Math / Data & Statistics

QuestionSuppose the weights of seventh-graders at a certain school vary according to a Normal distribution, with a mean of 100 poun and a standard deviation of 7.5 pounds. A researcher believes the average weight has decreased since the implementation of a new breakfast and lunch program at the school. She finds, in a random sample of 35 students, an average weight of 98 pounds.
What is the $P$ -value for an appropriate hypothesis test of the researcher's claim? $-1.578$ 0.115 0.943 0.057

Studdy Solution
Compare the P-value to the significance level (commonly $\alpha = 0.05$ ):
- If $P$ -value $< \alpha$ , reject $H_0$ . - If $P$ -value $\geq \alpha$ , do not reject $H_0$ .
Since $0.057 > 0.05$ , we do not reject $H_0$ .
The $P$ -value is:
$\boxed{0.057}$

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