Answer to Question #222269 in Statistics and Probability for Nileman

Question

The NCHS report indicatea tnat in 002 People paid an average of $3,302 Der ear on health care and presCription arugs An nvestigator hypothesizes that 2005
expenditures have decreased primarily due to the availability of generic drugs. To test the hypothesis, samples ot 100 peopie are Slected and their expenditures on health care and prescription drugs in 2005 are metasured. e sampie aata are summarized as follows:
n=100, -$3,190 and s=s890, 1S there statistical evidence of a reduction in penditures on health care and preseription drugs in 20057 1s the sample mean of $3,190 evidence of
a true reduction in the mean or is it within chance fluctuation?

Answer 1

$H_0:\mu=3,302$

$H_1:\mu<3,302$

$\bar{x}=3,190$

$s=890$

$n=100$

Let $\alpha=0.05$

$t=\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}}$

$t=\frac{3190-3302}{\frac{890}{\sqrt{100}}}$

$=-1.258$

$CV=t_{99,0.05}=-1.66$

Since the absolute value of the test statistic (1.258) is less than the absolute value of the critical value (1.66), we fail to reject the null hypothesis. There is no sufficient evidence to support the hypothesis that 2005 expenditures have decreased primarily due to the availability of generic drugs.