Question

In: Statistics and Probability

Like father, like son: In , the statistician Karl Pearson measured the heights of pairs of...

Like father, like son: In , the statistician Karl Pearson measured the heights of pairs of fathers and sons. The following table presents a sample of pairs, with height measured in inches, simulated from the distribution specified by Pearson.

Father's height

70.8

65.4

65.7

69

73.6

66.7

70.1

68.3

Son's height

69.8

66

70.9

69.1

74.9

68.8

73.3

68.3

Use the TI-84 calculator.

Construct a 95% confidence interval for the slope. Round the answers to at least four decimal places.

Solutions

Expert Solution

SSE =Syy-(Sxy)2/Sxx= 25.119
s2 =SSE/(n-2)= 4.1865
std error σ              = =se =√s2= 2.0461
std error of slope =se(β1) =s/√Sxx= 0.2771
sample size : n= 8
for 95 % CI value of t= 2.447 (from excel:tinv(0.05,6)
margin of error E=t*std error = 0.6781
lower bound=b1+E= 0.0835
Upper bound=b1+E= 1.4396

95 % confidence interval for the slope (0.0835 < ß1 <1.4396)

orchestra answered 1 year ago
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