Question

An instrument manufacturer of a weight scale claims that after calibration the scale will provide an unbiased estimate of the true weight with a standard deviation of σ = 0.01 grm where the weights will be normally distributed. A sample that weights precisely 2 grams is repeatedly weighed 25 times on the calibrated instrument with a resulting sample mean of 1.998 grams and sample standard deviation of .019. Do you think the scale lives up to both claims, that is that the scale is unbiased with a true standard deviation of σ=.01 grms?

Answer 1

null hypothesis:     Ho:				σ =	0.01
Alternate hypothesis: Ha:				σ ≠	0.01

df =n-1=25-1=24

for 5 % level and given df critical values of F      =			23.767		&	39.364
Decision rule:reject Ho if test statistic X2 in critical region:			23.767		< X2 >	39.364

test statistic X² =(n-1)*(s/σ)² =(25-1)*(0.019/0.01)² =86.64

as test statistic is in rejection region; we reject null hypothesis

we have sufficient evidence at 0.05 level to conclude that scale is not unbiased with a true standard deviation of σ=.01 grms