 # 1. A statistics tutor wants to assess whether her remedial tutoring...

## Question

1. A statistics tutor wants to assess whether her remedial tutoring has been effective for her 16 students (n = 16). To evaluate the changes that occur during the year, students’ grades were measured at the beginning and at the end of the year. Their grades revealed an average improvement of MD = 8 points with a sum of squares for the difference scores of SSD = 930.

Conduct the appropriate hypothesis test to determine if the data are sufficient to conclude that there was significant IMPROVEMENT? Use a one-tailed test with α = 0.01

-What is the null hypothesis (H0)
-What is the alternative hypothesis (H1)
-What are the degrees of freedom (df
-What is the tcritical value?
-What is the variance of the difference scores (s2D)?
-What is the estimated standard error for the sample mean difference (sMD)
-What is the t-statistic
-What is the conclusion?

Question 13 options:

A)
Fail to reject H0: Tutoring significantly improves grades

B)
Fail to reject H0: Tutoring DOES NOT significantly improve grades.

C)
Reject H0: Tutoring significantly improves grades.

D)
Reject H0: Tutoring DOES NOT significantly improve grades.

2. A researcher conducts an independent samples study examining how the brain neurotransmitter serotonin is related to aggression. One sample of rats serves as a control group and receives a placebo that does not affect normal levels of serotonin. A second sample of rats receives a drug that lowers brain levels of serotonin. Then the researcher tests the animals by recording the number of aggressive responses each of the rats display. The data are as follow:

Control: n = 10, M = 14, SS = 180.5

Low Serotonin: n = 15, M = 19, SS = 130

Conduct the appropriate hypothesis test to determine if the data are sufficient to conclude that the drug had a significant effect on aggression? Use a two-tailed test with α = 0.05.

-What is the null hypothesis (H0)
-What is the alternative hypothesis (H1)
-What are the degrees of freedom (df
-What is the tcritical value?
-What is the pooled variance (S2P)
-What is the estimated standard error for the sample mean difference (S(M1 – M2)
-What is the t-statistic?
-What is the conclusion?

Question 30 options:

A)
Fail to reject H0: Serotonin DOES NOT affect aggression.

B)
Fail to reject H0: Serotonin affects aggression.

C)
Reject H0: Serotonin DOES NOT affect aggression.

D)
Reject H0: Serotonin affects aggression.”

## Solution Preview

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1. A statistics tutor wants to assess whether her remedial tutoring has been effective for her 16 students (n = 16). To evaluate the changes that occur during the year, students’ grades were measured at the beginning and at the end of the year. Their grades revealed an average improvement of MD = 8 points with a sum of squares for the difference scores of SSD = 930.

Conduct the appropriate hypothesis test to determine if the data are sufficient to conclude that there was significant IMPROVEMENT? Use a one-tailed test with α = 0.01

-What is the null hypothesis (H0)
Null Hypothesis (Ho): There was no statistically significant improvement in population mean of students’ grades of measured at the beginning and at the end of the year.
Mathematically
Ho: µd=0
Where µd = population mean grades difference between the beginning and at the end of the year.

-What is the alternative hypothesis (H1)
Alternative Hypothesis (H1): There was a statistically significant improvement in population mean of students’ grades of measured at the beginning and at the end of the year.
Mathematically
H1: µd>0
Where µd = population mean grades difference between the beginning and at the end of the year.

-What are the degrees of freedom (df)
df = n-1 = 16-1 = 15...

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