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The Consumer Reports article described in Exercise 1 also listed the sodium content (in mg) for the various hot dogs tested. A test of the null hypothesis that beef hot dogs and meat hot dogs don't differ in the mean amounts of sodium yields a P-value of \(0.11 .\) Would a \(95 \%\) confidence interval for \(\mu_{\text {Meat}}-\mu_{\text {Beef}}\) include \(0 ?\) Explain.

Newspaper headlines recently announced a decline in science scores among high school seniors. In \(2000,\) a total of 15,109 seniors tested by The National Assessment in Education Program (NAEP) scored a mean of 147 points. Four years earlier, 7537 seniors had averaged 150 points. The standard error of the difference in the mean scores for the two groups was 1.22 a) Have the science scores declined significantly? Cite appropriate statistical evidence to support your conclusion. b) The sample size in 2000 was almost double that in \(1996 .\) Does this make the results more convincing or less? Explain.