A statistics tutor wishes to study the effect that his tutoring has on his students. He randomly selects 4 new students and records their current grades in their statistics courses. After half a semester of tutoring, the students' grades are recorded again. The statistics tutor then uses a paired, two-sample hypothesis test to determine if the differences between the before and after grades are statistically significant. (The tutor assumes a 5% level of significance.) Useful tools: Normal Distribution Calculator t-Distribution Calculator 1. Which of the following null and alternative hypotheses match this scenario? A. H0:Δμ≥0H0:Δμ≥0 Ha:Δμ=0Ha:Δμ=0 B. H0:Δμ≤0H0:Δμ≤0 Ha:Δμ>0Ha:Δμ>0 C. H0:Δμ>0H0:Δμ>0 Ha:Δμ≤0Ha:Δμ≤0 2. Which type of test should be applied? A. The alternative hypothesis indicates a right-tailed test. B. The alternative hypothesis indicates a left-tailed test. C. The alternative hypothesis indicates a two-tailed test. 3. Which type of distribution should be applied? A.The required distribution is a Normal Distribution. B.The required distribution is Student's t-Distribution. C. The required distribution is a Binomial Distribution approximated by a Normal Distribution. 4. Calculate the p-value from this hypothesis test. p= 5. Which of the following is an appropriate conclusion? A. Given that p<αp<α at a 5% level of significance, from the sample data, there is sufficient evidence to conclude that the tutor is, in fact, effective. B. Given that p>αp>α at a 5% level of significance, from the sample data, there is sufficient evidence to conclude that the tutor is, in fact, effective. C. Given that p>αp>α at a 5% level of significance, from the sample data, there is not sufficient evidence to conclude that the tutor is, in fact, effective. D. Given that p<αp<α at a 5% level of significance, from the sample data, there is not sufficient evidence to conclude that the tutor is, in fact, effective.
Testing Paired Samples
A statistics tutor wishes to study the effect that his tutoring has on his students. He randomly selects 4 new students and records their current grades in their statistics courses. After half a semester of tutoring, the students' grades are recorded again. The statistics tutor then uses a paired, two-sample hypothesis test to determine if the differences between the before and after grades are statistically significant. (The tutor assumes a 5% level of significance.)
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t-Distribution Calculator
1. Which of the following null and alternative hypotheses match this scenario?
A. H0:Δμ≥0H0:Δμ≥0
Ha:Δμ=0Ha:Δμ=0
B. H0:Δμ≤0H0:Δμ≤0
Ha:Δμ>0Ha:Δμ>0
C. H0:Δμ>0H0:Δμ>0
Ha:Δμ≤0Ha:Δμ≤0
2. Which type of test should be applied?
A. The alternative hypothesis indicates a right-tailed test.
B. The alternative hypothesis indicates a left-tailed test.
C. The alternative hypothesis indicates a two-tailed test.
3. Which type of distribution should be applied?
A.The required distribution is a Normal Distribution.
B.The required distribution is Student's t-Distribution.
C. The required distribution is a Binomial Distribution approximated by a Normal Distribution.
4. Calculate the p-value from this hypothesis test.
p=
5. Which of the following is an appropriate conclusion?
A. Given that p<αp<α at a 5% level of significance, from the sample data, there is sufficient evidence to conclude that the tutor is, in fact, effective.
B. Given that p>αp>α at a 5% level of significance, from the sample data, there is sufficient evidence to conclude that the tutor is, in fact, effective.
C. Given that p>αp>α at a 5% level of significance, from the sample data, there is not sufficient evidence to conclude that the tutor is, in fact, effective.
D. Given that p<αp<α at a 5% level of significance, from the sample data, there is not sufficient evidence to conclude that the tutor is, in fact, effective.
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