2. For the following problems, determine the null and alternative hypothesis. (a) In 2007, the standard deviation SAT score on the Reasoning Test for all students taking the exam was 113. A teacher believes that, due to changes in high school curricula, the standard deviation of SAT math scores has decreased. (b) According to a certain magazine, the mean charitable contribution per household in the U.S. in 2000 was \( \$ 1,623 \). A researcher believes that the level of giving has changed since then. (c) According to the Centers for Disease Control and Prevention, 16\% of children aged 6 to 11 years are overweight. A school nurse thinks that the percentage of 6 to 11 year olds who are overweight is higher in her school district.

For part (a), the null hypothesis would state that the standard deviation of SAT math scores is equal to 113, while the alternative hypothesis asserts that it has decreased from this value due to changes in high school curricula. In part (b), the null hypothesis would posit that the mean charitable contribution per household remains at \( \$ 1,623 \), while the alternative hypothesis claims that there has been a change in the mean contribution since the year 2000, indicating it could either be higher or lower. Finally, for part (c), the null hypothesis would contend that 16% of children aged 6 to 11 are overweight, while the alternative hypothesis suggests that this percentage is greater in the school district compared to the national statistic.