Question

The breaking strengths of cables produced by a certain manufacturer have a standard deviation of 91 pounds. A random sample of 90 newly manufactured cables has a mean breaking strength of 1700 pounds. Based on this sample, find a 95% confidence interval for the true mean breaking strength of all cables produced by this manufacturer. Then complete the table below. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 1700

sample standard deviation = s = 91

sample size = n = 90

Degrees of freedom = df = n - 1 = 90 - 1 = 89

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,89 = 1.987

Margin of error = E = t_/2,df * (s /n)

= 1.987 * (91 / 90)

Margin of error = E = 19.1

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

- E < < + E

1700 - 19.1 < < 1700 + 19.1

1680.9 < < 1719.1

(1680.9 , 1719.1)