Question

1. Use the significance level a, and confidence interval for estinating the population mean u. Assume that population has a normal distribution. An insurance company needs information about repairing costs of car being in accidents. A random sample of 20 cars has been drawn with a mean x = $1400 and standard deviation s-S250. Find 98% confidence interval for a true mean of all cars being in accidents.

Answer 1

$98\%~C.I.~for~true~mean~\mu~is\\ \left(\bar{x}-t_{0.01,19}\times \frac{s}{\sqrt{n}},~\bar{x}+t_{0.01,19}\times \frac{s}{\sqrt{n}} \right )=( 1258.04,~1541.96)\\ where,~n=20,~\bar{x}=1400,~s=250,~t_{0.01,19}=2.5395\\ Hence~98\%~C.I.~for~\mu~is\\ (\$1258.04,\$1541.96).$