Question

Topic 1: A study of foot pain was conducted for users of Nike and Adidas brand shoes. In all 650 subjects wore Nike and 44 experienced some foot pain. Of the 347 subjects who wore Adidas, 49 had some foot pain. a) Does the data provide convincing evidence that the two shoe brands differ in the proportion of people who experience some foot pain. Support your conclusion with a test of significance. Use \alpha=0.05. b) Find the margin of error for a 95% confidence interval for the difference in the proportions of people who experience some foot pain from these two shoes. You need not carry out all steps in constructing the confidence interval. c) In parts a and b, you should have used two different formulas for estimating the standard deviation of the randomization distribution of $\hat{p}_1 - \hat{p}_2$. Explain why it makes sense to do this.

          Topic 1:
A study of foot pain was conducted for users of
Nike and Adidas brand shoes. In all 650 subjects
wore Nike and 44 experienced some foot pain. Of
the 347 subjects who wore Adidas, 49 had some
foot pain.
a) Does the data provide convincing evidence
that the two shoe brands differ in the
proportion of people who experience some
foot pain. Support your conclusion with a
test of significance. Use \alpha=0.05.
b) Find the margin of error for a 95%
confidence interval for the difference in the
proportions of people who experience some
foot pain from these two shoes. You need
not carry out all steps in constructing the
confidence interval.
c) In parts a and b, you should have used two
different formulas for estimating the
standard deviation of the randomization
distribution of $\hat{p}_1 - \hat{p}_2$. Explain why it makes
sense to do this.

Added by Sean R.

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