturing, chemical manufacturing, and food industry). The
analyst found the performance indices of 15 companies with 5 being electronic manufacturing, 5
being chemical manufacturing, and 5 being in food industry. The table below shows the
performance indices of those 15 companies. Use the 0.05 significance level to test the claim that
the average performance was significantly different among the three industry sectors. Enter the
data in R with the correct format first and then follow the steps below for the test.
Electronic Chemical Food industry
manufacturing manufacturing
59 52 79
71 51 51
68 43 82
82 66 93
90 79 60
Step 1: (2pts) Formulate the null and alternative hypotheses
H0: mu of Electronic manufacturing = mu of Chemical manufacturing = mu of Food industry
Ha: at least two mean are different
Step 2: (2pts) Choose the one way anova test
Step 3: (2pts) Find the test statistic and p-value from R (keep 3 decimal places)
F = 1.824, p-value = 0.203
