At Rachel\'s 11 th birthday party, 8 girls were timed to see how long (in second

Question

At Rachel's 11th birthday party, 8 girls were timed to see how long (in seconds) they could hold their breath in a relaxed position. After a two-minute rest, they timed themselves while jumping. The girls thought that the mean difference between their jumping and relaxed times would be zero. Test their hypothesis at the 5% level.

29

A) State the distribution to use for the test.

B) What is the test statistic?

C) What is the p-value?

Relaxed Time (seconds) Jumping Time (Seconds)

29

22 48 41 31 28 22 21 23 25 45 43 37 35 29 32

Explanation / Answer

(A) t test for two independent sample (pooled variance)

where M1= 33 , ss1 = 642

where M2= 30.88 , ss2 =  486.88

Difference Scores Calculations

Treatment 1

N1: 8
df1 = N - 1 = 8 - 1 = 7
M1: 33
SS1: 642
s21 = SS1/(N - 1) = 642/(8-1) = 91.71


Treatment 2

N2: 8
df2 = N - 1 = 8 - 1 = 7
M2: 30.88
SS2: 486.88
s22 = SS2/(N - 1) = 486.88/(8-1) = 69.55


T-value Calculation

s2p = ((df1/(df1 + df2)) * s21) + ((df2/(df2 + df2)) * s22) = ((7/14) * 91.71) + ((7/14) * 69.55) = 80.63

s2M1 = s2p/N1 = 80.63/8 = 10.08
s2M2 = s2p/N2 = 80.63/8 = 10.08

t = (M1 - M2)/(s2M1 + s2M2) = 2.12/20.16 = 0.47

(c)

The t-value is 0.47329. The p-value is .643299.

Relaxed Time (x)   x-M (X-m)^2 29 -4 16 48 15 225 31 -2 4 22 -11 121 23 -10 100 45 12 144 37 4 16 29 -4 16

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