For Exercises 9.1 and 9.2, see page 458; for 9.3 and 9.4, see page 461; for 9.5 and 9.6, see page 462; for 9.7 and 9.8, see page 463; for 9.9 and 9.10, see page 465; for 9.11, see page 466; for 9.12 and 9.13, see page 471; for 9.14, see page 473; for 9.15, see page 474; and for 9.16, see page 475.

Question 9.11

9.11 Social media in the supply chain.

Sample proportions from Example 9.1 and the two-way table in Example 9.2 (page 456) report the same information in different ways. We saw in Example 8.9 (pages 442–443) that the statistic for the hypothesis of equal population proportions is with .

  1. Find the chi-square statistic for this two-way table and verify that it is equal (up to roundoff error) to .
  2. Verify that the 0.001 critical value for chi-square with (Table F) is the square of the 0.0005 critical value for the standard Normal distribution (Table D). The 0.0005 critical value corresponds to a P-value of 0.001 for the two-sided test.
  3. Explain carefully why the two hypotheses


    say the same thing about the population.

9.11

(a) . (b) . (c) The test null hypothesis indicates that the proportions are equal or that small and large companies use social media equally; in other words, the size of the company doesn’t matter in determining social media use—i.e., there is no relation between company size and social media use, the null hypothesis for the test.