You recently obtained a job with a sports analytics firm, and your first assignm
ID: 3361669 • Letter: Y
Question
You recently obtained a job with a sports analytics firm, and your first assignment is to write a report evaluating early evidence behind predictions for the 2017-18 NBA season. You will use your knowledge of hypothesis testing to assess the predictions.
1. For your analysis, you do not know the population standard deviation, so you will have to use the sample standard deviation instead. How will this affect the process for conducting a hypothesis test?
2. The 2017-18 season is Lebron James’s 15th season in league. Most players are past their peak at this career stage, and so some have predicted that Lebron’s performance will decline. Last season, Lebron’s average points per game was 26.4. In the first 8 games of this season, his average points per game is 25.6 with a standard deviation of 6.7. Conduct a hypothesis test to test this prediction using as the significance level.
Step 1: State the null and alternative hypotheses.
Step 2: Choose the significance level.
Step 3: Calculate the test statistic.
Step 4: Find the critical value(s).
Step 5: Compare the test statistic to the critical value(s).
Step 6: State the conclusion.
3. Dwight Howard joined the Charlotte Hornets for the 2017-18 season. His free throw percentage has been inconsistent during his NBA career, and people are curious as to whether or not he will be a strong free throw shooter with the Hornets. Last season, Howard’s free throw percentage was 53.3%. So far this season, he has made 25 out of 67 free throws. Test whether his free throw percentage is different from last season using a 0.02 level of significance.
4 .According to the Pew Research Center, 14% of adults rate basketball as their favorite sport to watch. Your boss believes this proportion may be higher among adults under age 35, and wants you to collect evidence to see if this is true. Your boss is comfortable with the probability of a Type I error being 0.05. You survey 60 adults under age 35, and find that 23% of them rate basketball as their favorite sport. Conduct a hypothesis test and state your conclusion.
5. Since your firm will base some expensive decisions on the results of the previous hypothesis test, your boss decides that you need to be more conservative in how you draw conclusions. How would do this? Discuss how your conclusion might change.
Explanation / Answer
answer q1 as per chegg policies
1)
if i dont know the value of population s.d. then i hvae to use one smaple t test instead of z test.
the value of sd in this test statistic is taken as the sample standard deviation
test statistic, t = (mean-u)/(sd/sqrt(n))
the change in value of test statistis, changes the critical region, which affects the decision. at 5% level of significance, z(a/2) = 1.96 and t=T.INV.2T(0.05,28)= 2.048.
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