Question

The quality control manager of Ridell needs to estimate the mean breaking point of a large shipment of helmets sent to the Philadelphia Eagles. Given the production process, the known standard deviation of the population of breaking points is 15.5 lbs. A random sample of 49 helmets were selected and subjected to increasing pressure until every one of them broke. The breaking point of each helmet was recorded, and average breaking point of the sample was 150 lbs.

What are the critical values from the z distribution associated with a 95% confidence interval?

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 150

Population standard deviation = = 15.5

Sample size = n = 49

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

The critical value is 1.96

Margin of error = E = Z_/2* ( /n)

= 1.96 * (15.5 / 49)

= 4.34

At 95% confidence interval estimate of the population mean is,

- E < < + E

150 - 4.34 < < 150 + 4.34

145.66 < < 154.34

(145.66 , 154.34)

The critical values from the z distribution associated with a 95% confidence interval is 1.96