A medical researcher wondered if there is a significant difference between the mean birth weight of boy and girl babies. Random samples of 5 babies' weights (pounds) for each gender showed the following:
Boys: 8.0 4.7 7.3 6.2 3.4
Girls: 5.3 2.8 6.4 6.8 7.4
To test the researcher's hypothesis, we should use the:

a) paired (dependent) samples t-test
b) independent samples t-test
c) large-sample z-test
d) t-test for correlation

b) independent samples t-test

So with the p value obtained and using the significance level given we have so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the mean of the group 1 (boys) is NOT significantly different than the mean for the group 2 (Girls).  

Step-by-step explanation:

The system of hypothesis on this case are:  

Null hypothesis:  

Alternative hypothesis:  

Or equivalently:  

Null hypothesis:  

Alternative hypothesis:  

Our notation on this case :  

represent the sample size for group 1  

represent the sample size for group 2  

We can calculate the mean and deviation for eaach group with the following formulas:

represent the sample mean for the group 1  

represent the sample mean for the group 2  

represent the sample standard deviation for group 1  

represent the sample standard deviation for group 2  

If we see the alternative hypothesis we see that we are conducting a bilateral test and with independnet samples t test.

b) independent samples t-test

The statistic is given by this formula:  

And now we can calculate the statistic:  

The degrees of freedom are given by:  

And now we can calculate the p value using the altenative hypothesis:  

So with the p value obtained and using the significance level given we have so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the mean of the group 1 (boys) is NOT significantly different than the mean for the group 2 (Girls).  

the correct answer is 5 6 and 7

you can first factor out the n to get n(1+5). we know that 1+5 is 6, so we just have 6n.