Statistics - Hypothesis Testing Projects

The moon appears larger near the horizon than when directly overhead, which led a number of psychologists

Question 1.

The moon appears larger near the horizon than when directly overhead, which led a number of

psychologists to propose a variety of theories. One particular theory by Holway and Boring suggested that the illusion was due to the fact that when the moon is on the horizon, the observer looked straight at it with eyes level, whereas when it was overhead, the observer had to elevate both his or her eyes and head to see it.

In order to test this theory, an apparatus was built to present two artificial "moons" of the same

initial size that could be adjusted by the viewer: one "horizon" moon appeared at the horizon, and

one "zenith" moon appeared directly overhead. The apparatus allowed the researchers to control

whether the subjects elevated their eyes or kept them level to see the zenith moon, while the horizon moon was always viewed with eyes level. A random sample of 10 subjects viewed the horizon moon and the zenith moon twice:

The horizon moon viewed with eyes level and the zenith moon viewed with eyes level
The horizon moon viewed with eyes level and the zenith moon viewed with eyes elevated

In each case, the subject adjusted the size of the horizon moon to match the perceived size of the

zenith moon. The researchers then recorded the ratio of size of the horizon moon to the size of the zenith moon a ratio of 1.2 indicates that the subject felt the horizon moon appeared 1.2 times as large as the zenith moon. If the theory by Holway and Boring was correct, this ratio would tend to be higher when subjects viewed the zenith moon with their eyes elevated than with their eyes level. The data moonratio.sav contains the following observations for the 10 subjects:

Subject: Subject ID number

Elevated: The ratio of apparent moon size (horizon moon to zenith moon), when the subject

viewed the zenith moon with eyes elevated

Level: The ratio of apparent moon size (horizon moon to zenith moon), when the subject

viewed the zenith moon with eyes level

(a) [1 mark] Are the elevated and level samples paired or independent? Write a sentence

justifying your choice.

(b) [5 marks] Carry out an appropriate hypothesis test to investigate whether the average ratio

is higher when the zenith moon is viewed with eyes elevated than with eyes level. Be sure to

state the null and alternative hypotheses, the observed test statistic, the null distribution, the

p-value, and an appropriate conclusion in plain language.

with eyes elevated and when viewed with eyes level. Write a sentence interpreting this interval

in plain language. Does this confidence interval support the decision made in part (b)?

(d) [4 marks] State and check the assumptions that are necessary for the analysis in parts (b)

and (c).

Question 2.

A person's critical flicker frequency is the highest frequency at which he or

she can detect that a light source is flickering. Above the critical flicker frequency, the light source appears to be continuous despite the fact that it is flickering. To determine critical flicker frequency, a random sample of 19 young adult males with either blue, green, or brown eyes were asked to identify whether a light source was flickering or not at various frequencies (measured in hz). The data appear in the eyeflicker.sav.

(a) [5 marks] Is there evidence that different eye colour groups for young adult males (blue,

green, and brown) have different average critical flicker frequencies? Be sure to state the null

and alternative hypotheses, the observed test statistic, the null distribution, the p-value, and an

appropriate conclusion in plain language.

(b) [3 marks] If appropriate, identify which eye colour groups have significantly different mean

critical flicker frequencies, with reference to appropriate SPSS output. If post-hoc tests are not

appropriate, explain the purpose of a post-hoc test and why it is not appropriate in this example.

Justify why or why not for each assumption.

Question 3.

Data relating to the annual seed production of trees has been collected1. This data set shows the

mean number of seeds produced in a year (Count) and the mean seed weight (Weight) in milligrams for 19 trees. Also within the data set are variables that have been calculated by taking the natural logarithm of the Count variable (LOG Count) and Weight variable (LOG Weight).

This data is available in the le seeds.sav.

In the following questions, ensure that you make it clear to the reader what variables you are talking about from the above data set.

(a) [2 marks] Produce a scatterplot with mean seed weight on the x-axis and mean number of

seeds on the y-axis and comment on its features.

(b) [2 marks] Produce another scatterplot with the natural logarithm of mean seed weight on the

x-axis and the natural logarithm of the mean number of seeds on the y-axis and comment on its

features.

number of seeds and the logarithm of the mean seed weight. Interpret the numbers in the regression equation.

(d) [1 mark] Use the regression equation to predict the logarithm of the mean number of seeds

for a tree for which the logarithm of the mean seed weight is 6.

(e) [1 mark] How much of the variation in the logarithm of the mean number of seeds is accounted for the in the linear regression on the logarithm of the mean seed weight?

(f) [6 marks] Is there a significant relationship between the logarithm of the mean number of seeds and the logarithm of the mean seed weight? Be sure to include the following in your answer:

_ the null and alternative hypotheses

_ the test statistic

_ the null distribution

_ the p-value

_ your conclusion

(g) [2 marks] Provide a 99% con_dence interval for the expected change in the logarithm of the

mean number of seeds when the logarithm of the mean seed weight increases by 1.

(h) [4 marks] List the assumptions of your analysis. To what degree are these assumptions satisfied? Include output from SPSS where appropriate.

Price: $28.36

Solution: The downloadable solution consists of 11 pages, 1736 words and 3 charts.
Deliverable: Word Document