Question

please answer all

15. You are measuring mass of pine cones in a population (in g). following results: 15, 18,22, 14 and 12g You obtain the For each question remember to show your calculations not just your result. a) Calculate the mean for this set of data. (1 point) b) Calculate the variance for this set of data. (2 points) c) Calculate the standard error (SE) for this data. (1 point) d) The formula for the 95% confidence interval (CI) for a set of data is Xt1.96 SE. Using the result you obtained in part (c) calculate the 95% CI for this data. (1 point)

Answer 1

15) Data set for mas of pines

15,18,22,14 and 12 g

a) Mean of the data set = (15 + 18 + 22 + 14 + 12 ) / 5 = 81/5 grams = 16.2 grams

b) Variance = $\sum (X - \mu )^{2} / N$

where X = data points , $\mu$ = mean , N = number of data points - 1 = 4

Variance = [ (15 - 16.2)² + (18 - 16.2)² + (22 - 16.2)² + ( 14 - 16.2)² + (12- 16.2)²] / 4

= [1.44+ 3.24 + 33.64 + 4.84 + 19.36] / 4 = 15.63 grams

c) Standard error = Standard deviation / (n)^1/2 , n = number of data points = 5

= (Variance)^1/2 / (5)^1/2 = 1.768 grams

d) 95 % confidence interval = $\mu$$\pm$ 1.96*SE = 16.2 $\pm$ 1.96*1.768 = 12.73472 to 19.66528