Final answer:
In this case, there is not enough evidence to conclude that the maximum vertical jumps before and after the training program are significantly different. This means that the training program did not have a significant effect on the players' maximum vertical jumps.
Step-by-step explanation:
To conduct a hypothesis test to determine whether there is a significant difference in maximum vertical jumps before and after the training program, we can use a paired t-test.
Step 1: State the null and alternative hypotheses:
Null hypothesis (H0): There is no difference in maximum vertical jumps before and after the training program.
Alternative hypothesis (Ha): There is a difference in maximum vertical jumps before and after the training program.
Step 2: Set the significance level (alpha):
Let's assume a significance level of 0.05, which is commonly used.
Step 3: Calculate the differences and their mean:
Calculate the differences between the before and after measurements for each player. Then, find the mean of these differences.
The differences are as follows:
Player1: -2
Player2: -2
Player3: 0
Player4: 2
Player5: -3
Player6: -1
Player7: 0
Player8: -2
Player9: 0
Player10: -2
Player11: -1
Player12: -2
Player13: -1
Player14: 1
Player15: 1
Player16: 0
Player17: 8
Player18: -2
Player19: -2
Player20: -1
The mean of the differences is: -0.6
Step 4: Calculate the standard deviation of the differences:
Calculate the standard deviation of the differences.
Using the differences calculated in step 3, the standard deviation of the differences is approximately 2.69.
Step 5: Calculate the test statistic:
Calculate the test statistic, which is the mean of the differences divided by the standard deviation of the differences, divided by the square root of the number of observations.
Using the mean of the differences (-0.6), the standard deviation of the differences (2.69), and the number of observations (20), the test statistic is approximately -0.32.
Step 6: Determine the critical value:
Determine the critical value for the t-test based on the significance level and the degrees of freedom (n-1).
With 20 observations, the degrees of freedom is 19. Looking up the critical value for a two-tailed test at a significance level of 0.05 and 19 degrees of freedom, the critical value is approximately ±2.093.
Step 7: Compare the test statistic to the critical value:
If the absolute value of the test statistic is greater than the critical value, we reject the null hypothesis. If the absolute value of the test statistic is less than the critical value, we fail to reject the null hypothesis.
In this case, the absolute value of the test statistic (0.32) is less than the critical value (2.093). Therefore, we fail to reject the null hypothesis.
Step 8: Interpret the results:
Based on the analysis, there is not enough evidence to conclude that the maximum vertical jumps before and after the training program are significantly different. This means that the training program did not have a significant effect on the players' maximum vertical jumps.
Your question is incomplete, but most probably the full question was:
The chinese olympic basketball team is trying a new training program to increase the maximum vertical jump of its players. the following are the maximum vertical jump of 20 players before and after the training program
Before After
Player1 24 22
Player2 22 20
Player3 19 19
Player4 22 24
Player5 28 25
Player6 26 25
Player7 28 28
Player8 24 22
Player9 30 30
Player10 29 27
Player11 25 24
Player12 20 18
Player13 17 16
Player14 18 19
Player15 18 19
Player16 28 28
Player17 16 24
Player18 27 25
Player19 27 25
Player20 24 23
Question: Conduct a complete hypothesis test to answer whether players had different maximum vertical jumps before and after the training program. Show all calculations.