Question

A sample of 20 heads of lettuce was selected. Assume that the population distribution of head weight is normal. The weight of each head of lettuce was then recorded. The mean weight was 2.2 pounds with a standard deviation of 0.1 pounds. The population standard deviation is known to be 0.2 pounds. Construct a 90% confidence interval for the population mean weight of the heads of lettuce. State the confidence interval, sketch the graph, and calculate the error bound.

Answer 1

Let's write the given information:

n = sample size = 20

Sample mean = = 2.2

population standard deviation = = 0.2

point estimate of population mean ( ) = = 2.2

the formula of confidence maximum error of estimate for µ is as follows:

Let's find critical z value for 90% confidence level:

here c = confidence level = 0.90

Therefore, level of significance = = 1 - c = 0.10

z_c = "=NORMSINV(0.95)" = 1.645

So,

The 90% confidence maximum error of estimate for µ is 0.0736

Let's obtain the 90% confidence interval for µ.

Lower limit = - E = 2.2 - 0.0736 = 2.1264

Upper limit = + E = 2.2 + 0.0736 = 2.2736

The 90% confidence interval for µ is as ( 2.1264, 2.2736)