A psychologist believes that a lack of sleep before students take the SAT will lead to them getting lower Math SAT scores. It is known that the mean Math SAT score is μ = 500 with a standard deviation of σ = 100. To test this belief, the psychologist recruited n=8 students who were scheduled to take the SAT. The night before the SAT, the researcher only let the n=8 students sleep for 2 hours. The mean Math SAT score for the n=8 students was M2hrSleep = 435. Perform a t-test by answering the questions below. Use an alpha-level of α=.05. 1. What is the research hypothesis, H1? 2. What is the null hypothesis, H0? 3. What is the degrees of freedom for this problem, df? 4. What is the critical value of t, tcrit? (Be sure to use a + or a - sign for your answer.) 5. What is the mean of the distribution of sample means, μM? 6. What is the standard deviation of the distribution of sample means, σM? 7. What is the z-score of the sample mean, M2hrSleep? 7. Based on the relation between the critical value of t and the t-score of the sample mean, can you reject the null hypothesis? 8. Based on whether or not you can reject the null hypothesis, can you accept the research hypothesis? Show your work for all problems.

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Description: A psychologist believes that a lack of sleep before students take the SAT will lead to them getting lower Math SAT scores. It is known that the mean Math SAT score is μ = 500 with a standard deviation of σ = 100. To test this belief, the psychologi

MATLAB: An Introduction with Applications

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A psychologist believes that a lack of sleep before students take the SAT will lead to them getting lower Math SAT scores. It is known that the mean Math SAT score is μ = 500 with a standard deviation of σ = 100. To test this belief, the psychologist recruited n=8 students who were scheduled to take the SAT. The night before the SAT, the researcher only let the n=8 students sleep for 2 hours. The mean Math SAT score for the n=8 students was M_2hrSleep = 435.

Perform a t-test by answering the questions below. Use an alpha-level of α=.05.

1. What is the research hypothesis, H₁?

2. What is the null hypothesis, H₀?

3. What is the degrees of freedom for this problem, df?

4. What is the critical value of t, t_crit? (Be sure to use a + or a - sign for your answer.)

5. What is the mean of the distribution of sample means, μ_M?

6. What is the standard deviation of the distribution of sample means, σ_M?

7. What is the z-score of the sample mean, M_2hrSleep?

7. Based on the relation between the critical value of t and the t-score of the sample mean, can you reject the null hypothesis?

8. Based on whether or not you can reject the null hypothesis, can you accept the research hypothesis?

Show your work for all problems.

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