The crab spider, Thomisus spectabilis , sits on flowers and preys upon visiting
ID: 3312741 • Letter: T
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 34 bees a choice between 2 flowers: one with, and one without a crab spider. In 23 of the 34 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.
Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P = 0.50
Alternative hypothesis: P 0.50
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample proportion is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method, shown in the next section, is a one-sample z-test.
Analyze sample data. Using sample data, we calculate the standard deviation () and compute the z-score test statistic (z).
= sqrt[ P * ( 1 - P ) / n ]
= 0.008575
z = (p - P) /
z = 20.57
where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.
Since we have a two-tailed test, the P-value is the probability that the z-score is less than - 20.57 or greater than 20.57.
Thus, the P-value = less than 0.001
Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we have to reject the null hypothesis.
From the above test we have sufficient evidence that honeybees distinguish between flowers that have crab spiders and flowers that do not.
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