A researcher in interested in whether students who are musicians have higher intelligence test scores than students in the general population.The researcher predicts that playing a musical instrument is associated with higher intelligence test scores.The researcher selects a sample of 75 musicians from local high schools and gives them an intelligence test.The mean for the sample is 105.The mean for the general population (µ)is 100 with a standard deviation ($\sigma$)of 15.What is z_obt for this sample? A).33 B)1.89 C)2.89 D)3.25

Question

Quizplus · Accepted Answer

The z-score is calculated using the formula: $ z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}} $. Here, $\bar{x} = 105$, $\mu = 100$, $\sigma = 15$, and $n = 75$. Plugging in these values gives $ z = \frac{105 - 100}{\frac{15}{\sqrt{75}}} = 2.89 $.

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A Researcher in Interested in Whether Students Who Are Musicians $\sigma$