26 When a female jewel wasp encounters a cockroach she sting

26. When a female jewel wasp encounters a cockroach, she stings and injects neurotoxins into its head that render the insect unable to initiate self-movement but not paralyzed. The wasp then holds the compliant (zombie) cockroach by the antenna and leads it to her next, where it will become live food for her larval offspring. The following graph compares the mean and self-initiated walking duration of stung and control cockroaches during the first 30 minutes after treatment. The error bars indicate approximate 95% confidence intervals. n=5 in each group.

a. Estimate the lower and upper limits of the confidence intervals for the control group.

b. Approximate the value of the standard error for the control group.

c. Identify two values of the population mean duration for the control group that are among the most plausible.

d. Identify two values of the population mean duration for the stung group that are less plausible.

e. Identify the main weakness in the construction of the graph. How would you improve it?

Solution

a)

We inspect the graph and the interval (in black) looks like

lower bound = 0.5
upper bound = 7.5

*****************

b)

Here,

margin of error (E) = (upper - lower)/2 = 3.5

As for n = 5, df = n - 1 = 4, the t value for 95% confidence is

t = 2.776445105

Thus, as

standard error (se) = E / t

Then

se = 1.26060479 [answer]

********************

c)

The point estimate for the control group is 4 (middle).

Thus, among the most plausible is 4, or 4.5. As long as it is close to 4, it is plausible.

**********************

d)

The point estimate for the stung group is around 0.25 (middle).

Thus, among the least plausible are the bounds of its confidence interval, around 0.1 or 0.5.

**********************

e)

The main weakness of the graph could be the scale. The scale is too big that the \"stung\" group can no longer be estimated properly.

You can improve this by making the intervals finer, like 0.2 increments, perhaps.