Question

The crab spider, Thomisus spectabilis, sits on flowers and preys upon visiting honeybees. Do honeybees distinguish between flowers that have crab spiders and flowers that do not? To test this, Heiling et al. (2003) gave 33 bees a choice between 2 flowers: one with, and one without a crab spider. In 24 of the 33 trials, the bees picked the flower that had the spider. In the other trials, the bees chose the spiderless flower.

With these data, carry out the appropriate hypothesis test (one- or two-tailed), using the normal approximation to the binomial distribution to determine Z. For a one-tailed test, use the formula =(1-NORM.DIST(Z,0,1,TRUE) in Excel calculate P. For a two-tailed test, use the formula =2(1-NORM.DIST(Z,0,1,TRUE).

State your answer for the value of P to three decimal places, and include the leading zero.

• Do all of the math in Excel
• DO NOT round the value of Z.
• Substitute the cell (e.g. B1) for Z in the formula for P.

Answer 1

ONE TAILED TEST

Let p₁ be thesample proportion of honey bees choosing flower with crab spider

and p₂ be the sample proportion of honey bees choosing flower without crab spider.

Let P₁ and P₂ be the corresponding population proportion.

H₀: P₁=P₂

H_A: P₁>P₂

Let Level of significance = 0.05

       Where ,              ,   

Therefore P=0.5     Q=1-p= 0.5

Calculating Z we get Z=3.6927

p-value = 0.000111

Since the p-value <0.05 reject the null hypothesis and conclude that bees prefer flowers with crab spider.

TWO TAILED TEST

H₀: P₁= P₂

H_A: P₁ P₂

We get Z=3.6927(Refer one tailed test)

p-value= 0.000222

p-value<0.05

Reject the null hypothesis and conclude that the proportion of bees prefer flowers with crab spider is not same as the proportion of bees prefer flowers with out crab spider.