Question

Activity IV CHECK WHAT YOU KNOW. Solve the following problems. (2 points each)

1. Given n = 12; = 120 ml;s = 6. The parent population is normally distributed.

Find:

a. The point estimate.

b. The interval estimate of mean.

2. Rochelle wants to know the mean of all entering trainees in a boot camp. The mean age of a

random sample of 25 trainees is 18 years and the standard deviation is 1.3 years. The sample

comes from normally distributed population. Use a = 0.1 to find the following:

a. The point estimate.

b. The error.

c. The interval estimate of the population of the mean.

Answer 1

$1:\\\hat{\mu}=\bar{x}=120\\\alpha =0.1\\Confidence\,\,Interval:\\\left( \bar{x}-\frac{s}{\sqrt{n}}t_{n-1,1-\frac{\alpha}{2}},\bar{x}+\frac{s}{\sqrt{n}}t_{n-1,1-\frac{\alpha}{2}} \right) =\\=\left( 120-\frac{6}{\sqrt{12}}\cdot 1.7959,120+\frac{6}{\sqrt{12}}\cdot 1.7959 \right) =\\=\left( 116.889,123.111 \right) \\2:\\a:\\\hat{\mu}=\bar{x}=18\\b:\\E=\frac{s}{\sqrt{n}}t_{n-1,1-\frac{\alpha}{2}}=\frac{1.3}{\sqrt{25}}\cdot 1.711=0.44486\\c:\\\left( \bar{x}-E,\bar{x}+E \right) =\left( 18-0.445,18+0.445 \right) =\left( 17.555,18.445 \right)$