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1. 1. A pharmaceutical manufacturer is concerned about the impurity concentration in pills, and it is anxious that this concentration not exceed 3%. It is known that from a particular production run. Impurity concentrations follow a normal distribution with standard deviation 4%. A random sample of sixty-four pills from a production run was checked and the sample mean impurity concentration was found to be 3.07%.
(a) a).
test at the 5%level the null hypothesis that the population mean impurity concentration is 3% against the alternative that it is more than 3%
(b) b) .find the p-value for this test
(c) c). suppose that the alternative hypothesis had been two-sided rather than one-sided (with null hypothesis H:u=3). State. Without doing the calculations. Whether the p-value of the test would be higher than. lower than. Or the same as that found in (b). sketch a graph to illustrate your reasoning.
(d) d). In the context of this problem explain why a one-sided alternative hypothesis is more appropriate than a two-sided alternative.
2. The cloze readability test was given to a random sample of 328 commercial bank loan officer trainees to check their understanding of financial report messages. Their mean score on the test was 55.3177 and the sample standard deviation was 10.8324. test the null hypothesis that the population mean is at least 57. The minimum score necessary to demonstrate adequate understanding of written material.
3. A company selling franchises advertises that operators obtain. On average during the first year a yield of 10% on their initial investments. A random sample of ten of these franchises produced the following yields for the first year of operation:
6.1
9.2
11.5
8.6
12.1
3.9
8.4
10.1
9.4
8.9
Assuming that population yields are normally distributed test the company’s claim.
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