Question

It is desired to estimate the average weight of a new born baby. The birth records of arandom sample of 60 babies' weights showed a mean of 7.0 lbs and standard deviation of 1.5 lbs.Construct a 95% confidence interval forμ.

Answer 1

95% confidence interval for the mean

(6.61251, 7.38749)

Explanation:

Step:-1

Given that a random sample 'n' = 60

Given that mean of the sample x⁻ = 7.0

Given that the standard deviation of the sample (S) = 1.5

Level of significance = 0.05

Degrees of freedom = n-1 = 60-1 = 59

t₍₀.₀₅ , ₙ₋₁₎ = 2.0010

Step(ii):-

95% confidence interval for the mean is determined by

`(x^(-) - t_(0.05,n-1) (S.D)/(√(n) ) , x^(-) + t_(0.05 , n-1) (S.D)/(√(n) ) )`

`( 7.0 - 2.0010 (1.5)/(√(60) ) , 7.0 + 2.0010 (1.5)/(√(60) ) )`

(7.0 - 0.38749 , 7.0 + 0.38749)

(6.61251 , 7.38749)

Final answer:-

95% confidence interval for the mean

(6.61251 , 7.38749)