You recently obtained a job with a sports analytics firm, and your first assignment is to write 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 17^thseason 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 was 24.6 with a standard deviation of 8.0. 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.Devonte' Graham joined the Charlotte Hornets as rookie for the 2018-19 season and put up a three-point percentage of 28.1%. Fans are curious as to whether he will have a better or worse three-point percentage this season. So far, he has made 31 three pointers out of 73 attempts. Test whether his three-point 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? Discuss how your conclusion might change.