Question

An analytical chemistry lab is conducting quality control tests on a drug. A single dosage of the drug should contain 8 mg of active ingredient. Of course, there will be a small amount of variability due to imperfections in the production process, but the mean of all dosages produced should be 8 mg, and the process is believed to be normally distributed. Eighteen doses are randomly selected, and the amount of the active ingredient was determined in each. Do these data suggest that the mean amount of active ingredient in all dosages produced is not 8 mg? Sample: 7.4, 7.5, 7.5, 7.6, 7.6, 7.7, 7.8, 7.8, 7.8, 7.8, 7.9, 8.0, 8.0, 8.0, 8.1, 8.1, 8.2, 8.2. (The probabilities and values in the problem below were calculated using the TI-84. Table values might be slightly different.)

( ) 51. How would you express the alternative hypothesis in this problem? (A) μ = 8. (B) μ > 8. (C) μ < 8. (D) μ ≠ 8. (E) μ1 = μ2. (F) At last one mean is different.

( ) 52. What test statistic would you use for this problem? (A) The z statistic, assuming that the population variance is known. (B) The t statistic, given that I have to estimate variability from a small sample. (C) The z statistic, because the sample size is large. (D) The F statistic, because I am comparing the means of multiple populations. (E) The χ2 statistic, because I am testing for fit to a normal distribution. (F) The z test for population proportion.

( ) 53. The value of the test statistic is: (A) -8.479. (B) -2.8589. (C) +1.645. (D) approaching negative infinity. (E) None of the above are correct.

( ) 54. Which of the following statements is correct? (A) I can reject H0 with 90% confidence but not with 95%. (B) I can reject H0 with 95% confidence but not with 99%. (C) I can reject H0 with 99% confidence but not with 99.9%. (D) I can reject H0 with more than 99.9%. (E) I will not reject H0 in this problem.

( ) 55. When you are monitoring the quality of your medicines, you want to know quickly if there is an issue. That being said, you would probably: (A) chose a lower confidence level to help reveal quality problems more rapidly. (B) choose a higher confidence level so that you can be sure of your result. (C) try to avoid a Type I error at all costs. (D) try to avoid both Type I and Type II errors equally. (E) None of the above, because all errors, whether false positives or false negatives, are equally bad.

Answer 1

Using Excel<data<megastat<hypotheis test<mean

Here is the output:

8.0000	hypothesized value
7.8333	mean Sample
0.2473	std. dev.
0.0583	std. error
18	n
17	df
-2.8589	t
.0109	p-value (two-tailed)
7.6644	confidence interval 99.% lower
8.0023	confidence interval 99.% upper
0.1690	margin of error

51. How would you express the alternative hypothesis in this problem?

(D) μ ≠ 8

52. What test statistic would you use for this problem?

(B) The t statistic, given that I have to estimate variability from a small sample.

53. The value of the test statistic is:

(B) -2.8589.

54. Which of the following statements is correct? .

(B) I can reject H0 with 95% confidence but not with 99%

55. When you are monitoring the quality of your medicines, you want to know quickly if there is an issue. That being said, you would probably:(D) try to avoid both Type I and Type II errors equally.