Question

Q5:

Given info: A sports team compared two versions of a basketball (denoted as J and K) with respect to the time it takes to reach the hoop when thrown. They randomly selected 100 basketball players, and then they randomly assigned 50 to each basketball version. Basketball J has a sample mean of 209 and an SD of 37, while Basketball K has a sample mean of 225 and an SD of 41.

Question: The sports team wants to know if there’s a significant difference between the two basketball versions with regards to the mean time they take to reach the hoop. To answer this, compute a 95% confidence interval for the difference in the mean time for the two basketball versions (J and K), and state hypothesis and conclusion

Answer 1

Confidence interval(in %) = 95
z @ 95.0% = 1.96
Since we know that

Required confidence interval = (209.0-225.0-15.3081, 209.0-225.0+15.3081)
Required confidence interval = (-31.3081, -0.6919)

The test hypothesis is

This is a two-sided test because the alternative hypothesis is formulated to detect differences from the hypothesized difference in mean values on either side.
Now, the value of test static can be found out by following formula:
Conclusion:
Now the whole confidence interval is less than 0, we can conclude that there is significant difference between the two basketball version with regards to the mean time they take to reach the hoop and Basketball K take more time to reach the hoop