Question

Solve the problem. Round your answer to one decimal place, if necessary 、 43) A-- 13) A random sample of 30 seventh grade students was selected from a particular school district The students were asked how many siblings they had. The responses are given below. Fi ,S (95%confidence interval for the mean number of siblings for ulation of seventh grade students in this school district. Assume standard deviation is 1.574 0 2 1 1 3 2 0 0 1 4 3 1 2 0 1 1 6 4 1 1 1 0 5 1 4 2 2 10 2 Na1S A)1 sibling < μ < 2.5 siblings B) 1.4 siblings <p < 2.1 siblings D) 1.3 siblings <p < 2.5 siblings C) 1.2 siblings <p < 2.3 siblings Iuo is a samnle statistic or a population parameter.

Answer 1

Since we know that
$Mean(\mu) = \frac{\sum_{i=1}^n x_i}{n}$
Where n is the number of data points
Now
$\sum_{i=1}^n x_i = 52.0$
and n = 30
This implies that
$\\Mean(\bar{x}) = \frac{52.0}{30} \\Mean(\bar{x}) = 1.7333$

Sample size (n) = 30
Standard deviation (s) = 1.574
Confidence interval(in %) = 95
z @ 95% = 1.96
Since we know that
$Confidence\; interval = \bar{x} \pm z\frac{s}{\sqrt{n}}$
Required confidence interval = $(1.7333-1.96\frac{1.574}{\sqrt{30}}, 1.7333&plus;1.96\frac{1.574}{\sqrt{30}})$
Required confidence interval = (1.7333-0.5632, 1.7333+0.5632)
Required confidence interval = (1.2, 2.3)

Option C is correct
Please hit thumps up if the answer helped you.