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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.
null hypothesis: m1pre - m2non >= 0 (claim)
alternative hypothesis: m1pre - m2non < 0
Type of test: 2Sample T test
Using my TI-84 I get:
value of test: t = -0.8546
df = 373.25
are we able to reject the claim?
Since the p-value is greater than 1%, fail to reject Ho.
The test results support the claim.