MATH221 PROJECT II (1)
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Brigham Young University, Idaho *
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221
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Mathematics
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Feb 20, 2024
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MATH 221B: Final Project
For the Final Project: Design the Study assignment, complete the first section titled Design the Study
.
For the Final Project: Completed Project, complete the sections titled Collect and Describe the Data
and Make Inferences and Take Action
.
DESIGN THE STUDY
This is an individual project. You will create your own research question using one of the data sets provided. Review the data sets below and think of a research question:
●
BoardGames-2016-2021.xlsx
●
DisneyPlusShowRatings.xlsx
●
FastFoodNutritionValues.xlsx
●
NBAGames-2016-2021.xlsx
●
USPublicFoodAssistance-SNAP-1969-2019.xlsx
●
VideoGameSales.xlsx
Below are several examples of research questions to help you create your own research question:
●
One Mean
(Sigma Known or Unknown): Is the average age of those buying a second home as an investment rental property different than the national average of 47 years?
●
Two Dependent Samples
: Is there a difference between the mean amounts of time required to start a fire using the flint-and-steel method and the battery-and-steel-wool method?
●
Two Independent Samples
: Do certified cars have a higher mean listing price than non-certified cars?
●
ANOVA
: Is the mean age of death for writers different for at least one of the writing categories (novelists, poets, nonfiction)?
●
One Proportion
: Were more than 65% of college students involved in an automobile accident within the last 5 years?
●
Two proportions
: Is the proportion of men who use label details when buying clothes different than the proportion of women who use label details when buying clothes?
●
Chi-squared
: Are family structure and plans to attend college independent for female students?
Answer the questions below to help you refine your research question:
1.
What is your research question? Do the home free throw percentages from 2020 have a lower mean than the away free throw percentages from 2020?
2.
What population(s) are you studying?
NBA games 2016-2020.
3.
What is the experimental unit of the study you are conducting? In other words, what is the smallest entity from which you are collecting a single piece of data to be used for analysis? For example, if you are interested in the average difference in the number of shoes owned by female college students vs. male college students, the experimental unit of the study is a college student.
One NBA game.
4.
What is the response variable of the study? In other words, what is the variable of interest your experimental unit is responding to? For example, if you are interested in the average difference in the number of shoes owned by female college students vs. male college students, the response variable is the number of shoes of one of the students.
Home free throw percentages vs. away free throw percentages.
The response variable is the free throw percents from the year 2020.
5.
Is the response variable quantitative or categorical?
the response variable is quantitative.
6.
Which statistical method are you going to use for the study? It should be one of the following eight methods:
a.
Quantitative, one sample, sigma known
b.
Quantitative, one sample, sigma unknown
c.
Quantitative, two samples, paired (dependent)
d.
Quantitative, two samples, independent
e.
Quantitative, three or more samples (ANOVA)
f.
Categorical, test of one proportion
g.
Categorical, test of two proportions
h.
Categorical, Chi-squared test 7.
What are the null and alternative hypotheses of the study you are conducting? Please review the format of the hypotheses so that your response here is in agreement with your answer to Question 6. Be sure to state the hypotheses using mathematical symbols if appropriate, and define any symbols that aren't obvious. Home free throw percentage mean is u1. The away free throw percentage is u2.
Ho: u1 = u2
Ha: u1 < u2
8.
Please review the requirements in the text for your chosen statistical method from Question 6. What requirements must be met to use the statistical method? Explain why your study is in alignment with the requirements.
For two independent samples, the requirements are 2 independent random samples and that both samples follow a normal distribution. My study is in alignment with these rules because I have selected random samples using Google’s random number generator. The min is 1 and the max is 724 for all the data from 2020. The first number generated is for the sample size I’ll use, which was 31. The sample size for u1 is 31. The second number generated is for the next sample size, which was 43. The sample size for u2 is 43. I used the generator again to pick a row until I collected each sample. For u1, I put in the min and max number corresponding with the column
of free throws. I then used the number generator to randomize my 31 samples. Then I repeated the process for u2, but generated the 43 randomized samples. My study is in alignment with the requirements because my sample sizes are large and normally distributed.
Study Design Approval
The instructor/grader will give approval for the study design as part of the rubric for the first Final Project assignment. I
f
the study design is not approved, you must revise and resubmit the study design until you acquire approval. Work with your instructor as needed. It often takes two or more rounds of revisions before a study design is approved.
As you complete the following sections of the project, if you stray from the outline of your project that you have provided above, your project is no longer approved.
COLLECT AND DESCRIBE THE DATA
Collect the Data
1.
Provide the raw data that you randomly pulled from the dataset for your sample(s). You may submit your raw data as a separate file.
2.
Describe the random sampling method (simple random, stratified, cluster, systematic) you will use to select a sample from the population (i.e. your selected dataset). Your description must include exactly how you will perform the random selection and the size of your sample (the sample size must be “big enough” for your selected statistical method).
a.
Sampling Method: Simple Random sample
b.
Random Selection Procedure: For each data set I used Google’s random number generator. I input a minimum of 1 and a max of 1397 and generated 31 random numbers to make up data set 1. I then generated 43 random numbers to make data set 2.
c.
Sample size: u1=31, u2=43
Describe the Data
1.
Provide summary statistics that describe your data for EACH sample group. For quantitative data, include the sample size, mean, median, quartile 1, quartile 3, and standard deviation. For qualitative data, include the sample size, the proportion of success, the number of successes, the proportion of failure, and the number of failures.
Sample size: 31 Sample size: 43 Mean: .797 Mean: .775
Median: .8 Median: .792
Quartile 1: .75 Quartile 1: .692
Quartile 3: .8 Quartile 3: .85
Standard Deviation: .112 Standard deviation: .094
Provide well-labeled and helpful graphs of your data for EACH sample group. For quantitative data, you should provide a histogram AND a boxplot. For categorical data, you should provide a bar graph AND a pie chart.
Free
Throw
Percentag
es
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Box Plots for Home and Away Free Throw Percentages
2.
Do your descriptive statistics and graphs suggest that you should reject or fail to reject the null hypothesis? Explain. Note that you should NOT refer to any inferential statistics (i.e. test statistic, p-value, confidence interval, etc.) in your response.
The mean being about .8 for both data sets suggests that the mean for both are the same. The histogram for data set 1, is normally distributed with the most data in bins 5 and 6. The histogram for data set 2 is approximately normally distributed with most data in bin 6.
MAKE INFERENCE AND TAKE ACTION
Make Inference
1.
Check the requirements of the statistical method.
The requirement for two independent sample tests is to have a random sample, a large sample size, and a normal distribution.
u1 has a sample size of 31, greater than 30 (Central Limit Theorem), was randomly generated through a number generator, and has a normally distributed histogram.
u2 has a sample size of 43, greater than 30 (Central Limit Theorem), was randomly generated through a number generator, and has an approximately normal distributed histogram.
The requirements have been met.
2.
State the null and alternative hypotheses in words and symbols.
u1 = u2, The mean of the home free throw percentages are equal to the mean of the away free throw percentages.
u1 < u2, The mean of the home free throw percentages is less than the mean of the away free throw percentages.
3.
State the level of significance that you have chosen to use for your hypothesis test.
a
= .05
4.
State the test statistic and degrees of freedom (if applicable).
Test Statistic: .903
Degrees of Freedom: 57.653
5.
State the p-value.
P-value: .815
6.
Make a statement on rejecting or failing to reject the null hypothesis by comparing the p-value to the level of significance.
Since the P-value is greater than a
, we fail to reject the null hypothesis.
7.
State your conclusion in terms of the alternative hypothesis.
There is insufficient evidence to suggest that the mean of the home free throw percentages is less than the mean of the away free throw percentages. 8.
Calculate and interpret a confidence interval, using a confidence level of your choosing. If your chosen statistical
method is ANOVA or Chi-squared, you may skip this prompt.
Confidence Level: 95%
Confidence Interval: (-0.027, 0.072)
Interpretation: We are 95% confident that the true difference of means lies between the interval from -0.027 percent and 0.072 percent. 9.
Compare the confidence interval to the null hypothesis to determine whether the null hypothesis should be rejected. If your chosen statistical method is ANOVA or Chi-squared, you may skip this prompt.
As the null hypothesis is u1 = u2, we should fail to reject the null hypothesis.
Take Action
1.
What action(s) would you recommend based on the results of your hypothesis test?
Based on the results of the study, I would recommend a follow-up study using two independent samples and a larger confidence interval to find out if the mean of home free throw percentages is less than the mean of the away free throw percentages.