Question

When engaging in weight-control (fitness/fat burning) types of exercise, a person is expected to attain about 60% of their maximum heart rate. For 20-year-olds, this rate is approximately 120 bpm. A simple random sample of 200 20-year-olds was taken, and the sample mean was found to be 107 bpm with a standard deviation of 45 bpm. Researchers wonder if this is evidence to conclude that the expected level is lower than 120 bpm. a. (2 points) What are the conditions for inference? And are they satisfied? b. (3 points) Test the following hypotheses at 5% significance level – follow the five steps. H0:u=120 Ha:u>120

Answer 1

Solution :

= 120

= 107

s = 45

n = 200

a ) This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :   = 120

H_a :     120

b ) Test statistic = t

= ( - ) / s / n

= (107-120) / 45 / 200

= −4.086

Test statistic t = −4.086

it is observed that t = 4.086 ≤ tc​ = 1.653, it is then concluded that the null hypothesis is not rejected

c ) P-value = 1

= 0.05  

P-value >

1 > 0.05

d ) The null hypothesis is not rejected

the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean μ is greater than 120, at the 0.05 significance level.