Answer:
Since the calculated value of t= 2.8782 does not fall in the critical region so we accept H0 and may conclude that the drug is <u>not </u>effective in increasing sleep.
Step-by-step explanation:
d d²
1.0, 1
0.8, 0.64
1.1, 1.21
0.1, 0.01
- 0.1, 0.01
4.4, 19.36
1.5, 2.25
1.6, 2.56
4.6, 21.16
<u>3.4 11.56 </u>
<u>∑18.4 ∑59.76</u>
1: We state our null hypothesis as
H0 : μd= 0 against the claim Ha: μd ≠ 0
2: The significance level is set at ∝ = 0.01
3: The test statistic under H0 is
t= d`/ sd /√n
4:The critical region is t ≥ t ( 0.005) 9 = 3.250
<u>5:Computation:</u>
d`= ∑d/n= 18.4/10= 1.84
Sd² = ∑(di- d`)²/n-1 = 1/n-1 [∑di²- (∑di)² /n]
= 1/9 [59.76 - (18.4)²/10]
=(59.76 - 33.856)/9
= 25.904/9
= 2.8782
<u>6: Conclusion:</u>
Since the calculated value of t= 2.8782 does not fall in the critical region so we accept H0 and may conclude that the drug is <u>not</u><u> </u>effective in increasing sleep.
This is because we have taken H0 as the mean of the difference is zero.
This can only be zero when the drug is not effective.