Question

The data below is from a small group of third graders. Using the data, compare whether there are differences in energy expenditure (average METs/day) in 10 third graders between a day with physical education (w/PE) and a day without physical education (w/o PE). Perform each of the calculations and/or answer each of the questions as indicated.

Subject	Day w/PE (x1)	Day w/o PE (x2)
1	2.1	2.1
2	2.1	1.6
3	2.6	2.5
4	2.1	1.9
5	2.7	2.6
6	2.0	1.7
7	2.0	1.8
8	4.4	2.8
9	4.7	3.4
10	4.1	3.4

-Create a null and alternative hypothesis for the scenario discussed above.

H₀:

H₁:

-Calculate the mean and standard deviation for each variable (x₁ and x₂). Show the equation you used and simple substitution for full credit.

-What kind of t-test would you run on this sample? Why (be specific)?

Answer 1

Here in this Question it is given that The data below is from a small group of third graders. Using the data, compare whether there are differences in energy expenditure (average METs/day) in 10 third graders between a day with physical education (w/PE) and a day without physical education (w/o PE). Perform each of the calculations and/or answer each of the questions as indicated.

Now our claim is that there is difference in energy expenditure in day/wpe and x1 and day /o x2. To test this claim we have to use two sample t test because here the population standard deviations is unknown.

Before performing test we need to compute the sample Standerd deviation of both data,

The sample Standerd deviation is calculated using following formula,

The standard deviations for x1 is 1.085 and for x2 sd is 0.6696.

Now the appropriate hypothesis for above claim is given below,

null and alternative hypothesis :

H₀: There is no difference in x1 and x2.

H₁: There is difference in x1 and x2.

Now the two tailed two sample t test is performed as below,

For better understanding we assumed the 0.05 level of significance as below,

In above test performed we used the two sample t test because here the population standard deviations is unknown. Here there are two groups therefore we need to use two sample t test.

Hope you understood.

Thank you.