Question

As a Christmas tree farmer, you want to know what seed type is the fastest growing. You plant 14 seeds and wait three years. After three years of growth, the 14 seeds have an average height of 4.24ft and a standard deviation of 0.404ft. The tallest tree has is 4.79ft tall; (a) what is the probability that is random chance? Assume the data follows a normal distribution. (b) Should you use a t-score (t distribution) or a z-score (normal distribution)?

Answer 1

(a)Let X be the height of a tree

X has mean = 4.24 and standard deviation = 0.404

z score is given by

z score = (X-mean) / standard deviation

The z score of the tallest tree is

P( X > 4.79) = P( z > 1.36)

From z table

P( z > 1.36) = 0.0869

Considering that , probability of getting a tree of height 4.79 or more is 0.0869

Therefore , probability of random chance = 0.0869

b) We use z score here

As t distribution is used when we compare the sampling distribution of sample mean with hypothesized mean. But here in this problem , we compare a value of single random variable (X)with the mean ( not with a hypothesized mean) .

Thus z score is used given by

z score = (X-mean) / standard deviation

while t score is given by

where is the hypothesized mean , s is the sample standard deviation , n is the sample size