Confined to 629 valid cases whose age was no higher than 40 in the GSS 2018 data, do we have enough evidence to show a difference of mean BMI between the male and female young adult populations? Use the two-independent-sample T test to answers this question. Descriptive statistics of the BMI for male and female samples are given below in the Table 1. And let's assume that male and female populations have the same variance of BMI. Please follow the 7-step SOP of hypothesis testing to draw your conclusion.

Table 1 Descriptive statistics of the BMI for young male and female cases of the GSS 2018 data

N Mean Standard Deviation

Male 298 27.642 6.128

Female 331 28.597 7.415

1.Write down the alternative (research) hypothesis for this two-independent-sample T test.

H1:_________

2.Let's use the for this hypothesis test.

Calculate the t statistic:

t =

Given the =0.10, we use t critical values of 1.647 for this hypothesis test.

Can you reject the null hypothesis? Yes or No?

How to explain your conclusion? Please complete blanks in the following paragraph.

For the entire population of American young adults, the mean BMI of males and the mean BMI of females are / are not significantly different. This conclusion could be wrong but the probability of making the ______________ Error is no higher than ______________ .