Many animals, including humans, tend to avoid direct eye contact and even patterns that look like eyes. Some insects, including moths, have evolved eye-spot patterns on their wings to help ward off predators. Scaife (1976) reports a study examining how eye-spot patterns affect the behavior of birds. In the study, the birds were tested in a box with two chambers and were free to move from one chamber to another. In one chamber, two large eye-spots were painted on one wall. The other chamber had plain walls. The researcher recorded the amount of time each bird spent in the plain chamber during a 60-minute session. Suppose the study produced a mean of in the plain chamber with for a sample of birds. (Note: If the eye spots have no effect, then the birds should spend an average of in each chamber.)

Question

Many animals, including humans, tend to avoid direct eye contact and even patterns that look like eyes. Some insects, including moths, have evolved eye-spot patterns on their wings to help ward off predators. Scaife (1976) reports a study examining how eye-spot patterns affect the behavior of birds. In the study, the birds were tested in a box with two chambers and were free to move from one chamber to another. In one chamber, two large eye-spots were painted on one wall. The other chamber had plain walls. The researcher recorded the amount of time each bird spent in the plain chamber during a 60-minute session. Suppose the study produced a mean of in the plain chamber with for a sample of birds. (Note: If the eye spots have no effect, then the birds should spend an average of in each chamber.)

Is this sample sufficient to conclude that the eye-spots have a significant influence on the birds' behavior? Use a two-tailed test with .
Compute the estimated Cohen’s d to measure the size of the treatment effect.
Construct the 95% confidence interval to estimate the mean amount of time spent on the plain side for the population of birds.

Answer 1

Means not given.

Answer 2

To determine whether the eye-spot patterns have a significant influence on the birds' behavior, we can conduct a hypothesis test.

Step 1: State the hypotheses:
The null hypothesis (H0): The eye-spots have no significant influence on the birds' behavior. The population mean amount of time spent in the plain chamber is μ = 30.
The alternative hypothesis (Ha): The eye-spots have a significant influence on the birds' behavior. The population mean amount of time spent in the plain chamber is not equal to 30 (μ ≠ 30).

Step 2: Set the significance level (α):
The significance level (α) is not provided in the given information. Let's assume a commonly used α value of 0.05, which corresponds to a 95% confidence level.

Step 3: Compute the test statistic:
The test statistic used for a two-tailed test with unknown population variance and a sample size greater than 30 is the t-test. However, we are not provided with the sample mean or standard deviation, so we cannot calculate the test statistic.

Step 4: Compute the estimated Cohen's d:
Cohen's d is a measure of the effect size and quantifies the difference between two means. It is computed using the formula:

Cohen's d = (Sample Mean - Population Mean) / Sample Standard Deviation

Unfortunately, we are not given the sample mean or standard deviation, so we cannot calculate the estimated Cohen's d.

Step 5: Construct the 95% confidence interval:
To construct the 95% confidence interval, we need the sample mean and sample standard deviation. Since they are not provided, we cannot calculate the confidence interval.

In conclusion, we cannot determine whether the eye-spots have a significant influence on the birds' behavior without the necessary sample statistics.

Answer 3

To determine whether the eye-spot patterns have a significant influence on the birds' behavior, we can perform a two-tailed hypothesis test and calculate Cohen's d to measure the size of the treatment effect. We can also construct a 95% confidence interval to estimate the mean amount of time spent on the plain side for the population of birds.

1. Hypothesis Testing:
The null hypothesis, denoted as H0, assumes that the eye-spots have no significant influence on the birds' behavior. The alternative hypothesis, denoted as Ha, assumes that the eye-spots do have a significant influence.

H0: μ1 = μ2 (the mean amount of time spent in the plain chamber is equal to the mean amount of time spent in the chamber with eye-spots)
Ha: μ1 ≠ μ2 (the mean amount of time spent in the plain chamber is not equal to the mean amount of time spent in the chamber with eye-spots)

We'll use a two-tailed test with an alpha level (significance level) of α = 0.05.

2. Computing Cohen's d:
Cohen's d is a measure of effect size, which indicates the standardized difference between two means. It helps us understand the magnitude of the treatment effect.

Cohen's d can be calculated using the formula:

d = (x̄1 - x̄2) / s

where x̄1 is the sample mean of the plain chamber, x̄2 is the sample mean of the chamber with eye-spots, and s is the pooled standard deviation of the two samples.

3. Constructing the 95% confidence interval:
The confidence interval provides a range of values within which we can reasonably expect the population mean to lie.

A 95% confidence interval can be calculated using the formula:

CI = x̄ ± (t * (s / √n))

where x̄ is the sample mean, t is the critical value from the t-distribution for a given alpha level and degrees of freedom, s is the sample standard deviation, and n is the sample size.

Now, without the actual values provided in the question for the sample mean in the plain chamber, sample mean in the chamber with eye-spots, standard deviation, and sample size, we cannot compute the exact values for the hypothesis test, Cohen's d, and the confidence interval. However, given the information provided, the steps outlined above should guide you through the analysis once you have the necessary data.