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vladimir2022 [97]
3 years ago
12

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 decre

ased 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 _________.
Mathematics
1 answer:
Fantom [35]3 years ago
7 0

Answer:

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

Step-by-step 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=\frac{\=x-\mu}{\frac{\sigma}{\sqrt{n} } }

 t=\frac{9.7-9.6}{\frac{0.1}{\sqrt{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

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