Question: Ann and Sam are both testing the hypothesis that 40% of plain M&Ms in a bag are orange. Ann draws a sample of M&Ms and 30% of her sample is orange. She calculates a test statistic of z = -1. Sam draws a sample of M&Ms and 45% of his sample is orange. He calculates a test statistic of z = 1. Mark each statement as true or false and explain your reasoning.

1. Ann's data provide stronger evidence against the null hypothesis because 0.30 if further from 0.40. False. The relevant difference is not 0.30 - 0.40 = -0.10, but the difference in standard terms: (0.30-0.40)/ SE = -1. Both Ann and Sam got values 1 SE away from the expected value.
2. Sam must have drawn a smaller sample than Ann. False. To see why we need to calculate the sample sizes. This requires calculating the SD of the box:

SD = (1 - 0) \(\sqrt{0.4\times 0.6}\) = 0.4898

For Ann we have: -1 = \(\frac{0.3-0.4}{0.4898/\sqrt{n}}\) . For Sam we have: \(\frac{0.45-0.4}{0.4898/\sqrt{n}}\)

Solving n for Ann we have = 23.99

Solving n for Sam we have = 95.96

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