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.
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.