91影视

One survey was done on Homework assistance for accounting students. Seventy-five junior-level accounting majors were taken as samples. Among them, 20 students were given complete solutions, 25 students were given check figures at various solution steps, and the remaining 30 students were given no solution. Two tests were conducted before giving these things and after giving this solution. The means are given for three groups.

Here, the sample mean of the "no solution" group is $2.43$, the sample mean of the "Check figures" group is $2.72$, and the sample mean of the "Complete solution" group is $1.95$.

From "no solution" to "Check solution," the sample mean increased, but from "Check solution" to "complete solution," the sample mean decreased.

So, from checking the mean, it cannot be said that the researchers' theory "as a level of homework assistance increased, the test score improvement from pretest to posttest would decrease" is not correct.

Only from the mean is it not possible to know about the variability or the spread of the probability distribution of the population.

So, the sample mean is insufficient for making inferences about the population mean knowledge gains for the three groups.

Let$\mathrm{渭}$is the mean knowledge gained for the student in the "no solution" group and the mean knowledge gained for the student in the "check figure" group.

The Hypothesis is given by:

Null Hypothesis:

${\mathrm{H}}_0:({\mathrm{渭}}_1鈭�{\mathrm{渭}}_2)=0$.There is no significant difference between the mean knowledge gained for the two groups of students.

Alternative Hypothesis:

${\mathrm{H}}_1:({\mathrm{渭}}_1鈭�{\mathrm{渭}}_2)>0$There is evidence to say the mean knowledge gained by students in the "no solution" group is greater than the mean knowledge gained in the "check figure" group.

The significance level of $t$the test is $0.8248$and $伪=0.05$.

If role="math" localid="1652695802085" $p$-value role="math" localid="1652695808508" $<伪$, then reject the null Hypothesis role="math" localid="1652695811737" ${\mathrm{H}}_0$.

If role="math" localid="1652695798375" $p$-value, role="math" localid="1652695805481" $>伪$then fail to reject the null Hypothesis role="math" localid="1652695814880" ${\mathrm{H}}_0$.

From the given information, the role="math" localid="1652695886251" $p$-value $=0.8248$

Conclusion:

Here,$p$-the value is greater than the level of significance.

That is,$p$-value $(=0.8248)>伪(=0.05)$.

The reject criterion does not deny the Null Hypothesis.

Thus, it can be concluded that there is insufficient result to say that the mean knowledge gain of students in the "no solution" group is greater than the mean knowledge gain of students in the "check figure" group $伪=0.05$.

Let${\mathrm{渭}}_2$is the mean knowledge gained for the student in the "check figure" group and the mean knowledge gained for the student in the "complete solution" group.

The Hypothesis is given by:

Null Hypothesis:

${\mathrm{H}}_0:({\mathrm{渭}}_2-{\mathrm{渭}}_3)=0$

There is no significant difference between mean knowledge gains for the two groups of students.

Alternative Hypothesis:

${\mathrm{H}}_1:({\mathrm{渭}}_2-{\mathrm{渭}}_3)>0$

There is evidence to say the mean knowledge gained by students in the "check figure" group is greater than the mean knowledge gained in the "complete solution" group.

The significance level of$t$the test is$0.1849$and$伪=0.05$.

Calculation:

Decision:

If $p$-value $<伪$, then reject the null Hypothesis$H_0$.

If role="math" localid="1652696409921" $p$-value role="math" localid="1652696413312" $>伪$, then fail to reject the null Hypothesis $H_0$.

From the given information, the role="math" localid="1652696346800" $p$-value role="math" localid="1652696351540" $=0.1849$

Conclusion:

Here,$p$-the value is greater than the level of significance.

That is, $p$- value $(=0.1849)>伪(=0.05)$.

The reject criterion does not deny the Null Hypothesis.

Thus, it can be concluded that there is insufficient result to say that the mean knowledge gain of students in the "check figure" group is greater than the mean knowledge gain of students in the "complete solution" group.

The Hypothesis is given by:

Null Hypothesis:

${\mathrm{H}}_0:({\mathrm{渭}}_1-{\mathrm{渭}}_3)=0$

There is no significant difference between mean knowledge gains for the two groups of students.

Alternative Hypothesis:

role="math" localid="1652696508287" ${\mathrm{H}}_1:({\mathrm{渭}}_1-{\mathrm{渭}}_3)>0$

There is evidence to say the mean knowledge gained by students in the "no solution" group is greater than the mean knowledge gained in the "complete solution" group.

There is a preliminary result to say that the mean knowledge gained by students in the "no solution" group is greater than the mean knowledge gained in the "complete solution" group.

The significance level of $t$the test is $0.2726$and role="math" localid="1652696894149" $伪=0.05$.

Ifrole="math" localid="1652696873877" $p$-valuerole="math" localid="1652696902174" $<伪$, then reject the null Hypothesis$H_0$.

Ifrole="math" localid="1652696870754" $p$-value,$>伪$then fail to reject the null Hypothesis$H_0$.

From the given information, the role="math" localid="1652696801227" $p$-value role="math" localid="1652696806196" $=0.2726$

Conclusion:

Here,role="math" localid="1652696865840" $p$-the value is greater than the level of significance.

That is, role="math" localid="1652696862302" $p$- value $(=0.2726)>伪(=0.05)$.

The reject criterion does not deny the Null Hypothesis.

Thus, it can be concluded that there is insufficient result to say that the mean knowledge gain of students in the "no solution" group is greater than the mean knowledge gain of students in the "complete solution" group.