A study had subjects read a passage and take a comprehension test on what they read. The researchers randomly assigned subjects so that half of them listened to music with lyrics while reading, while the other half listened to music without lyrics while reading. Here are their scores on the comprehension test: \begin{tabular}{llllll} \hline Music with lyrics & 75 & 62 & 65 & 41 & 54 \ Music without lyrics & 64 & 71 & 88 & 77 & 62 \end{tabular} The researchers want to test if these results represent a significant difference in the average score between the groups. Assume that the necessary conditions for inference were met. Which of these is the most appropriate test and alternative hypothesis? Choose 1 answer: (A) Paired $t$ test with $\mathrm{H}_{\mathrm{a}}: \mu_{ ext {difference }}0$ (B) Paired $t$ test with $\mathrm{H}_{\mathrm{a}}: \mu_{ ext {difference }} eq 0$ (C) Two-sample $t$ test with $\mathrm{H}_{\mathrm{a}}: \mu_{ ext {lyrics }}\mu_{ ext {without }}$ (D) Two-sample $t$ test with $\mathrm{H}_{\mathrm{a}}: \mu_{ ext {lyrics }} eq \mu_{ ext {without }}$ (E) Two-sample $t$ test with $\mathrm{H}_{\mathrm{a}}: \mu_{ ext {lyrics }}

Q: A study had subjects read a passage and take a comprehension test on what they read. The researchers randomly assigned subjects so that half of them listened to music with lyrics while reading, while the other half listened to music without lyrics while reading. Here are their scores on the comprehension test: \begin{tabular}{llllll} \hline Music with lyrics & 75 & 62 & 65 & 41 & 54 \\ Music without lyrics & 64 & 71 & 88 & 77 & 62 \end{tabular} The researchers want to test if these results represent a significant difference in the average score between the groups. Assume that the necessary conditions for inference were met. Which of these is the most appropriate test and alternative hypothesis? Choose 1 answer: (A) Paired $t$ test with $\mathrm{H}_{\mathrm{a}}: \mu_{\text {difference }}>0$ (B) Paired $t$ test with $\mathrm{H}_{\mathrm{a}}: \mu_{\text {difference }} \neq 0$ (C) Two-sample $t$ test with $\mathrm{H}_{\mathrm{a}}: \mu_{\text {lyrics }}>\mu_{\text {without }}$ (D) Two-sample $t$ test with $\mathrm{H}_{\mathrm{a}}: \mu_{\text {lyrics }} \neq \mu_{\text {without }}$ (E) Two-sample $t$ test with $\mathrm{H}_{\mathrm{a}}: \mu_{\text {lyrics }}<\mu_{\text {without }}$

∻Solution by Steps∻ ‖ step 1 ⋮ Determine the type of data we have to decide between a paired t-test and a two-sample t-test. ‖ ‖ step 2 ⋮ Since the subjects were randomly assigned to two different groups and the scores are independent of each other, a two-sample t-test is appropriate. ‖ ‖ step 3 ⋮ Choose the correct alternative hypothesis based on the research question. The researchers want to know if there is a significant difference, not specifically which one is higher. ‖ ‖ step 4 ⋮ The alternative hypothesis that allows for any difference (not specifying direction) is $\mu_{\text{lyrics}} \neq \mu_{\text{without}}$. ‖ ∻1 Answer∻ ***D*** ∻Key Concept∻ ⚹Two-sample t-test vs. Paired t-test⚹ ∻Explanation∻ ⚹A two-sample t-test is used when comparing the means of two independent groups, while a paired t-test is used for dependent groups or matched pairs. In this scenario, the groups are independent.⚹◊What is the formula for calculating the t-statistic in a two-sample t-test?⍭ Generate me a similar question◊

Question

A study had subjects read a passage and take a comprehension test on what they read. The researchers randomly assigned subjects so that half of them listened to music with lyrics while reading, while the other half listened to music without lyrics while reading. Here are their scores on the comprehension test:
\begin{tabular}{llllll}
\hline Music with lyrics & 75 & 62 & 65 & 41 & 54 \
Music without lyrics & 64 & 71 & 88 & 77 & 62
\end{tabular}

The researchers want to test if these results represent a significant difference in the average score between the groups. Assume that the necessary conditions for inference were met.

Which of these is the most appropriate test and alternative hypothesis?
Choose 1 answer:
(A) Paired $t$ test with $\mathrm{H}_{\mathrm{a}}: \mu_{	ext {difference }}>0$
(B) Paired $t$ test with $\mathrm{H}_{\mathrm{a}}: \mu_{	ext {difference }} 
eq 0$
(C) Two-sample $t$ test with $\mathrm{H}_{\mathrm{a}}: \mu_{	ext {lyrics }}>\mu_{	ext {without }}$
(D) Two-sample $t$ test with $\mathrm{H}_{\mathrm{a}}: \mu_{	ext {lyrics }} 
eq \mu_{	ext {without }}$
(E) Two-sample $t$ test with $\mathrm{H}_{\mathrm{a}}: \mu_{	ext {lyrics }}<\mu_{	ext {without }}$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Determine the type of data we have to decide between a paired t-test and a two-sample t-test. ‖ ‖ step 2 ⋮ Since the subjects were randomly assigned to two different groups and the scores are independent of each other, a two-sample t-test is appropriate. ‖ ‖ step 3 ⋮ Choose the correct alternative hypothesis based on the research question. The researchers want to know if there is a significant difference, not specifically which one is higher. ‖ ‖ step 4 ⋮ The alternative hypothesis that allows for any difference (not specifying direction) is $\mu_{ ext{lyrics}} eq \mu_{ ext{without}}$. ‖ ∻1 Answer∻ ***D*** ∻Key Concept∻ ⚹Two-sample t-test vs. Paired t-test⚹ ∻Explanation∻ ⚹A two-sample t-test is used when comparing the means of two independent groups, while a paired t-test is used for dependent groups or matched pairs. In this scenario, the groups are independent.⚹◊What is the formula for calculating the t-statistic in a two-sample t-test?⍭ Generate me a similar question◊

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