Question

An article gave the following summary data on shear strength (kip) for a sample of 3/8-in. anchor bolts: n = 75, x = 4.50, s = 1.80. Calculate a lower confidence bound using a confidence level of 90% for true average shear strength. (Round your answer to two decimal places.)

pls show work and formulas used in detail

Answer 1

Given that,

= 4.50

s =1.80

n = 75

Degrees of freedom = df = n - 1 = 75- 1 = 74

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

= 0.1

t /2,df = t0.1,74 = 1.293    ( using student t table)

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

=1.293 * (1.80 / 75) = 0.27

The 90% confidence interval estimate of the population mean is,

- E

4.50 - 0.27

4.23

lower bound =4.23