We are interested in whether children’s educational computer software costs less, on average, than children’s entertainment software. Thirty-six educational software titles were randomly picked from a catalog. The mean cost was $\backslash (31.14$with a standard deviation of $\backslash )4.69$. Thirty-five entertainment software titles were randomly picked from the same catalog. The mean cost was $\backslash (33.86$with a standard deviation of$\backslash )10.87$. Decide whether children’s educational software costs less, on average, than children’s entertainment software.

Given in the question that, We are interested in whether children’s educational computer software costs less, on average, than children’s entertainment software. Thirty-six educational software titles were randomly picked from a catalog. The mean cost was $\$31.14$with a standard deviation of $\$4.69$. Thirty-five entertainment software titles were randomly picked from the same catalog. The mean cost was $\$33.86$with a standard deviation of $\$10.87$. We need to check that whether children’s educational software costs less, on average, than children’s entertainment software

a. The null hypothesis is $H_0:{\mu }_1\ge {\mu }_2$

b. The Alternate hypothesis is

$H_a:{\mu }_1<{\mu }_2$

c. $\overline{X_1}-\overline{X_2}$Is there a distinction between children's instructional computer software and children's entertaining computer software?

d. Student's t distribution.

e. Fill in all requirements using Minitab's two sample t test option.

The result will be

$-1.36$is the test statistics

f. The output has a $p$-value of $0.090$.

g. Create a graph of the region(s) that correspond to the p-value.

$\text{i.}\alpha =0.05$

ii. Conclusion: the null hypothesis should not be rejected.

iii. Justification for Decision: p- value$>\alpha$

Conclusion: At the $5\%$level of significance, there is insufficient evidence to establish that the mean cost of educational computer software for children is cheaper than the mean cost of entertainment computer software for children.