Math  /  Data & Statistics

QuestionLeft-Handed Lawyers Approximately 10%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 lefthanded. 1{ }^{1} Test the hypothesis that the proportion of left-handed lawyers differs from the proportion of left-handed Americans. 1{ }^{1} Schachter, S. and Ransil, B., "Handedness Distributions in Nine Professional Groups," Perceptual and Motor Skills, 1996; 82: 51-63.
Part 1
Clearly state the null and alternative hypotheses. Let pp be the proportion of left-handed lawyers. eTextbook and Media Save for Later Attempts: 0 of 5 used Submit Answer
Part 2
Calculate the test statistic and pp-value. Round your answer for the test statistic to two decimal places, and your answer for the pp-value to three decimal places. test statistic == \square i \square pp-value == eTextbook and Media

Studdy Solution
Determine the p p -value for the two-tailed test using the standard normal distribution.
The p p -value is calculated as:
p-value=2×P(Z>z)p\text{-value} = 2 \times P(Z > |z|)
Using a standard normal distribution table or calculator:
P(Z>1.79)0.0367P(Z > 1.79) \approx 0.0367
Thus, the p p -value is:
p-value=2×0.03670.0734p\text{-value} = 2 \times 0.0367 \approx 0.0734
The test statistic is approximately 1.79 1.79 and the p p -value is approximately 0.073 0.073 .

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