Question

An article in Medicine and Science in Sports and Exercise "Electrostimulation Training Effects on the Physical Performance of Ice Hockey Players," (2005, Vol. 37, pp. 455–460) considered the use of electromyostimulation (EMS) as a method to train healthy skeletal muscle. EMS sessions consisted of 30 contractions (four-second duration, 85 Hz) and were carried out three times per week for three weeks on 17 ice hockey players. The ten-meter skating performance test showed a standard deviation of 0.09 seconds. Construct a 90% confidence interval of the standard deviation of the skating performance test. Assume population is approximately normally distributed. Round your answers to 3 decimal places.

Answer 1

Answer:

0.0702 < δ < 0.0128

Step-by-step explanation:

Data: First, we calculate the confidence from the standard deviation:

the significance level = 1 - 0.90

                                   = 0.10

the standard deviation of the sample, δ = 0.09

From the Χ² table, we get = 7.96 and 26.30

The confidence interval of the population is given by the following:

$0.09*\sqrt{\frac{16}{26.30} } < \sigma < 0.09 * \sqrt{\frac{16}{7.96} } \\ 0.0702 < \sigma < 0.128$

Answer 2

Answer: $0.070$

Step-by-step explanation:

Confidence interval for population standard deviation :-

$s\sqrt{\dfrac{n-1}{\chi^2_{\alpha/2, n-1}}}$

Given : Significance level : $\alpha: 1-0.90=0.10$

Sample size : n= 17

Sample standard deviation: $s= 0.09$

Then by using the chi-square distribution table, we have

$\chi^2_{1-\alpha/2, n-1}}=\chi^2_{0.95, 16}=7.96$

$\chi^2_{\alpha/2, n-1}}=\chi^2_{0.05, 16}=26.30$

Confidence interval for population standard deviation will be :-

$( 0.09)\sqrt{\dfrac{16}{26.30}}$

Hence, 90% confidence interval of the standard deviation of the skating performance test.: $0.070$