Instructions: The goal of a one sample z-test is to explore whether a sample significantly differs from the entire population from which the sample is drawn. The Miami Heat are a sample of players, drawn from a bigger population (the entire NBA). Can we say that the Heat is representative of the average field goal percentages in the rest of the NBA?
In the 2022/2023 season, the average field goal percentage for players in the whole entire NBA (the population) was 47.832, and the standard deviation was 7.621.
Your job is to determine if sample (the Miami Heat) differs from the whole population (the whole NBA)). In other words, are the players on the Miami Heat representative of the rest of the NBA in terms of field goal percentage? Please find table attached.
1-State the null hypothesis
• Ho: The sample average is different from the population average,, or M # u
• Ho: The sample average is not different from the population average, or M = u
2-State the alternative hypothesis
• H1: The sample average is different from the population average, or M # M
• H1: The sample average is not different from the population average, or M = H
3-Indicate the level of risk used in psychology
• The level of risk is. 1
• The level of risk is .05
• The level of risk is.01
• The level of risk is .5
4-Determine the best statistical test to use
• One-sample Z test
• T-test
• Correlational test
• Critical value test
• ANOVA
5- First, you’ll have to calculate the SEM. Use the values provided and the formula in the book/lecture to calculate the SEM. Put your value below. Round your response out to three decimal places.
6- Now, Compute the test statistic (Use the formulas in the book / lecture to calculate the correct statistic). Round to three decimal places.
7- The value needed to reject the null hypothesis (the critical value) is
1.96
3.25
2.10
0.05
8- Does the obtained value exceed the critical value (that is, is the obtained value larger than the critical value)?
Yes or no
9- Based on your answer to the previous question, the decision is to
• Reject the null hypothesis
• Fail to reject the null hypothesis
10- Write up your results as you would see it in a results section of an APA style empirical research paper.
11- Now, you want to test out whether just Centers on the Heat were different from the whole population (from the whole NBA).
What is the z value for comparing this sample of centers on the Heat to the whole population? Round your answer out to three decimal places. What is the z value for comparing this new smaller sample to the population? Round your answer out to three decimal places
5 Centers on the Heat. Field Goal %
Bam Adebayo 54
Cody Zeller 62.7
Orlando Robinson 52.8
Dewayne Dedmon 49.6
Omer Yurtseven 59.3
12- Is this sample of 5 centers from the Heat significantly different from the rest of the NBA in terms of number of points scored per game?
• Yes
• No
• There is not enough information to answer this question
13- Explain why you made the decision you did in the previous question (that is, explain why you believe it is or is not significantly different).
14- Would your answer to the previous two questions have been different if we had been exploring a directional hypothesis? why or why not?
