Approximately 10% of Americans are left-handed (we will treat this as a known population parameter). A study on the relationship between handedness and profession found that in a random sample of 105 lawyers, 16 of them were left- handed 1 . Test the hypothesis that the proportion of left-handed lawyers is higher than the proportion of left-handed Americans. Use α = 0.01. H 0 : Lawyers are just as likely to
Approximately 10% of Americans are left-handed (we will treat this as a known
population parameter). A study on the relationship between handedness and
profession found that in a random sample of 105 lawyers, 16 of them were left-
handed 1 . Test the hypothesis that the proportion of left-handed lawyers is higher than
the proportion of left-handed Americans. Use α = 0.01.
H 0 : Lawyers are just as likely to be left-handed as other Americans: p = 0.10
H 1 : Lawyers are more likely to be left-handed than other Americans: p > 0.10.
a. Check to see if the null hypothesis sampling distribution is normal. Keep in mind
whether you are dealing with means or proportions.
b. Draw the null hypothesis sampling distribution (a normal curve). Label its center.
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.
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