1. A certain prescription allergy medicine is supposed to contain an average of 245 parts per million (ppm) of a certain chemical. If the concentration is higher than 245 ppm, the drug will likely cause unpleasant side effects, and if the concentration is below 245 ppm, the drug may be ineffective. The manufacturer wants to check whether the mean concentration in a large shipment is the required 245 ppm or not. To this end, a random sample of 64 portions from the large shipment is tested, and it is found that the sample mean concentration is 248 ppm with a sample standard deviation of 10.5 ppm. (a) Construct 95% confidence interval for the population mean concentration. Carry out the hypothesis test (b) State the appropriate hypothesis. (c) What is the standardized test statistics under null hypothesis?

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1. A certain prescription allergy medicine is supposed to contain an average of 245 parts
per million (ppm) of a certain chemical. If the concentration is higher than 245 ppm, the
drug will likely cause unpleasant side effects, and if the concentration is below 245 ppm,
the drug may be ineffective. The manufacturer wants to check whether the mean
concentration in a large shipment is the required 245 ppm or not. To this end, a random
sample of 64 portions from the large shipment is tested, and it is found that the sample
mean concentration is 248 ppm with a sample standard deviation of 10.5 ppm.
(a) Construct 95% confidence interval for the population mean concentration.
Carry out the hypothesis test
(b) State the appropriate hypothesis.
(e) What is the standardized test statistics under null hypothesis?
(d) What is the null distribution of the TS?
(e) What is the rejection region for the test at a = 0.05?
() Is the test significant at a= 0.05?
(g) State any assumption that are need for the validity of this test.
Transcribed Image Text:1. A certain prescription allergy medicine is supposed to contain an average of 245 parts per million (ppm) of a certain chemical. If the concentration is higher than 245 ppm, the drug will likely cause unpleasant side effects, and if the concentration is below 245 ppm, the drug may be ineffective. The manufacturer wants to check whether the mean concentration in a large shipment is the required 245 ppm or not. To this end, a random sample of 64 portions from the large shipment is tested, and it is found that the sample mean concentration is 248 ppm with a sample standard deviation of 10.5 ppm. (a) Construct 95% confidence interval for the population mean concentration. Carry out the hypothesis test (b) State the appropriate hypothesis. (e) What is the standardized test statistics under null hypothesis? (d) What is the null distribution of the TS? (e) What is the rejection region for the test at a = 0.05? () Is the test significant at a= 0.05? (g) State any assumption that are need for the validity of this test.
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Given information:

n= 64 Sample size x= 248 Sample mean s = 10.5 Sample standard deviation. μ= 245 Population mean 

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