On a certain hearing ability test, the mean is 300 and the standard deviation is 20. The better you can hear, the higher your score. Can people who clean their ears frequently hear better than others? You take a sample of 31 people who clean their ears frequently. Their sample mean test score is 308. Do a hypothesis test with α = 0.01. H 0 : People who clean their ears regularly hear at the same level that everyone else does: µ = 300. c. Calculate your test statistic and draw it on your null hypothesis curve. This is just your sample statistic ( or ) converted to a Z-score on your null hypothesis sampling distribution. Make sure you are using the appropriate SE formula! Use for proportions and for means. d. Treat your test statistic as a Z-score and look up the area beyond it in the Z-table. That is your p-value. It may be helpful to shade this on your curve. (Remember, if you have a < in your alternative hypothesis, you’re looking at the area below your test statistic. If you have a > then you’re looking at the area above your test statistic.) e. Make your final rejection decision based on the following: • If your p-value is below α, reject your null • If your p-value is above α, fail to reject your null. f. Give a “plain English” interpretation of your findings.
On a certain hearing ability test, the mean is 300 and the standard deviation is 20. The
better you can hear, the higher your score. Can people who clean their ears frequently
hear better than others? You take a sample of 31 people who clean their ears
frequently. Their sample mean test score is 308. Do a hypothesis test with α = 0.01.
H 0 : People who clean their ears regularly hear at the same level that everyone else
does: µ = 300.
c. Calculate your test statistic and draw it on your null hypothesis curve. This is just
your sample statistic ( or ) converted to a Z-score on your null hypothesis sampling
distribution. Make sure you are using the appropriate SE formula! Use for
proportions and for means.
d. Treat your test statistic as a Z-score and look up the area beyond it in the Z-table.
That is your p-value. It may be helpful to shade this on your curve. (Remember, if
you have a < in your alternative hypothesis, you’re looking at the area below your
test statistic. If you have a > then you’re looking at the area above your test
statistic.)
e. Make your final rejection decision based on the following:
• If your p-value is below α, reject your null
• If your p-value is above α, fail to reject your null.
f. Give a “plain English” interpretation of your findings.
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