a) Explain the reasons for the data set not being paired. b) Determine the s

a) The weights of 35 babies whose mothers did not smoke and 22 babies whose mothers smoked were compared.
The two samples were taken from two independent populations, one is the weight of all babies whose mothers smoke and the other is weight of all babies whose mothers don't smoke.
They cannot be paired sample, because they do not represent the same sample treated with different conditions or the two measures of same set of subjects, being independent of each other.
b) The StatCrunch output shows that the sample difference of means is 725. Here, the first sample is the sample of babies with no smoking mothers and the second sample is the sample of babies with smoking mothers.
As the obtained sample difference is greater than 0, it shows that the sample mean weight of babies of non-smoking mothers is greater than the sample mean weight of babies of smoking mothers.
c) The claim is to twst whether the population mean birth weight is greater for mothers who do not smoke using a significance level of 0.05.
A hypothesis test is conducted through the following steps.
Step 1:
Consider ${\displaystyle {\mu }_1}$ and ${\displaystyle {\mu }_2}$ as the population mean weight of babies of no smoking and smoking mothers, respectively. So, the hypotheses are:
${\displaystyle H_0:{\mu }_1={\mu }_2}$
${\displaystyle H_a:{\mu }_1>{\mu }_2}$
Step 2:
Assumptions for performing a hypothesis test for comparing two population means:
The samples drawn from two independent populations are random samples and the observations are independent.
The two samples are independent of each other.
The two populations are approximately normal or the sample size of both the samples is 25 or more.
Requirement check:
The sample of babies whose mothers smoke and don't smoke are random samples and each member is independent of the other.
The two samples are independent.
Both the distributions are assumed to be normal.
All the conditions are satisfied.
Step 3:
The provided StatCrunch output shows that the t-statistic value is 3.19. The p-value is displayed as 0.0016.
Step 4:
Decision based of the p-value method:
If p-value ${\displaystyle \le \alpha }$, reject ${\displaystyle H_0}$.
If p-value ${\displaystyle >\alpha }$, fail to refect $H_0$.
Since p-value ${\displaystyle \left(0.0016\right)<0.05}$, the null hypothesis is rejected.
Conclusion:
Since there is sufficient evidence to reject the null hypothesis, it can be concluded that "the population mean birth weight is larger for mothers who do not smoke".