Question

A standard metal bar weighs exactly 12.4 kg. We have two scales of unknown accuracy and precision. In particular, unknown to us, using Scale #1, measurements of the bar’s weight act like random draws from a ?(12.2,0.05) distribution while, using Scale #2, measurements of the bar’s weight act like random draws from a ?(12.4,0.2) distribution. Using each scale, we take 10 measurements and compute a 95% confidence interval for the true weight of the bar. Neither includes 12.4 kg.

a. What is the best explanation for why the confidence interval based on the Scale #1 measurements does not contain 12.4 kg?

b. What is the best explanation for why the confidence interval based on the Scale #2 measurements does not contain 12.4 kg?

Answer 1

Answer:

Given,

Consider,

Null hypothesis Ho : mu = 12.4 &

Alternative hypothesis H1 : mu not equivalent to 12.4

Here we know whether our confidence interval does not contain the theorized value(here 12.4) at that point we have enough proof to reject the Ho i.e., null hypothesis.

a)

The confidence interval dependent on the estimations does not contain 12.4 kg implies that we have enough proof to reject the Ho i.e., null hypothesis

i.e,

the mean genuine weigh of the bar estimated on this scale isn't equivalent to 12.4 kg.

b)

Now the confidence interval dependent on the estimations does not contain 12.4 kg implies that we have enough proof to reject the Ho i.e., null hypothesis

i.e,

the mean genuine weigh of the bar estimated on this scale isn't equivalent to 12.4 kg.