Answer:
There is significant difference in difference in the amount of food ferns eat ; and the preferred is TAB-a-cat.
(0.216, 5.984)
Step-by-step explanation:
This is a 2 sample t test test problem :
The hypothesis :
H0 : μ1 = μ2
H1 : μ1 ≠ μ2
x1 = 85.2 ; x2 = 82.1 ; n1 = 31 ; n2 = 30 ; s1 = 3.45 ; s2 = 4.62
The test statistic :
T = (x1 - x2) / √(s1²/n1 + s2²/n2)
T = (85.2 - 82.1) / √(3.45²/31 + 4.62²/30)
T = 3.1 / 1.0466
T = 2.96
Using the Pvalue from Tstatistic calculator :
df = smaller n - 1 = 30 - 1 = 29
Pvalue(2.96, 29) = 0.006075
α = 0.05
Pvalue < α ; We reject the Null and conclude that there is significant difference in difference in the amount of food ferns eat.
99% Confidence interval :
The test statistic :
(x1 - x2) ± Tcritical *√(s1²/n1 + s2²/n2)
Tcritical at 99% = Tcritical(0.01, 29) = 2.756
(85.2 - 82.1) / 2.756*√(3.45²/31 + 4.62²/30)
3.1 ± 2.8844296
Lower boundary = (3.1 - 2.8844296) = 0.216
Upper boundary = (3.1 + 2.8844296) = 5.984
(0.216, 5.984)
Since interval does not contain 0, then, we reject the Null.
