Question

Aria 28:46 n 2 of 12 (10 points) 10 2 An ecologist randomly samples 11 plants of a specific species and measures their heights. He finds that this sample has a mean of 16 cm and a standard deviation of 1 cm. r we assume that the height measurements are normally distributed, find a 90% confidence interval for the mean height of all plants of this Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)

Answer 1

Given, Mean, $\small \mu$ = 16 Standard deviation = 1 n=11

standard Error s = S.D/√n = 1/√11 = 0.30

$\large z = (x - \mu ) / s$

$\large x = \mu \pm z*s$

a) For 90% confidence interval z = 1.645

Lower limit x = 16 - 1.645*0.30 = 15.506 = 15.5 . (round off)

Upper limit x = 16 + 1.645*0.30 = 16.494 = 16.5

Ans. 15.5 , 16.5

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