Paired-samples t test and graduate admissions: Is it harder to get into graduate programs in psychology or in history? We randomly selected five institutions from among all U.S. institutions with graduate programs. The first number for each is the minimum grade point average (GPA) for applicants to the psychology doctoral program, and the second is for applicants to the history doctoral program. These GPAs were posted on the Web site of the well-known college guide company Peterson’s. Wayne State University: 3.0, 2.75 University of Iowa: 3.0, 3.0 University of Nevada, Reno: 3.0, 2.75 George Washington University: 3.0, 3.0 University of Wyoming: 3.0, 3.0

The participants are not people; explain why it is appropriate to use a paired-samples t test for this situation.

Conduct all six steps of a paired-samples t test. Be sure to label all six steps.

Calculate the effect size and explain what this adds to your analysis.

Report the statistics as you would in a journal article.

Determine whether the BEST, most common interpretation of the given statement is:

     TRUE - Select 1

     FALSE - Select 2

Question 1 options:

Question 2 (20 points)

3.

(3 pt) A certain data scientist is testing his predictor (essentially a tool given historical

data and would make predictions using said data) that would make predictions about

Philadelphia’s temperatures. The predictor produces a correct temperature if the

prediction falls within three standard deviations from the target value. Assume that the

expected value of each prediction equals the target value. What is the accuracy of the

predictor if the distribution of measurements is uniform?

Two plots at Rothamsted Experimental Station were studied for production of wheat straw. For a random sample of years, the annual wheat straw production (in pounds) from one plot was as follows.

Use a calculator to verify that, for this plot, the sample variance is s² ≈ 0.305.

Another random sample of years for a second plot gave the following annual wheat production (in pounds).

Use a calculator to verify that the sample variance for this plot is s² ≈ 0.685.

Test the claim that there is a difference (either way) in the population variance of wheat straw production for these two plots. Use a 5% level of signifcance.

(a) What is the level of significance?

State the null and alternate hypotheses.

H_o: σ₁² = σ₂²; H₁: σ₁² > σ₂²
H_o: σ₁² > σ₂²; H₁: σ₁² = σ₂²    
H_o: σ₂² = σ₁²; H₁: σ₂² > σ₁²
H_o: σ₁² = σ₂²; H₁: σ₁² ≠ σ₂²

(b) Find the value of the sample F statistic. (Use 2 decimal places.)


What are the degrees of freedom?

What assumptions are you making about the original distribution?

The populations follow independent normal distributions.
The populations follow independent normal distributions. We have random samples from each population.    
The populations follow independent chi-square distributions. We have random samples from each population.
The populations follow dependent normal distributions. We have random samples from each population.

(c) Find or estimate the P-value of the sample test statistic. (Use 4 decimal places.)

p-value > 0.200
0.100 < p-value < 0.200    
0.050 < p-value < 0.100
0.020 < p-value < 0.050
0.002 < p-value < 0.020
p-value < 0.002

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(e) Interpret your conclusion in the context of the application.

Fail to reject the null hypothesis, there is sufficient evidence that the variance in annual wheat production differs between the two plots.
Reject the null hypothesis, there is insufficient evidence that the variance in annual wheat production differs between the two plots.
Reject the null hypothesis, there is sufficient evidence that the variance in annual wheat production differs between the two plots.
Fail to reject the null hypothesis, there is insufficient evidence that the variance in annual wheat production differs between the two plots.

Suppose that the weight of an newborn fawn is Uniformly distributed between 2.5 and 3.2 kg. Suppose that a newborn fawn is randomly selected. Round answers to 4 decimal places when possible.

a. The mean of this distribution is

b. The standard deviation is

c. The probability that fawn will weigh exactly 3.1 kg is P(x = 3.1) =

d. The probability that a newborn fawn will be weigh between 2.7 and 3 is P(2.7 < x < 3) =

e. The probability that a newborn fawn will be weigh more than 2.74 is P(x > 2.74) = f. P(x > 2.6 | x < 3) =

g. Find the 50th percentile.

A) Use the results of Groth (1992), where researchers conducted a large observational study where n=3647 crossbills were observed in the wild, 1752 of which were right-billed and 1895 of which were left-billed to conduct a z-test. Report your test statistic, p-value, and estimated effect size, each rounded to four decimal places:

z-score:
p-value:
est. effect size:

B) Create a 95% confidence interval for the true proportion of European cross-bills that are right-billed. Submit your lower and upper bounds rounded out to four decimal places.

CI( , )

1. The real estate broker claims that “on average, 70 people passes by the store every hour.” A sample of 12 hours revealed the following number of people passes by.

64, 66, 64, 66, 59, 62, 67, 61, 64, 58, 54, 66

1. 1. What is the point estimate of the population mean, i.e. sample mean?
2. 2. What is the sample standard deviation? (I didn’t show you how to do this using your calculator this year, therefore, I am giving you the answer here; however, in the exam, it is expected you know how to compute it using your own calculator.)
3. 3. Develop a 90% confidence interval for the population mean.
4. 4. Develop a 95% confidence interval for the population mean.
5. 5. Comment on the validity of the claim made by real estate broker.

I think this claim is (Valid / Invalid).             Reasons:

For each description below, identify each underlined number as a parameter or statistic. Use appropriate notation to describe each number, e.g., p^ = 0.96.

A) The National Center for Health Statistics reports that the mean systolic blood pressure for males 35 to 44 years of age is 128 and the standard deviation is 15. The medical director of a large company looks at the medical records of 72 executives in this age group and finds that the mean systolic blood pressure for these executives is 126.07.

B) A 1993 survey conducted by the Richmond Times-Dispatch one week before Election Day asked voters which candidate for the state’s attorney general they would vote for. 37% of the respondents said they would vote for the Democratic candidate. On Election Day, 41% actually voted for the Democratic candidate.

Mr. Mario Mendoza is a famous baseball player (Shortstop) in the Major League Baseball. Usually, he can successfully hit 2 out of 10 at bats. Therefore, the Mendoza line is named after him.

1. In a particular season, he attempted 100 at bats. Define X as the number of hits he will have. Write down how X is distributed.
2. What is the probability that he makes exactly 25 hits? (There are two ways to do this part, either way is fine.)  
3. Construct a 90% Confidence Interval for the average number of hits he will have in 100 at bats

Let that across the two semesters of this statistics course, you have been shown both Bayesian and Classical approaches to Inference. A fellow student in a biological sciences course is working with statistics, but does not understand the two approaches. Provide them with a short explanation of the differences and similarities between the approaches, to help them with their use of statistics. {approx. 500 words}.

We play a game with a deck of 52 regular playing cards, of which 26 arered and 26 are black. They’re randomly shuffled and placed face down ona table. You have the option of “taking” or “skipping” the top card. Ifyou skip the top card, then that card is revealed and we continue playingwith the remaining deck. If you take the top card, then the game ends;you win if the card you took was revealed to be black, and you lose if itwas red. If we get to a point where there is only one card left in the deck,you must take it. Prove that you have no better strategy than to take thetop card – which means your probability of winning is 1/2.

Hint: Prove by induction the more general claim that for a randomlyshuffled deck ofncards that are red or black – not necessarily with thesame number of red cards and black cards – there is no better strategy than taking the top card

Geo stats question:

2)Drivers wishing to turn left at a particular intersection arrive at an average rate of five per minute. (i) if the left-turn arrow is red for 30 seconds, and there is room in the left-turn lane for five cars, what is the probability that the capacity of the lane will be exceeded for a given cycle of the signal? (ii) Given that transportation planners and traffic engineers wish to reduce the probability to less then 0.05 by shortening the length of the red signal, how would you determine the maximal time the signal could remain red?

popgro~h lexp gnppc safewa~r
-------------+------------------------------------
popgrowth | 1.0000
lexp | -0.4750 1.0000
gnppc | -0.4902 0.6948 1.0000
safewater | -0.3935 0.8177 0.7063 1.000

Given this table,

1. The correlation between life expectancy and population growth =
2. The correlation between life expectancy and access to safe water =
3. The correlation between life expectancy and GNP per capita =
4. The correlation between population growth and access to safe water = _
5. The correlation between population growth and GNP per capita = __
6. The correlation between access to safe water and GNP per capita = _
7. The correlation between population growth and life expectancy is (positive / negative).
8. The correlation between population growth and GNP per capita is (positive / negative).  
9. The correlation between population growth and access to safe water is (positive / negative).
10. The correlation between life expectancy and GNP per capita is (positive / negative).
11. The correlation between life expectancy and access to safe water is (positive / negative).

The FBI wants to determine the effectiveness of their 10 Most Wanted list. To do so, they need to find out the fraction of people who appear on the list that are actually caught.

Suppose a sample of 879 suspected criminals is drawn. Of these people, 677 were not captured. Using the data, construct the 95% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list. Round your answers to three decimal places. Answer