Question 150495: 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 255 individuals for prescription allergy relief medicine. The sample mean is found to be 17.8 dollars/year, with a sample standard deviation of 5.1 dollars/year. They have also collected data for non-prescription allergy relief medicine. An independent random sample of 245 individuals yielded a sample mean of 18.2 dollars/year, and a sample standard deviation of 4.3 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 0.10 level of significance?
Perform a one-tailed test and answer the questions below.
Carry your intermediate computations to at least three decimal places and round your answers to three as well.
1) The null hypothesis
2) The alternative hypothesis
3) The type of test statistic (ex. Z, t, Chi-Square, etc.)
4) The value of the test statistic
5) The p value
6) YES or NO. Can we reject the claim that the mean spending on prescription allergy relief medication is greater than or equal to the mean spending on non-precription allergt relief medication?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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.
Ho: u(m1) >= u(m2)
Ha: u(m1) < u(m2)
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A health insurance company conducted an independent study and collected data from a random sample of 255 (n1) individuals for prescription allergy relief medicine. The sample mean is found to be 17.8 (x1-bar) dollars/year, with a sample standard deviation of 5.1 dollars/year(s1).
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They have also collected data for non-prescription allergy relief medicine. An independent random sample of 245 (n2) individuals yielded a sample mean of 18.2 dollars/year (x2-bar), and a sample standard deviation of 4.3 dollars/year(s2).
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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.
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Is there sufficient evidence to reject the claim made by the research department of the company, at the 0.10 level of significance?
Perform a one-tailed test and answer the questions below.
Carry your intermediate computations to at least three decimal places and round your answers to three as well.
1) The null hypothesis (above)
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2) The alternative hypothesis (above)
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3) The type of test statistic (ex. Z, t, Chi-Square, etc.)
That depends on your text. Some use "t" for all means-test; some use
t only if n < 30. Since n > 30 for both samples, use a z test statistic.
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4) The value of the test statistic
z = 2.3263
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5) The p value
I ran a 2-sample z test with a TI calculator and got
p-value = 0.1712 or greater than 17%
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6) YES or NO. Can we reject the claim that the mean spending on prescription allergy relief medication is greater than or equal to the mean spending on non-precription allergt relief medication?
Since p-value is greater than 1%, fail to reject Ho.
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Cheers,
Stan H.
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