Question

The labeled potency of a tablet dosage form is 100 mg. Ten individual tablets of a batch are assayed according to a quality control specification. The 10 assay results shown in Table 5.1 are assumed to be sampled from a normal distribution. The sample mean is 103.0 mg and the standard deviation is 2.22. Table 5.1 Assay Results for 10 Randomly Selected Tablets (mg) 101.8 104.5 102.6 100.7 99.8 106.3 104.9 100.6 103.8 105.0 ?X = 103.0 S = 2.22 A. Using Excel, answer the following questions of interest at significance level 0.05 1) Is the mean tablet potency of the batch is statistically equal to 100 assuming the standard deviation of the batch (?) is estimated as 2 mg. 2) Is the mean tablet potency of the batch is significantly higher than 100 assuming the standard deviation of the batch (?) is estimated as 2 mg. 3) Is the mean tablet potency of the batch is statistically equal to 100 assuming the standard deviation of the batch (?) is unknown. 4) Is the mean tablet potency of the batch is significantly higher than 100 assuming the standard deviation of the batch (?) is unknown.

          The labeled potency of a tablet dosage form is 100 mg. Ten individual tablets of a batch are assayed according to a quality control specification. The 10 assay results shown in Table 5.1 are assumed to be sampled from a normal distribution. The sample mean is 103.0 mg and the standard deviation is 2.22.

Table 5.1 Assay Results for 10 Randomly Selected Tablets
(mg)
101.8 104.5
102.6 100.7
99.8 106.3
104.9 100.6
103.8 105.0
?X = 103.0 S = 2.22

A. Using Excel, answer the following questions of interest at significance level 0.05
1) Is the mean tablet potency of the batch is statistically equal to 100 assuming the standard deviation of the batch (?) is estimated as 2 mg.
2) Is the mean tablet potency of the batch is significantly higher than 100 assuming the standard deviation of the batch (?) is estimated as 2 mg.
3) Is the mean tablet potency of the batch is statistically equal to 100 assuming the standard deviation of the batch (?) is unknown.
4) Is the mean tablet potency of the batch is significantly higher than 100 assuming the standard deviation of the batch (?) is unknown.

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The labeled potency of a tablet dosage form is 100 mg. Ten individual tablets of a batch are assayed according to a quality control specification. The 10 assay results shown in Table 5.1 are assumed to be sampled from a normal distribution. The sample mean is 103.0 mg and the standard deviation is 2.22.

Table 5.1 Assay Results for 10 Randomly Selected Tablets
(mg)
101.8 104.5
102.6 100.7
99.8 106.3
104.9 100.6
103.8 105.0
?X = 103.0 S = 2.22

A. Using Excel, answer the following questions of interest at significance level 0.05
1) Is the mean tablet potency of the batch is statistically equal to 100 assuming the standard deviation of the batch (?) is estimated as 2 mg.
2) Is the mean tablet potency of the batch is significantly higher than 100 assuming the standard deviation of the batch (?) is estimated as 2 mg.
3) Is the mean tablet potency of the batch is statistically equal to 100 assuming the standard deviation of the batch (?) is unknown.
4) Is the mean tablet potency of the batch is significantly higher than 100 assuming the standard deviation of the batch (?) is unknown.

Added by Bill W.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Sheryl Ezze

01/06/2023

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The labeled potency of a tablet dosage form is 100 mg. Ten individual tablets of a batch are assayed according to a quality control specification. The 10 assay results shown in Table 5.1 are assumed to be sampled from a normal distribution. The sample mean is 103.0 mg and the standard deviation is 2.22. Table 5.1 Assay Results for 10 Randomly Selected Tablets (mg) 101.8 104.5 102.6 100.7 99.8 106.3 104.9 100.6 103.8 105.0 X = 103.0 S = 2.22 A. Using Excel, answer the following questions of interest at significance level 0.05 1) Is the mean tablet potency of the batch is statistically equal to 100 assuming the standard deviation of the batch (̃σ) is estimated as 2 mg. 2) Is the mean tablet potency of the batch is significantly higher than 100 assuming the standard deviation of the batch (σ) is estimated as 2 mg. 3) Is the mean tablet potency of the batch is statistically equal to 100 assuming the standard deviation of the batch (σ) is unknown. 4) Is the mean tablet potency of the batch is significantly higher than 100 assuming the standard deviation of the batch (σ) is unknown.

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Transcript

00:01 For your setting, you asked about using excel, and i can't help you with that, but i can help you with doing the problem.

00:06 And so we have the setup that we have 10 samples, and we know that the mean is 103 milligrams, and the sample standard deviation is 2 .22.

00:16 And you have two questions that are dealing with, assuming that the population standard deviation is 2 milligrams.

00:24 And one, you want to find out, do you have evidence that it is different from 100? and so that is a z test, but a two -tail test.

00:33 And since we have 0 .05, as our significance level, we're going to put 0 .05, we're going to put 0 .025 in each tail.

00:43 And our critical values are 1 .96 and negative 1 .96.

00:47 And so we can see where we reject the null.

00:50 And our test statistic, our z value, is 103 minus 100 over the population standard deviation over the square root of n.

01:00 Value comes out to be 4 .72.

01:03 Now that is in the rejection region.

01:07 So we have evidence to reject the null and we can say that there is sufficient evidence that the mean is different from 100.

01:15 Now question two is very similar except now it's a one tail test which means our critical value changes and our critical value is now having all 5 % in that upper tail rather than 2 .5 % for a 2 .5 % for a 2 .5 % tail test and that now changes that critical value to 1 .645 and the z value will remain the same...

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