1a. Is there a significant difference made by review sessions in the final exam?
b) H 0 : μ 1 = μ 2
Vs
H a : μ 1 ≠ μ 2
c) Independent Samples T-test
| Final exam points | |||
| Equal Variance assumed | Equal variances not assumed | ||
| Levene’s Test for Equality of Variances | F Sig | .219 .641 | |
| t-test for Equality for Means | t df Sig. (2-tailed) Mean Difference Std. Error Difference 95% Confidence interval of the Lower Difference Upper | -1.405 103 .163 -2.300 1.637 -5.546 .996 | -1.415 69.363 .162 -2.300 1.626 -5.543 .993 |
d) The group means are not statistically significantly different (t 69.363 =-1.415, p-value> 0.05).The p-value (value in the “sig. (2 tailed)” row is greater than 0.05, thus it is not significant. The p-value is 0.163. It is greater than the alpha=value of 0.05. 0.641> 0.05. Therefore, do not reject null hypothesis (H 0 )
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e) On average review sessions do not help in student performance. The final exam points are the same regardless of whether a student attended or failed to attend the review sessions. Review sessions do not have any effect on student performance.
2a) Is there a significant difference in previous GPA between the sample students and the past known population value of 2.75?
b) H 0 : μ= xˉ
Vs
H a : μ ≠ xˉ
c) A one sample t-test.
One-Sample Test | ||||||
Test Value = 2.75 | ||||||
t | df | Sig. (2-tailed) | Mean Difference | 95% Confidence Interval of the Difference | ||
Lower | Upper | |||||
| Previous GPA | .387 | 104 | .699 | .02886 | -.1190 | .1767 |
d) There is no significant difference between the sample mean and the population mean(t 104 =0.387, p-value >0.05). The p-value is 0.699 and it is thus not significant. It is greater than the alpha-value. 0.0699> 0.05. Do not reject null hypothesis(H 0 ).
e) The sample mean of the students in Stat_Grades.sav is similar or equal to the mean value of 2.75 of the population. On average, the students in this class had a mean GPA of 2.75 which is similar to the population mean.
3a). Is there a significant difference in the average student performance between Quiz 1 and Quiz 3?
b) H 0 :μ d = 0
Vs
H a : μ d ≠ 0
c) Paired sample t-test.
| t | df | sig.(2-tailed) | ||||||
| Mean | Std. Deviation | Std. Error Mean | 95% Confidence Interval of the Difference | |||||
| lower | upper | |||||||
| pair 1 Quiz 1 points- Quiz 3 points | -.514 | 1.287 | .126 | -.763 | -.263 | -4.095 | 104 | .000 |
d) There is a significant average difference between Quiz 1 and Quiz 3(t 104 =-4.095, p-value>0.05).The p-value is 0.000. The p-value is less than the alpha value and it is therefore significant. 0.000< 0.05. Reject null hypothesis(H 0 ).
e) On average, the students recorded higher points on Quiz 1 compared to Quiz 2.
4a) H 0 : μ= xˉ
Vs
H a : μ ≠ xˉ
b) One sample t-test.
c) The p-value is 0.000
d) Since the p-value is less than the alpha value, it is significant and we therefore reject null hypothesis. There is a significant difference (t 104 = 5.030, p-value <0.05) between the mean score of sample of students in quiz 5 and the population mean of 7.
e) The mean obtained by the sample of students in quiz 5 is different or not equal to the population mean of 7. On average, the students had a different mean compared to the known population mean.
f) 105 students. The mean for the sample is different than for the known population value for Quiz 5. It is statistically significantly different. Significantly different happens when p-value is less than the specified alpha value, implying that the difference between the variables is caused by anything other than chance.
