Question

1. 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

5.1	5.9	6.1	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

1.5	1.9	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	1.7

(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

2. A study of parental empathy for sensitivity cues and baby temperament (higher scores mean more empathy) was performed. Let x₁ be a random variable that represents the score of a mother on an empathy test (as regards her baby). Let x₂be the empathy score of a father. A random sample of 37 mothers gave a sample mean of x₁ = 67.00. Another random sample of 27 fathers gave x₂ = 61.04. Assume that σ₁ = 10.92 and σ₂ = 11.62.

(a) Let μ₁ be the population mean of x₁ and let μ₂ be the population mean of x₂. Find a 95% confidence interval for μ₁ – μ₂. (Use 2 decimal places.)

lower limit
upper limit

Answer 1

Question 1

Part a)

X1 = 5.49

S1 = 0.56

X2 = 1.49

S2 = 0.22

Confidence interval :-

t(α/2, DF) = t(0.01 /2, 43 ) = 2.695

DF = 43

99% confidence interval is ( 3.72 , 4.26 )

Question 2

Confidence interval :-

Z(α/2) = Z (0.05 /2) = 1.96

Lower Limit = 0.34
Upper Limit = 11.58
95% Confidence interval is ( 0.34 , 11.58 )