Question

The following data represent petal lengths (in cm) for independent random samples of two species of Iris.

Petal length (in cm) of Iris virginica: x₁; n₁ = 35

5.3	5.6	6.3	6.1	5.1	5.5	5.3	5.5	6.9	5.0	4.9	6.0	4.8	6.1	5.6	5.1
5.6	4.8	5.4	5.1	5.1	5.9	5.2	5.7	5.4	4.5	6.4	5.3	5.5	6.7	5.7	4.9
4.8	5.9	5.1

Petal length (in cm) of Iris setosa: x₂; n₂ = 38

1.4	1.6	1.4	1.5	1.5	1.6	1.4	1.1	1.2	1.4	1.7	1.0	1.7	1.9	1.6	1.4
1.5	1.4	1.2	1.3	1.5	1.3	1.6	1.9	1.4	1.6	1.5	1.4	1.6	1.2	1.9	1.5
1.6	1.4	1.3	1.7	1.5	1.6

(a) Use a calculator with mean and standard deviation keys to calculate x₁, s₁, x₂, and s₂. (Round your answers to two decimal places.)

x1 =
s1 =
x2 =
s2 =

(b) Let μ₁ be the population mean for x₁ and let μ₂ be the population mean for x₂. Find a 99% confidence interval for μ₁ − μ₂. (Round your answers to two decimal places.)

lower limit
upper limit

Answer 1

	Values ( X )	Σ ( Xi- X̅ )2	Values ( Y )	Σ ( Yi- Y̅ )2
	5.3	0.0356	1.4	0.0067
	5.6	0.0124	1.6	0.014
	6.3	0.6584	1.4	0.0067
	6.1	0.3738	1.5	0.0003
	5.1	0.151	1.5	0.0003
	5.5	0.0001	1.6	0.014
	5.3	0.0356	1.4	0.0067
	5.5	0.0001	1.1	0.1456
	6.9	1.992	1.2	0.0793
	5	0.2387	1.4	0.0067
	4.9	0.3464	1.7	0.0477
	6	0.2615	1	0.2319
	4.8	0.4742	1.7	0.0477
	6.1	0.3738	1.9	0.1751
	5.6	0.0124	1.6	0.014
	5.1	0.151	1.4	0.01
	5.6	0.0124	1.5	0.0003
	4.8	0.4742	1.4	0.0067
	5.4	0.0078	1.2	0.0793
	5.1	0.151	1.3	0.033
	5.1	0.151	1.5	0.0003
	5.9	0.1692	1.3	0.033
	5.2	0.0833	1.6	0.014
	5.7	0.0447	1.9	0.1751
	5.4	0.0078	1.4	0.0067
	4.5	0.9773	1.6	0.014
	6.4	0.8306	1.5	0.0003
	5.3	0.0356	1.4	0.0067
	5.5	0.0001	1.6	0.014
	6.7	1.4675	1.2	0.0793
	5.7	0.0447	1.9	0.1751
	4.9	0.3464	1.5	0.0003
	4.8	0.4742	1.6	0.014
	5.9	0.1692	1.4	0.0067
	5.1	0.151	1.3	0.033
			1.7	0.0477
			1.5	0.0003
			1.6	0.014
Total	192.1	10.715	56.3	1.5572

Mean X̅ = Σ Xi / n
X̅ = 192.1 / 35 = 5.49
Sample Standard deviation S_X = √ ( (Xi - X̅ )² / n - 1 )
S_X = √ ( 10.7155 / 35 -1 ) = 0.56

Mean Y̅ = ΣYi / n
Y̅ = 56.3 / 38 = 1.48
Sample Standard deviation S_Y = √ ( (Yi - Y̅ )² / n - 1 )
S_Y = √ ( 1.5572 / 38 -1) = 0.21

Part a)

X1 = 5.49

S1 = 0.56

X2 = 1.48

S2 = 0.21

Part b)

Confidence interval :-

t(α/2, DF) = t(0.01 /2, 42 ) = 2.698

DF = 42

Lower Limit =
Lower Limit = 3.74
Upper Limit =
Upper Limit = 4.28
99% Confidence interval is ( 3.74 , 4.28 )