Problem #1An evaluation of a group of students was undertaken to analyze their student loan status. 1620 students were looked at. Of thatgroups, 899 did not require any loans to go to school. The mean scholarship amount received by this group (the group that didnot require loans) was $3890. The remaining 721 students received an average scholarship amount of $4320. As a result, therewas a $430 difference between the two groups which seems reasonably large. A scholarship committee suggests that thisdifference to state that they do a pretty good job of giving some additional scholarship assistance to students who have to takeout loans. The standard deviation of this difference is given here: $340. (Note: This is the SD - not the standard error. So we donot have to divide by the square root of n.)Do a complete hypothesis test, demonstrating your understanding of each step. (You don't have to explain in extreme detail, justdemonstrate your understanding of the steps involved). Use the standard value for alpha.Your answer should be done in the traditional ("older") hypothesis test format. That is, do not use the confidence interval methodfor this question. You will do so in a question below.In addition, complete your analysis by answering the following in non-statistical terms: Does this data support the coordinators'statement? This is because, as we have discussed previously, at the end of the day, the analyst must be able to describe theirstatistical calculations in "real world" language to assist non-experts in making their decisions.Friendly Hint: Note that we are looking at two groups to see if the difference of $430 is different from 0, or if it isn't.

The objective of this scenario is to check whether the difference between the average amount received by the group that do not require loans and the group that require loans is different from zero. The null hypothesis is,Ho: The difference between the average amount received by the group that do not require loans and the group that require loans is equal to zero. The alternative hypothesis is,H1: The difference between the average amount received by the group that do not require loans and the group that require loans is different from zero (not equal to zero). The sample size of the group that do not require loans is, n1=899 The sample size of the group that require loans is, n2=721 The average difference between the amount received by the group that do not require loans and the group that require loans is,x¯1-x¯2=430. The standard deviation of the difference between the amount received by the group that do not require loans and the group that require loans is, sx1-x2=340 The test statistic is, t=x¯1-x¯2s2X1-X21n1+1n2 =43034021899+1721 =43016.99765 =25.298(rounded to three decimals) Assume the prior level of significance, α=0.05. The degrees of freedom is, df=n1+n2-2 =899+721-2 =1618 Since the alternative hypothesis is two-tailed, we use two-tailed critical value. At 0.05 level of significance with 1618 degrees of freedom, the two-tailed critical value is, t(α/2,df)=t(0.05/2,1618) =TINV(0.05,1618) =±1.961 Using excel function, "=TINV(0.05,1618)" the critical value obtained.Decision rule: Reject the null hypothesis, if the test statistic is greater than the critical value (or) if the test statistic is less than the critical value i.e.,t<-1.961(or) t>+1.961 The test statistic t= 25.298 is greater than 25.298, so reject the null hypothesis and conclude that the difference between the average amount received by the group that do not require loans and the group that require loans is different from zero. This analysis supports the coordinators statement that the difference of amount has a pretty good job of giving some additional scholarship to students who have to take out loans.