Question

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

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 μ1μ2. (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 μ1μ2. (Use 2 decimal places.)

 lower limit upper limit

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 )

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