Mathematics: The mean birth weight of a sample of 195 boys is 32.7 hg with standard deviation 6.6 hg. Give the lower and upper endpoints of a 95% confidence interval for the mean birth weight of all boys. Round your answer to one decimal place.

The mean birth weight of a sample of 195 boys is

alannaamarriee

23.01.2022

Lower end point = 31.8 hg

Upper end point = 33.7 hg

Step-by-step explanation:

We are given the following in the question:

Sample mean, $\bar{x}$ = 32.7 hg

Sample size, n = 195

Alpha, α = 0.05

Standard deviation, s = 6.6 hg

Degree of freedom = n - 1 = 194

95% Confidence interval:

$\bar{x} \pm t_{critical}\displaystyle\frac{s}{\sqrt{n}}$

Putting the values, we get,

$t_{critical}\text{ at degree of freedom 194 and}~\alpha_{0.05} = \pm 1.972$

$32.7 \pm 1.972(\dfrac{6.6}{\sqrt{195}} )\\\\ = 32.7 \pm 0.932\\ = (31.768 ,33.632)\\\approx (31.8,33.7)$

Lower end point = 31.8 hg

Upper end point = 33.7 hg

0,0(0 оценок)