Question

A random sample of 7 apples were compiled with the following weights: 120 g, 118 g,...

A random sample of 7 apples were compiled with the following weights: 120 g, 118 g, 122 g, 126 g, 123 g, 121 g, 120 g. A random sample of 7 oranges were complied with the following weights: 130 g, 128 g, 128 g, 131 g, 133 g, 129 g, 134 g.

What is a 95% confidence interval in the difference of the mean weights between apples and oranges?

Homework Answers

Answer #1

answer)

As the population s.d is unknown here we will use t distribution to conduct the test

First we need to find the mean and s.d for apples and oranges

Apple

u1 = 121.4286

S1 = 2.5728

N1 = 7

Oranges

u2 = 130.4286

S2 = 2.3705

N2 = 7

Degrees of freedom is = smaller of n1-1, n2-1

Df = 6

For df 6 and 95% confidence level, critical value t from t table is = 2.447

Margin of error (MOE) = t*standard error

t = 2.447

Standard error = √{(s1^2/n2)+(s2^2/n2)}

MOE = 3.23556619315

Confidence interval is given by

(u1-u2)-MOE < (u1-u2) < (u1-u2)+MOE

−12.235566193<(u1-u2)<−5.7644338068

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