STAT 200_ Lab Activity for 4.3.2

STAT 200: Lab Activity for 4.3 part 2 Activity 1: Hypothesis tests, start to finish For this activity we will use NFL Scouting Combine data (Stat200NFL file on Canvas) for drafted running backs and wide receivers from years 2012-2014. The combine is a series of tests to evaluate college football players ahead of the NFL Draft. The dataset is available on Canvas. To perform the hypothesis tests below, you will need to upload the data to StatKey and select the appropriate columns. For guidance, refer to the StatKey guide. Data Dictionary The dataset contains the following variables: year Year player participated in combine position Running Back (RB) or Wide Receiver (WR) height height in inches weight weight in pounds fortyyd forty yard dash time in seconds threecone threecone time in seconds (run between 3 cones in an L shape) vertical vertical jump height in inches broad broad jump distance in inches bench number of bench press repetitions with 225lbs round round player was drafted (1-7) 1. Research Question : Is there a linear association between a player’s strength, measured using the bench variable, and the round he was drafted in? a. State the hypotheses of interest. i. Ho: p=0 ii. Ha: p≠0 b. What is the notation and value of the sample statistic? i. r=0.059 c. Use StatKey to generate a randomization distribution for these hypotheses. Remember, you will have to upload the dataset to StatKey and select the correct variables. What is the p-value? i. P value = 0.578 d. Complete the p-value interpretation below: If there is no linear association between the round he was drafted in and a player’s strength in the population, the chance of seeing a sample correlation of 0.059 or -0.059 is 0.578. e. What is the formal conclusion and conclusion in context using a significance level of 0.05? i. Fail to reject Ho: evidence suggests there is some correlation between bench press and round player was drafted Research Question : How fast are NFL Players? Prior to 2012, the average forty yard dash time for running backs and wide receivers was 4.53. On average, were NFL players between 2012-2014 significantly faster than in previous years? a. State the hypotheses of interest. i. Ho: mu=4.53 ii. Ha: mu < 4.53 iii.

b. What is the notation and value of the sample statistic? i. Xbar = 4.511 c. Use StatKey to generate a randomization distribution for these hypotheses. What is the p-value? i. p value= 0.035 d. Interpret the p-value. i. If the true mean time is 4.53, the chance of running 4.511 from 2012-2014 is 0.035. e. What is the formal conclusion and conclusion in context using a significance level of 0.05? i. Reject Ho; evidence suggests that the mean time is less than 4.53. 2. Research Question : Are running backs shorter than wide receivers? Assuming that running backs are group 1 and wide receivers are group 2, determine if, on average, running backs are shorter than wide receivers. a. State the hypotheses of interest. i. Ho: mu1≥mu2 ii. Ha: mu1<mu2 b. What is the notation and value of the sample statistic? i. X bar 1 - x bar 2 c. Use StatKey to generate a randomization distribution for these hypotheses. What is the p-value? i. 0.00 d. Interpret the p-value. i. Reject e. What is the formal conclusion and conclusion in context using a significance level of 0.05? i. Strong evidence to support reject Activity 2: Which kind of inference? For each of the examples below, decide whether it makes more sense to use a hypothesis test or a confidence interval. Also decide on the parameter of interest. If you want, you can also write the null and alternative hypotheses (as relevant) for practice. 1. A statistics professor wants to know what proportion of students use their TA’s office hour. She takes a random sample of students from all stats classes and ask each student if they have ever visited their TA’s office hour. a. Confidence Interval b. p 2. The same statistics professor wants to know if it is worth hiring an undergraduate student to lead group study sessions. She will only hire one if more than 20% of students would join the study sessions. She asks the same students from question 1 whether they would join, and she hopes to gather enough evidence to justify hiring an undergraduate. a. Hypothesis Test b. p 3. A new father is trying to decide which daycare to use for his baby. He decides to ask a random sample of parents from the daycare on campus the following question: How many days this winter was your baby too sick to go to daycare? If he finds evidence that, on average, babies from this daycare spent more than 6 days sick, he will choose to take his baby somewhere else. a. Hypothesis Test