Question

The average time for 100-meter race that Usain Bolt used is 9.6 seconds on average. He wants to test whether his speed has decreased or not. His speed was tested for 16 times, and the average time is 9.7 seconds. Assume the population standard deviation is 0.1 second. At a 5% significance level, the decision is to _________.

Answer 1

At a 5% significance level we reject the Null hypothesis
`H_0`

Explanation:

From the question we are told that:

Distance
`d= 100`

Mean
`\mu=9.6`

Sample size
`n=16`

Sample mean
`\=x=9.7`

Standard deviation
`\sigma= 0.1`

significance level
`\alpha=5%=>0.05`

Generally the Hypothesis is mathematically given by

`H_0=\mu=9.6`

`H_a=\mu=9.6`

Generally the equation for t test statistics is mathematically given by

`t=(\=x-\mu)/((\sigma)/(√(n) ) )`

`t=(9.7-9.6)/((0.1)/(√(16) ) )`

`t=4`

Therefore P-Value from table

`P-Value=0.000`

`\alpha>P-value`

Therefore

At a 5% significance level we reject the Null hypothesis
`H_0`