Question

The manager wants to find out the average (population mean) time required to inflate a rubber raft. Assuming that the manager knows the population standard deviation is 1.6 seconds. A random sample of 45 rafts is inflated, yielding an average inflation time of 7.6 seconds (sample mean). Using sample information to construct:

(i) 95% confidence interval for the average inflation time of all rubber rafts.

(ii) 99% confidence interval for the average inflation time of all rubber rafts.

Answer 1

GIVEN:

Sample size of rubber rafts inflated

Sample mean inflation time seconds

Population standard deviation seconds

(i) 95% CONFIDENCE INTERVAL FOR AVERAGE INFLATION TIME OF ALL RUBBER RAFTS:

FORMULA USED:

The formula for 95% confidence interval for population mean is,

where is the z critical value at 95% confidence level.

CRITICAL VALUE:

The two tailed z critical value at 95% confidence level is .

CALCULATION:

The 95% confidence interval for average inflation time of all rubber rafts is,

  

  

Thus the 95% confidence interval for average inflation time of all rubber rafts is .

(ii) 99% CONFIDENCE INTERVAL FOR AVERAGE INFLATION TIME OF ALL RUBBER RAFTS:

FORMULA USED:

The formula for 99% confidence interval for population mean is,

where is the z critical value at 99% confidence level.

CRITICAL VALUE:

The two tailed z critical value at 99% confidence level is .

CALCULATION:

The 99% confidence interval for average inflation time of all rubber rafts is,

  

  

Thus the 99% confidence interval for average inflation time of all rubber rafts is .