Bolt competed in the men\'s 100m track and field race in the 2016 Rio Olympics w
ID: 3207998 • Letter: B
Question
Bolt competed in the men's 100m track and field race in the 2016 Rio Olympics winning the gold medal on Sunday. He ran the 100m race three times (round 1, semifinal, and final) with the following times (in seconds):
10.07 9.86 9.81
1)Construct a 99% confidence interval for the mean of Usain Bolt's 100m race time.
2)Construct a 95% confidence interval for the variability of Usain Bolt's 100m race time.
3)Does the data provide sufficient evidence to indicate the standard deviation of Usain Bolt's 100m race time is greater than 1/10 of a second (i.e., 0.1 seconds)? Perform an appropriate test at the 10% level of significance using the P-value approach.
Explanation / Answer
Mean=(10.07+9.86+9.81)/3
Mean=9.91
Sd=0.137
a)
99% confidence interval= mean+-z(sd/sqrt(n))
=9.91+-2.56(0.137/sqrt(3))
=9.708,10.112
99%confidence interval is (9.708,10.112)
b)
95% confidence interval=9.91+-1.96*00.0790
=9.91+-0.154
=9.706,10.064
95confidence interval is (9.706,10.064)
C)
Standard deviation is greater than 0.1sec