Michael wants to investigate whether the distribution of his classmates’ favorite NBA players of all time is different from the one reported by the NBA. He randomly surveys his classmates. The table below contains the percentages reported by the NBA and the observed counts from his random sample.

| Player | NBA Percentages | Observed Counts |
|----------------|-----------------|-----------------|
| LeBron James | 20% | 23 |
| Kobe Bryant | 30% | 28 |
| Steph Curry | 15% | 10 |
| Michael Jordan | 19% | 15 |
| Others | 16% | 11 |

Michael wants to carry out a statistical inference procedure for this scenario using the [tex]\chi^2[/tex]-distribution. Which of the following conditions must be met? (Select all that apply.)

A. There must be at least 3 levels of the categorical variable.
B. There must be at least 10 successes and 10 failures for each level of the categorical variable.
C. There must be an expected count of at least 5 for each level of the categorical variable.
D. The observations must be independent.
E. The difference in all calculated proportions must be at least 5.
F. The sample size must be at least 30 or the population data must be normally distributed.

There are a few conditions that must be met in order for Michael to carry out a statistical inference procedure for this scenario using the chi-squared distribution.

The conditions are as follows:

There must be at least 3 levels of the categorical variable. There must be an expected count of at least 5 for each level of the categorical variable.
The observations must be independent. There must be at least 10 successes and 10 failures for each level of the categorical variable.
In this scenario, the categorical variable is the favorite NBA player of Michael's classmates. There are 5 different players, so there are at least 3 levels of the categorical variable.
To check if the expected counts for each level of the variable are at least 5, we can use the formula:

E = (row total x column total) / sample size

For example, the expected count for LeBron James would be:

E = (23 + 28 + 10 + 15 + 11) x 0.20 = 15.4

Since the expected count for each level of the variable is at least 5, this condition is met. We are also told that Michael randomly surveyed his classmates, so the observations are independent. Finally, we can use the formula:

n x p ≥ 10 and n x (1 - p) ≥ 10to check if there are at least 10 successes and 10 failures for each level of the variable.

For example, for LeBron James:

n = 23 + 28 + 10 + 15 + 11 = 87p = 0.20n x p = 87 x 0.20 = 17.4n x (1 - p) = 87 x 0.80 = 69.6

Since both n x p and n x (1 - p) are greater than or equal to 10, this condition is also met.

Therefore, the conditions that must be met for Michael to carry out a statistical inference procedure for this scenario using the chi-squared distribution are:

There must be at least 3 levels of the categorical variable.

There must be an expected count of at least 5 for each level of the categorical variable.

The observations must be independent.

There must be at least 10 successes and 10 failures for each level of the categorical variable.

Learn more about chi square test here: https://brainly.com/question/4543358

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