Question

The heart rate of 20 randomly selected adults was on average 85 beats per minute (bpm) with a standard deviation of 5 bpm. Build a 95% confidence interval for the mean heart rate of adults in the population. Interpret the interval you have created.

Answer 1

Answer: (82.66, 87.34).

Explanation:

When population standard deviation is unknown and sample size is small , then the formula is used to find the confidence interval for
`\mu` is given by :-

`\overline{x}\pm t^*(s)/(√(n))`

, where n = sample size ,
`\overline{x}`= sample mean , t*= two tailed critical value s= sample population standard deviation, .

Given,
`\overline{x}=85`, s=5, n=20 , degree of freedom = 19 [∵df=n-1]

For 95% confidence level ,
`\alpha=0.05`

By t-distribution table ,

t-value for
`\alpha/2=0.025` (two tailed) and df =19 is t*=2.0930

Now , the 95% confidence interval for the mean heart rate of adults in the population will be :

`85\pm (2.0930)(5)/(√(20))`

`=85\pm (2.0930)(1.118034)`

`\approx85\pm 2.34`

`=(85- 2.34,\ 85+2.34)\\\\=(82.66,\ 87.34)`

Hence, the required interval is (82.66, 87.34).

Interpretation : A person can be 95% confident that the mean heart rate of adults in the population lies between (82.66, 87.34).