**Effect of Listening to Music on Knowledge Acquisition****Overview:**A researcher conducted a study to investigate the effect of listening to music on knowledge acquisition among students. She selected 82 students from her Introduction to Psychology course and divided them into two groups. One group was asked to listen to music of their choice while studying for an exam, and the other group was asked not to listen to any music while studying. After the exam, the researcher computed the exam scores and obtained the following results:**Exam Scores:**| | Music group (m) | No music group (nm) ||--------------------|---------------------|-----------------------|| Mean \((\bar{X})\) | \(\bar{X}_m = 97.3\) | \(\bar{X}_{nm} = 93.1\) || Standard Deviation \((s)\) | \(s_m = 9.0\) | \(s_{nm} = 10.0\) |**Statistical Analysis:**To determine if listening to music has an effect on knowledge acquisition, the researcher needs to conduct a two-tailed statistical test with a significance level (\(\alpha\)) of 0.05.**Hypothesis Testing:**The null hypothesis for this statistical analysis can be selected from the following options:1. \( \mu = 0 \)2. \( \mu_m - \mu_{nm} = 0 \)3. \( \mu_m - \mu_{nm} = 4.2 \)4. \( \bar{X}_m - \bar{X}_{nm} = 0 \)**Explanation of Hypotheses:**- **Null Hypothesis (H0):** There is no difference in knowledge acquisition (exam scores) between the music group and the no music group. - **Alternative Hypothesis (H1):** There is a difference in knowledge acquisition (exam scores) between the music group and the no music group.In this context, the most appropriate null hypothesis is: **\( \mu_m - \mu_{nm} = 0 \)**, indicating that the mean scores of the two groups are equal, and any observed difference is due to random chance.**Conclusion:**The researcher needs to perform appropriate statistical tests (e.g., t-test) to evaluate the null hypothesis, considering the provided means, standard deviations,

It is given thatx̄m = 97.3, sm = 9x̄nm = 93.1, snm = 10

Answered: Select the null hypothesis for this…

A First Course in Probability (10th Edition)

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Select the null hypothesis for this statistical analysis. Ⓒμ=0 0 0 0 0 Hm-Pnm = 0 Hm - Hnm = 4.2 X -X =0 m nm