Question

A study titled “Heat Stress Evaluation and Worker Fatigue in a Steel Plant" (American Industrial Hygiene Association, Vol. 64, pp. 352-59) assessed fatigue in steel-plant workers due to the heat stress. A random sample of 29 casting workers had a mean post-work heart rate of 78.3 beats per minute (bpm). Assume that the population standard deviation of post-work heart rates for casting workers is 11.2 (bpm). You want to test that the mean post-work heart rate for casting workers exceeds the normal resting heart rate of 72 bpm?

Write down appropriate null and alternative hypotheses to test that the mean post-work heart rate for casting workers exceeds the normal resting heart rate of 72 bpm. Do the data provide enough evidence to conclude that at 5% significance level the mean post-work heart rate for casting workers exceeds the normal resting heart rate of 72 bpm? Calculate p value and explain.

Answer 1

## it is one sample z test :

we have given :

n  = sample size  = 29

x̄ = sample mean  = 78.3

μ = population mean = 72

σ = population standard deviation  = 11.2

α = 5 % = 0.05

Claim  :

to test that the mean post-work heart rate for casting workers exceeds the normal resting heart rate of 72 bpm?.

## step1 : null and alternative Hypothesis :

Ho : μ = 72   vs H1: μ  > 72

it is one tailed test : right tailed

## step 2 : Test statistics :

z = (x̄ - μ) *√ n /  σ

z  = ( 78.3 - 72 ) * √ 29 / 11.2

= 3.0292

## step 3 :  level of significance  = 0.05

## step 4 :  P value

=      ( use statistical table )

P [ z > 3.0292 ] = 0.001227

step 5 : Decision  :

We reject Ho if p value is less than α value using p value approach here
p value is  less than α value we reject Ho at given level of significance .

Step 6 : Conclusion :

There is Sufficient evidence to conclude that   the mean post-work heart rate for casting workers exceeds the normal resting heart rate of 72 bpm .