Question

The Olympic Summer Games is an international multi-sport event that has been held every four years since 1896. Competitors from countries across the world compete against one another, representing their countries, in one or more sports events such as wrestling, rowing, high jump, running races, etc. Events may be separated by the sex of the competitors (male or female) or may be mixed (i.e. males and females competing with each other in the same event). At the end of each event, the top three competitors are awarded a medal: bronze for third place, silver for second place, and gold for first place.  

The dataset.csv file you will be working with contains results from the Olympic Summer Games for a subset of the years that these Games have run. There are 9 columns (i.e. vectors) in the dataset, and 7974 rows (i.e. observations). There are NO missing values in the dataset.csv file. A description of the columns is as follows:

Name of vector	Description of data	Example values
sex	Character vector that gives the sex (M=male or F=female) of the athlete	M F
age	Integer vector the gives the age (in years) of the athlete	28
height	Integer vector that gives the height (in centimetres) of the athlete	175
weight	Integer vector that gives the weight (in kilograms) of the athlete	64
event	Character vector that identifies the event in which the athlete participated	Athletics Men’s Long Jump
year	Integer vector that identifies the year in which the athlete participated in the Games	1992
sport	Character vector the identifies the generic category of sport the athlete participated in	Basketball Athletics
season	Character vector that identifies the season during which the Games occurred; all values are Summer	Summer
medal	Character vector that identifies the type of medal (bronze, silver, or gold) won by the athlete	Gold Silver Bronze

The Research Question: Is there a relationship between the weight and height of male competitors of the Summer Olympic Games?

1) Based on the information provided, which of the following inference procedures is most appropriate to address the Research Question?

A.	t test for the population mean
B.	large sample test for the population proportion
C.	t test for the difference between means
D.	large sample test for the difference between proportions
E.	t test for slope
F.	one-factor ANOVA

2) Write the pair of statistical hypotheses (i.e. null and alternative) in sentence form that would be relevant, based on the inference procedure you selected in part a. Your hypotheses should be phrased in the context/language of the specific research question/scenario.

3) (i) write each condition required for the hypothesis test to be valid, and,

(ii) below each condition, briefly describe/identify the method (i.e. how?) you should use to evaluate the validity of the condition. For conditions that involve manipulating/investigating some aspect of the data, use R to produce the R output necessary for evaluation using the dataset.csv file you were provided. Include the R code and output in your answer

(iii) Provide the R code and Output you used to conduct the inference procedure. It should be clear from the code you report (and any brief #comments) where any values/vectors you use as arguments come from (i.e. we should be able to figure out/recreate what you did based on your code).

(iv) Provide a proper scientific conclusion for the results of your analysis.

Answer 1

1)

option E)

t test for slope

2)

Ho :beta1 = 0

Ha: beta1 <> 0

3)

model <- lm(weight ~ Height , data = tableName)

summary(model)

you can check p-value of slope

if p-value < alpha, we reject the null hypothesis