Question

A lumber company typically only agrees to log a plot of land if they have strong evidence that a large proportion of the trees on the plot have usable wood. A consultant to the lumber company takes a random sample of 80 trees from Plot A and determines a confidence interval of (0.659, 0.821) for the proportion of trees on Plot A that have usable wood, however she never reports the level of confidence.

a) Determine the percent of usable wood that was observed on Plot A in that sample.

b) Determine the level of confidence for the interval given above.

Answer 1

Solution:

Given:  A consultant to the lumber company takes a random sample of 80 trees from Plot A and

determines a confidence interval of (0.659, 0.821) for the proportion of trees on Plot A that have usable wood.

Sample size = n = 80

Lower limit = 0.659

Upper limit = 0.821

Part a) Determine the percent of usable wood that was observed on Plot A in that sample.

Part b) Determine the level of confidence for the interval given above.

Use following steps:

Find margin of Error E:

Now use following formula:

thus

Look in z table for z = 1.6 and 0.05 and find corresponding area.

P( Z< 1.65) = 0.9505

that is:

thus c = confidence level is:

Thus the level of confidence is 90%