A simple random sample of 56 men results in a standard deviation of 10.09 beats per minute. Use thesample results to test the claim that men have pulse rates that have a standard deviation equal to thepopulation standard deviation of 10.63 beats per minute at the 5% significance level. Assume that thesample is from a normally distributed population.What are the correct hypotheses? (Select the correct symbols and values.)Hg: Select an answerbeats per minute Original claim = Select an answerH;: Select an answerbeats per minuteEnter the critical values, along with the significance level and degrees of freedom xg.dr, below thegraph. (Graph is for illustration only. No need to shade.)(a,df)X- Distribution0.12010.080.060.040.02(Round to three decimal places.)Test Statistic =(Round to three decimal places.)Decision: Select an answerConclusion: [Select an answerhave a standard deviation equal to the population standard deviation of 10.63 beats per minute.the claim that men have pulse rates thatEETEOT2619Probability

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A simple random sample of 56 men results in a standard deviation of 10.09 beats per minute. Use the
sample results to test the claim that men have pulse rates that have a standard deviation equal to the
population standard deviation of 10.63 beats per minute at the 5% significance level. Assume that the
sample is from a normally distributed population.
What are the correct hypotheses? (Select the correct symbols and values.)
Hg: Select an answer
beats per minute Original claim = Select an answer
H;: Select an answer
beats per minute
Enter the critical values, along with the significance level and degrees of freedom xg.dr, below the
graph. (Graph is for illustration only. No need to shade.)
(a,df)
X- Distribution
0.12
01
0.08
0.06
0.04
0.02
(Round to three decimal places.)
Test Statistic =
(Round to three decimal places.)
Decision: Select an answer
Conclusion: [Select an answer
have a standard deviation equal to the population standard deviation of 10.63 beats per minute.
the claim that men have pulse rates that
EET
EOT
26
19
Probability

Expert Solution

Step 1

The claim of the test is that men have pulse rates that have a standard deviation equal to the population standard deviation $(σ)$ of 10.63 beats per minute. The hypothesis is,

Null hypothesis:

$H_{0} : σ = 10.63$ beats per minutes

Alternative hypothesis:

$H_{1} : σ \neq 10.63$ beats per minutes

The original claim is men have pulse rates that have a standard deviation equal to the population standard deviation of 10.63 beats per minute. That is, $H_{0}$ .

Thus, the original claim is $H_{0}$ .

Step 2

The sample size is 56. The significance level is 5%. The degrees of freedom is,

$\begin{array}{rcl} d f & = & n - 1 \\ = & 56 - 1 \\ = & 55 \end{array}$

The degrees of freedom is 55.

Critical value for $χ_{L}^{2}$ :

The right-tail area is,

$\begin{array}{rcl} \frac{1 + α}{2} & = & \frac{1 + 0.95}{2} \\ = & 0.975 \end{array}$

The critical value of at 55 degrees of freedom can be obtained using the excel formula “=CHISQ.INV.RT(0.975,55)”. The critical value is 36.398.

The value of $χ_{L}^{2}$ is 36.398.

Critical value for $χ_{U}^{2}$ :

The right-tail area is,

$\begin{array}{rcl} \frac{1 - α}{2} & = & \frac{1 - 0.95}{2} \\ = & 0.025 \end{array}$

The critical value of at 55 degrees of freedom can be obtained using the excel formula “=CHISQ.INV.RT(0.025,55)”. The critical value is 77.380.

The value of $χ_{U}^{2}$ is 77.380.

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