tutor promises to improve GMAT scores of students by more than 36 points after three lessons. To see if this is true, the tutor takes a sample of 49 students’ test scores after and before they received tutoring. The mean difference was 39 points better after tutoring, with a standard deviation of the difference equal to 14 points. Let µD denote the mean of the difference: score after tutoring minus score before tutoring. Which of the following is the correct value of the test statistic?Multiple Choicez = 1.5000t48 = 1.5000t48 = 1.4643z = 1.4643
Question
tutor promises to improve GMAT scores of students by more than 36 points after three lessons. To see if this is true, the tutor takes a sample of 49 students’ test scores after and before they received tutoring. The mean difference was 39 points better after tutoring, with a standard deviation of the difference equal to 14 points. Let µD denote the mean of the difference: score after tutoring minus score before tutoring. Which of the following is the correct value of the test statistic?Multiple Choicez = 1.5000t48 = 1.5000t48 = 1.4643z = 1.4643
Solution
The correct value of the test statistic is t48 = 1.4643.
Here's how you calculate it:
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First, you need to set up your null and alternative hypotheses. The null hypothesis (H0) is that the mean difference µD is equal to 36 (the score improvement the tutor promises). The alternative hypothesis (H1) is that µD is greater than 36 (the tutor improves scores by more than he promises).
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Next, you calculate the sample mean difference (x̄D), which is given as 39.
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You also have the standard deviation of the differences (sD), which is given as 14.
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The sample size (n) is 49.
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You can now calculate the test statistic using the formula for a one-sample t-test: t = (x̄D - µD) / (sD / √n)
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Plugging in the given values: t = (39 - 36) / (14 / √49) = 1.4643
So, the correct answer is t48 = 1.4643.
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