Question

Problem 10-9 A sample of 40 observations is taken from a population of unknown mean wherein the standard deviation is assumed to be 5 grams. The computed value of the sample mean is 38.0 grams. Construct confidence intervals for each of the following levels of confidence: (a) 90% Confidence Interval

Answer 1

Answer: (36.7, 39.3)

Step-by-step explanation:

Confidence interval for population mean:

$\overline{x}\pm z^c\dfrac{\sigma}{\sqrt{n}}$ , where n= sample size, $\overline{x}$= sample mean, $\sigma$ = population standard deviation, $z^c$ = critical z value.

Given: n= 40 , $\sigma=5\ g,\ \ \ \overline{x} = 38.0\ g$

Critical z-value for 90% confidence = 1.645

Then, required confidence interval:

$38.0\pm(1.645)\dfrac{5}{\sqrt{40}}\\\\= 38.0\pm (1.645)(0.79057)\\\\\approx38.0\pm1.30\\\\= (38-1.30,\ 38+1.30)=(36.7,\ 39.3)$

Hence, a 90% Confidence Interval =  (36.7, 39.3)