Question 508294: A study conducted by the research department of a pharmaceutical company claims that the annual spending (per person) for prescription drugs for allergy relief, m1, is greater than or equal to the annual spending (per person) for non-prescription allergy relief medicine, m2. A health insurance company conducted an independent study and collected data from a random sample of 205 individuals for prescription allergy relief medicine. The sample mean is found to be 17.8 dollars/year, with a sample standard deviation of 5.5 dollars/year. They have also collected data for non-prescription allergy relief medicine. An independent random sample of 235 individuals yielded a sample mean of 18.2 dollars/year, and a sample standard deviation of 4.1 dollars/year. Since the sample size is quite large, it is assumed that the population standard deviation of the sales (per person) for prescription and non-prescription allergy relief medicine can be estimated by using the sample standard deviation values given above. Is there sufficient evidence to reject the claim made by the research department of the company, at the 0.1 level of significance? Perform a one-tailed test.
I believe my null is h0:m1>=M2
alternative is h1:m1
I also believe that it needs to be a ztest, and I must find the p value along with deciding if the 0.1 level of significance can be rejected.
I believe that I need to do a z-test, but it may need to be a chi-square, t, or f if I am not thinking in the right processes.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A health insurance company conducted an independent study and collected data from a random sample of 205 individuals for prescription allergy relief medicine. The sample mean is found to be 17.8 dollars/year, with a sample standard deviation of 5.5 dollars/year.
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They have also collected data for non-prescription allergy relief medicine. An independent random sample of 235 individuals yielded a sample mean of 18.2 dollars/year, and a sample standard deviation of 4.1 dollars/year.
Since the sample size is quite large, it is assumed that the population standard deviation of the sales (per person) for prescription and non-prescription allergy relief medicine can be estimated by using the sample standard deviation values given above.
Is there sufficient evidence to reject the claim made by the research department of the company, at the 0.1 level of significance?
Perform a one-tailed test.
null hypothesis: m1pre - m2non >= 0 (claim)
alternative hypothesis: m1pre - m2non < 0
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Type of test: 2Sample T test
Using my TI-84 I get:
value of test: t = -0.8546
p-value: 0.1967
df = 373.25
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are we able to reject the claim?
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Since the p-value is greater than 1%, fail to reject Ho.
The test results support the claim.
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Cheers,
Stan H.
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