You wish to test the following claim (H) at a significance level of a = 0.10.H₂:1 = 12Ha: 12You believe both populations are normally distributed, but you do not know the standard deviationsfor either. However, DON'T assume that the variances of the two populations are equal. You obtaina sample of size n₁ = 16 with a mean of 1 = 78.9 and a standard deviation of SD₁ = 11.9 from= 87.7 and a standardthe first population. You obtain a sample of size n₂ = 25 with a mean of ₂deviation of SD2 = 19.4 from the second population.What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic =What is the p-value for this sample? (Report answer accurate to four decimal places.)p-value =The p-value is...O less than (or equal to) aOgreater than aThis test statistic leads to a decision to...O reject the nullO accept the nullO fail to reject the null As such, the final conclusion is that...O There is sufficient evidence to warrant rejection of the claim that the first population mean isnot equal to the second population mean.O There is not sufficient evidence to warrant rejection of the claim that the first populationmean is not equal to the second population mean.O The sample data support the claim that the first population mean is not equal to the secondpopulation mean.O There is not sufficient sample evidence to support the claim that the first population mean isnot equal to the second population mean.

From the provided information, n1=16x1=78.9s1=11.9n2=25x2=87.7s2=19.4α=0.10The hypotheses for this test are as follow: H0: µ1 = µ2 Ha: µ1 ≠ µ2 The test statistic for this sample can be obtained as: t=x1-x2s12n1+s22n2=78.9-87.711.9216+19.4225=-1.80 The test statistic is -1.80.The degrees of freedom can be obtained as: df=s12n1+s22n22s12n12n1-1+s22n22n2-1=11.9216+19.4225211.9216216-1+19.4216225-1≈20 The degrees of freedom is 20.The p value of test statistic can be obtained using excel function as: =T.DIST.2T(1.80,20) The excel output is as follow: The p value is 0.0870. The p value is less than level of significance (α). This test statistic leads to a decision to reject the null hypothesis. As such the final conclusion is that the sample data supports the claim that the first population mean is not equal to the second population mean.