Stats Final Exam

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Rowan College, Burlington County *

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Statistics

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Feb 20, 2024

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*Information was found using the covid tracker from the cdc website as well as basketball.realgm.com for the NBA Statistics Question 1) Using the spreadsheet labeled Covid-19 Cases/Deaths by Ethnicity find the Summary Statistics for Covid-19 cases by ethnicity. Describe the shape of the distribution. Do any of your findings seem unreasonable? Do the findings coincide with the proportion of ethnicities throughout the United States? Mean Median Mode Std Dev Skewness Tot C19 Cases 2,285,135 842,422 #N/A 2977977.974 1.502475451 % C19 Cases 14.29% 5.30% #N/A 18.6% 1.504677937 Once graphing the information, it is seen that the data set has three peaks with a positive kurtosis of 1.457. This means that most of the data is more towards the tails of the distribution rather than the mean. With a mean of roughly 2.3 million cases, the only race that is remotely close to that amount is the black population. This information does not surprise me because it aligns with the proportion of races in the United States pretty well. That means the most Covid-19 cases come from the most populous race in the country which is caucasion and subsequently all the data follows that same standard.

Question 2) A light bulb manufacturer makes the claim that their light bulbs have a mean lifespan of 400 hours. A loyal customer of this company feels that their light bulbs last longer than 400 hours and plans on performing a hypothesis test to prove it. The hypotheses are Ho: μ=400 hours and Ha: μ>400 hours. Assume the results of the test result in us accepting the null hypothesis. Determine whether there would be a Type 1 Error, Type 2 Error, or a Correct Decision was made if in fact the mean lifespan of these light bulbs was in fact greater than 400 hours. This would be considered a Type 2 error because the customer failed to reject the null hypothesis when it was false. With the light bulbs actually averaging more than 400 hours the wrong decision was made to accept the null hypothesis, thus we classify this as a type 2 error to correct the mistake. Question 3a) Create a Scatterplot showing the total new Covid-19 cases per US State/Territory. Interpret your findings. I can tell from this plot that the information was already in order from most covid cases to least. I see one data value well above the rest and 5 data values that truly separate themselves from the rest. Once passing these values there is a large group of values that trend down in a linear fashion from about 11,000 cases all the way to 0 cases. 3b) Run the Summary Statistics of new Covid-19 cases per state. Do any of the findings surprise you? Mean Median Mode Std Dev Skewness New C19 cases per state 5,345 2,634 0 6445.984206 1.93760834

The findings here do not surprise me at all. The mean and and median being so low shows that there are many values close to zero bringing the mean down. The median being less than the mean shows that there are also multiple outlying values that are much higher than the average new Covid-19 cases. Florida and Michigan are the top two values being well above the mean for the set of data. Question 4a) Using the Spreadsheet labeled Covid-19 Cases by State(Last 7 Days) determine the following: Probability that a new Covid-19 case is from Florida Probability that a new Covid-19 case is from a state beginning with the letter A Probability that a state/territory has no new Covid-19 cases in the last week P(New C19 cases from Florida) = 0.096 P(New C19 case from state beginning with A) = 0.026 P(No new C19 cases in past week) = 0.068 4b) Justin is a Michigan native and is interested in seeing if the reported Covid-19 cases are accurate for his state. He takes an online random sample of 25 Michigan residents finding that 3 of them have recently been diagnosed with Covid-19. Using the appropriate binomial test, test the hypothesis that the proportion of Covid cases in Michigan to the entire US is not 0.07 at a significance level of 0.01. Ho:p=0.07 Ha:p ≠0.07 Alpha=0.01 Reject Ho of z>2.326 or z<-2.326 Pop. Proportion: 3/25 = 0.12 z=0.12-0.07/sqr((0.07*0.93)/25)=0.312 Accept Ho because 0.312<2.326 At an alpha level of 0.01 the population proportion of new Covid-19 cases in Michigan is 0.07. Question 5) James is a die hard NBA fan and wants to test to see the correlation between different team statistics within the game. Before testing for correlation, write out the 6 hypotheses you will be testing. Using the spreadsheet labeled NBA Team Game Averages, find the correlation between Points Per Game and the following: 3 Point Shots Made Per Game, Field Goal %, Assists Per Game, Steals Per Game, Blocks Per Game and Total Rebounds Per Game. Ho: There is no relationship between points per game and 3 point shots made per game. Ha: There is a positive relationship between Points Per Game and 3 Point Shots Made per game because as you make more valuable shots, you get more points per game. Ho: There is no relationship between points per game and field goal % . Ha: There is a positive relationship between Points Per Game and Field Goal % because the better a team shoots, the more points they get per game.

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Ho: There is no relationship between points per game and assists per game. Ha: There is a positive relationship between Points Per Game and Assists Per Game, because as more shots are assisted on, more shots are made. This leads to more points being scored per game. Ho: There is no relationship between points per game and steals per game. Ha: There is a positive between Points Per Game and Steals Per Game because as you steal the ball more you get more transition baskets leading to more points per game. Ho: There is no relationship between points per game and blocks per game. Ha: There is a positive relationship between Points Per Game and Blocks Per Game because good defense leads to good offense. Ho: There is no relationship between points per game and total rebounds per game. Ha: There is a positive relationship between Points Per Game and Total Rebounds per game because if you have more rebounds, you have the ball more. This allows for more points per game. Correlation Coefficient 3 Pointers Made Per Game Field Goal % Assists Per Game Total Rebounds Per Game Steals Per Game Blocks Per Game Points Per Game 0.43971134 72 0.75335432 75 0.38285983 53 0.36013993 44 0.04007842 244 0.13314822 43 I was correct with my predictions, predicting that all the relationships between the stats would be positive. The strongest correlation by far is between Field Goal % and Points Per Game which makes the most sense thinking about from an outside perspective. Scoring more efficiently directly correlates to more points. While the correlation between points per game and steals/blocks per game was barely positive at all, more so closer to no correlation at all. This also makes sense because defensive stats do not always lead to more points. Question 6) The owner of the Milwaukee Bucks feels that his team scores an above average amount of points compared to the rest of the league. The league average for points per game is 112. Across the past 10 games, the Bucks have averaged 122.1 points per game with a standard deviation of 4 points. Test the hypothesis that the bucks average more than the league average at a significance level of 0.10. Ho: μ=112 points Ha: μ>112 points Alpha: 0.10 Reject Ho if t>1.311 Df: 29(30 teams in the NBA)

t=(122.1-112)/(4/sqr(30))=13.829 Reject Ho because 13.829>1.311 At an alpha level of 0.10, the population mean points for the Milwaukee Bucks is greater than 112 points per game. Question 7) Alex is interested in finding out if there is a difference between rebounds per game of Eastern Conference teams compared to Western Conference teams. Each conference has 15 teams. Using the spreadsheet NBA Team Game Averages, conduct a two-sample T-test to determine whether one conference gets more rebounds on average than the other. Use an alpha level of 0.05. μ1= average rebounds of Eastern Conference Teams μ2= average rebounds of Western Conference Teams Ho: μ1= μ2 Ha: μ1≠ μ2 Alpha = 0.05 μ1= 44.17 μ2= 44.39 Std Dev for Eastern Teams: 1.723 Std Dev for Western Teams: 1.841 Reject Ho if t>1.761 or t<-1.761 44.49-44.17=0.32 Pooled Variance: 3.179 Pooled Std Dev: 1.783 t=0.478 Accept Ho because 0.478<1.761 At an alpha level of 0.05 the population mean rebounds per game for each conference is the same. Question 8) Using the spreadsheet NBA Team Totals find the Min, Max, and Range of the Field Goal %. Create a Histogram showing the Field Goal % by team. Determine the modality and kurtosis of the information presented in the graph. Does anything shock you? Min Max Range Field Goal % 0.43 0.492 0.062

The distribution is Unimodal and slightly left tailed. The one peak of the distribution is between 0.46 and 0.48. The Kurtosis of the distribution is -0.507. The tails are thin, and this distribution would be considered platykurtic or negative kurtosis. Question 9) A claim is made that 72% of people who eat a particular super food on a daily basis experience increased energy. A random sample of 100 participants ate the superfood daily and 65 of them reported an increase of energy. Test the validity of the claim at an alpha level of 0.05. Ho: p=0.72 Ha: p<0.72 alpha=0.05 Reject Ho if z<-1.645 Sample proportion: 65/100= 0.65% z= (0.65-0.72)/sqr((0.72)(1-0.72))/100=-1.559 Accept Ho because -1.559>-1.645 At an alpha level of 0.05 the population proportion is equal to 0.72. Question 10) A New Jersey School District claims that on average their high school students have 9.2 hours of homework per week. In order to test this claim a survey was given to 400 random freshman students across the district. In this sample, the average amount of homework hours reported was 7.9 hours with a standard deviation of 2 hours. Does this data show a decrease in homework hours for high school students in this district? Let alpha be equal to 0.01.

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Ho: μ=9.2 hours Ha: μ<9.2 hours alpha=0.01 Reject Ho if t < -2.336 Df:99 t=7.9-9.2/(2/sqr(400)=-13 Reject Ho because -13<-2.336 At an alpha level of 0.01 the population mean is less than 9.2 hours of homework per week.

Stats Final Exam

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