Never forget that evensmall effects can be statistically significant if the samples arelarge. To illustrate this fact, consider a sample of 104 smallbusinesses. During a three-year period, 10 of the 71 headed by menand 6 of the 33 headed by women failed.
(a) Find the proportions of failures for businesses headed bywomen and businesses headed by men. These sample proportions arequite close to each other. Give the P-value for the test of thehypothesis that the same proportion of women's and men's businessesfail. (Use the two-sided alternative). What can we conclude (Use?=0.05?=0.05)?
The P-value was so we conclude that
Choose a conclusion.The test showed strong evidence of asignificant difference.The test showed no significantdifference.
(b) Now suppose that the same sample proportion came from asample 30 times as large. That is, 180 out of 990 businesses headedby women and 300 out of 2130 businesses headed by men fail. Verifythat the proportions of failures are exactly the same as in part(a). Repeat the test for the new data. What can we conclude?
The P-value was so we conclude that
Choose a conclusion.The test showed strong evidence of asignificant difference.The test showed no significantdifference.
(c) It is wise to use a confidence interval to estimate the sizeof an effect rather than just giving a P-value. Give 95% confidenceintervals for the difference between proportions of men's andwomen's businesses (men minus women) that fail for the settings ofboth (a) and (b). (Be sure to check that the conditions are met. Ifthe conditions aren't met for one of the intervals, use the sametype of interval for both)
Interval for smaller samples:___ to ___
Interval for larger samples: ___to ___
What is the effect of larger samples on the confidenceinterval?
Choose an effect.The confidence interval is unchanged.Theconfidence interval's margin of error is reduced.The confidenceinterval's margin of error is increased.
