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 2019-20 NBA season. You will use your knowledge of hypothesis testing to assess the predictions.

1. When conducting a hypothesis test for the population mean, you will not know the population standard deviation, so you will have to use the sample standard deviation instead. How will this affect the process?

2. The 2019-20 season is Lebron James’s 17th 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 27.4. In the first 9 games of this season, his average points per game is 24.6 with a standard deviation of 8.0. Conduct a hypothesis test to test this prediction using � = 0.1 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.

Answer 1

Ans:

1)As,population standard deviation will be unknown,we will use student's t distribution.
2)

step 1)

step 2)

significance level ,alpha=0.1

step 3)

Test statistic:

t=(24.6-27.4)/(8/SQRT(9))

t=-1.05

step 4)

critical t value=-1.397

Rejection region<-1.397

step 5)

As,test statistic is not less than critical value,we fail to reject the null hypothesis.

step 6)

There is not sufficient evidence to support the prediction  that Lebron’s performance will decline.