Question

To assess the accuracy of a laboratory scale, a reference weight known to weigh exactly 1010 grams (g) is weighed repeatedly. The scale readings are Normally distributed with standard deviation ?=0.0002σ=0.0002 g. The reference weight is weighed five times on that scale. The mean result is 10.002310.0023 g. The output from Minitab is shown for these data:

(a) Do the five weighings provide strong evidence that the scale is not well calibrated (that is, its mean, ?μ , for weighing this weight is not 1010 g)?

(1) What hypotheses should we use to test if the scale is not well calibrated? Select from below:

A) ?0:?=10.0H0:μ=10.0 versus ??:?>10.0Ha:μ>10.0

B) ?0:?=10.0H0:μ=10.0 versus ??:?≠10.0Ha:μ≠10.0

C) ?0:?<10.0H0:μ<10.0 versus ??:?>10.0Ha:μ>10.0

D) ?0:?≠10.0H0:μ≠10.0 versus ??:?=10.0Ha:μ=10.0

(2) What conclusion can we make based on the reported ?P‑value? Select from below:

A) We have extremely strong evidence that the scale is not well calibrated since the ?P‑value is close to 11 .

B) We have extremely strong evidence that the scale is not well calibrated since the ?P‑value is nearly zero.

C) We have no evidence that the scale is not well calibrated since the ?P‑value is nearly zero.

D) We have extremely weak evidence that the scale is not well calibrated since the ?P‑value is nearly zero.

(3) What is the 95%95% confidence interval derived from this random sample for estimating the mean weight on this scale for all possible measurements of the reference weight? (Enter your answers rounded to four decimal places.)

lower bound =

upper bound =

(4) Based on the values of the confidence interval, what can you conclude? Select from below:

A) Since 10.010.0 is not contained within the 95%95% confidence interval, we have evidence that the scale is not well calibrated.

B) Since 10.010.0 is contained within the 95%95% confidence interval, we have evidence that the scale is not well calibrated.

C) Since 10.010.0 is contained within the 95%95% confidence interval, we have evidence that the scale is well calibrated.

D) Since 10.010.0 is not contained within the 95%95% confidence interval, we have evidence that the scale is well calibrated.

(5) Given the two methods used so far, select the proper explanation for why the confidence interval is more informative than the test result. Select from below:

A) The test result only indicates how different from 1010 ?μ is whereas the confidence interval tells us the true value of ?μ .

B) The test result only indicates that ?≠10μ≠10 whereas the confidence interval tells us what to expect for ?μ and by about how much we should recalibrate the scale.

C) The test result only indicates that ?<10μ<10 whereas the confidence interval tells us a range of likely values for ?μ .

D) The test result only indicates that ?>10μ>10 whereas the confidence interval tells us the true value of ?μ .

Answer 1

Solution:

a)Yes, the five weighings provide strong evidence that the scale is not well calibrated.

1) Correct option B) H0:μ=10.0 versus Ha:μ≠10.0

2) P Value Results

Test statistic, Z=25.71 (attached below)

The two-tailed P value is less than 0.0001

By conventional criteria, this difference is considered to be extremely statistically significant.

Correct option is B) We have extremely strong evidence that the scale is not well calibrated since the P‑value is nearly zero.

3) 95 % Confidence Interval (attached below) :

Lower bound= 10.0021

Upper Bound = 10.0025

4)Option A) Since 10.0 is not contained within the 95%confidence interval, we have evidence that the scale is not well calibrated.

5) Option B) The test result only indicates that μ≠10 whereas the confidence interval tells us what to expect for μ and by about how much we should recalibrate the scale.