Question 746946: To evaluate the effect of a treatment, a sample is obtained from a population with a mean of μ =75,
and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found
to be M =79.6 with a standard deviation of s =12.
a. If the sample consists of n= 16 individuals, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with = .05?
b. If the sample consists of n = 36 individuals, are the data sufficient to conclude that the treatment
has a significant effect using a two-tailed test with= .05?
c. Comparing your answer for parts a and b, how does the size of the sample influence the outcome of a
hypothesis test?
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 M =37 minutes in the plain chamber with SS = 288 for a sample of n = 9 birds. (Note: If the eye-spots have no effect, then the birds should spend an average of μ = 30 minutes in each chamber.)
a. Is this sample sufficient to conclude that the eyespots have a significant influence on the birds’ behavior? Use a two-tailed test with = .05.
b. Compute the estimated Cohen’s d to measure the size of the treatment effect.
c. Construct the 95% confidence interval to estimate the mean amount of time spent on the plain side for
the population of birds.
Answer by mikeebsc(26)   (Show Source):
You can put this solution on YOUR website! 1.
A. This is not a very complicated answer, but actually trying to type it out may well take a very long time, so I will assume you know what null and alternative hypotheses are and simply solve the problem.
On paper:
1. State the claim value as Ho: u=75 (CLAIM)(Null Hypothesis must have equality)
2. State the Alternative as Ha: u<>75
Make sure to write claim next to the claim value for easier solving later on. Ho is not always the claim value as it is in this problem. If the problem had said < or > 75, we would be writing claim next to the Ha value (Ha would be the claim value). Ho is only determined by the fact that it MUST have some sort of equality.
The equation to solve this is relatively long and complex, so much so that even textbooks tell us to use technology to solve the problems in today's world, so this is what I will do. I use a TI-83 or TI-84, either will produce the same results.
For part A:
Press STAT
Goto TESTS
3. Scroll to #2, T-test, as the sample size is very low. (Generally, anything with a sample size under 30 will use a T test unless the population size is being used and/or the standard deviation is not known.)
make sure you are on Stats, then enter the values: Mean, Sample Mean, Sample Standard Deviation, Sample Size, and choose a 2 tailed test(the "not equal to symbol".
**
Mean = 75
Sample mean = 79.6
Sample Std. Dev. = 12
Sample Size = 16
Make sure the "not equal to" ( the 2 tail test) sign is highlighted and press enter.
Goto Calculate and press enter.
Write down the P-Value, leave a small space and write down the .05 value (the level of significance) and compare the two.
*p=.146
.146 > .05
If the P-value is less than or equal to the level of significance, then we reject Ho.
If the P-value is greater than the level of significance, we do not reject Ho (can be interpreted as reject Ha, but this is not the "correct" way of saying it.)
In this case, we do not reject Ho, so we cross out Ha, which leaves Ho.
We then interpret this as, "There is enough evidence to support the claim that the treatment has a significant effect." because Ho (the claim value in this case) was not rejected.
B.
Again we write the Ho and Ha hypotheses.
This time, on the calculator:
Press STAT
Goto TESTS
Use Z-test (#1), as the sample size is over 30.
Make sure you are on STATS.
Enter the values as needed:
Mean:75
Std Dev.:12
Sample Mean:79.6
Sample Size:36
Make sure the "not equal to" (the 2 tailed test) sign is highlighted and press enter
Press enter on calculate
Again, take note of the p-value and compare it to the level of significance:
p=.021
.021 <= .05
Since p <= .05 we reject Ho and keep Ha.
We interpret this as "There is not enough evidence to support the claim that the treatment has a significant effect." because Ho (the claim value) was rejected.
C.
In comparing the answers from A and B, the evidence shows that the larger the sample size, the less likely it will be that the evidence will support the claim that the treatment has a significant effect.
Sorry, but someone else will have to take part 2, as this has taken me quite a while to write out. If noone has, I will do it in a day or 2, good luck!
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