Statistics Projects for High School Students

Explain why the tandart deviation would likely not be reliable measure of variability for a distribution of data that includes at least one extreme outlier.

Is there a relationship between gender and relative finger length? To find out, we randomly selected 452 U.S. high school students who completed a survey. The two-way table summarizes the relationship between gender and which finger was longer on the left hand (index finger or ring finger)

. $\begin{array}{lc}& \text{Gender}\\ \text{Longer finger}& \begin{array}{lcrr}& \text{ Female }& \text{ Male }& \text{ Total }\\ \text{ Index finger }& 78& 45& 123\\ \text{ Ring finger }& 82& 152& 234\\ \text{ Same length }& 52& 43& 95\\ \text{ Total }& 212& 240& 452\end{array}\end{array}$

Suppose we randomly select one of the survey respondents. Define events R: ring finger longer and F: female. Find P(R|F). Interpret this value in context.

To state:The null and alternative hypotheses.
The sample of 223 sales executives are presented by sales scenarios. Each subject was assigned to the one of the five closing techniques. Sales executives wereasked about their level of trust in the 7-point scale.

Whether the given study is observational or designed experiment and the reason.

The following two-way contingency table gives the breakdown of the population of adults in a town according to their highest level of education and whether or not they regularly take vitamins:
$\begin{array}{|ccc|}\hline \text{Education}& \text{Use of vitamins takes}& \text{Does not take}\\ \text{No High School Diploma}& 0.03& 0.07\\ \text{High School Diploma}& 0.11& 0.39\\ \text{Undergraduate Degree}& 0.09& 0.27\\ \text{Graduate Degree}& 0.02& 0.02\\ \hline\end{array}$
You select a person at random. What is the probability the person does not take vitamins regularly?

Describe a study design to test whether consuming fish atleast twice a week causes decreased activity in rheumatoid arthritis patients.

Explain what is wrong with the study design.
In a study to determine the factors that are associated with strong academic performance. 20 students are considered who are having perfect GPAs of 4.0. The explanatory variables like high school GPA and average amount of time spent studying per day are measured.

Using the daily high and low temperature readings at Chicago's O'Hare International Airport for an entire year, a meteorologist made a scatterplot relating $y=high$ temperature to $x=low$ temperature, both in degrees Fahrenheit.
After verifying that the conditions for the regression model were met, the meteorologist calculated the equation of the population regression line to be ${\displaystyle [{\mu }_y=16.6+1.02]with[\sigma =6.6{+}^{\circ }F]}$.
About what percent of days with a low temperature of ${\displaystyle {40}^{\circ }}$ F have a high temperature greater than ${\displaystyle {70}^{\circ }}$ F?

Basic Computation: zScore and Raw Score A normal distribution has $\mu =30$ and $\sigma =5$.
(c)Find the raw score corresponding to $z=-1.3$.

In this exercise, you will use the correlation and regression applet to create scatter plots with 10 points that have a correlation close to 0.7. The lesson here is that many models may have the same correlation. Always compile your data before trusting correlations. (a) Stop after adding the first two points. What is the value of correlation?
(Enter your answer, rounded to four decimal places).
r=?
Why does correlation matter? Two is the minimum number of data points required to calculate the correlation. This value is the default correlation.
Because two points define a line, correlation always matters.
The mean of these two values always has this value.

Case: Dr. Jung’s Diamonds Selection
With Christmas coming, Dr. Jung became interested in buying diamonds for his wife. After perusing the Web, he learned about the “4Cs” of diamonds: cut, color, clarity, and carat. He knew his wife wanted round-cut earrings mounted in white gold settings, so he immediately narrowed his focus to evaluating color, clarity, and carat for that style earring.
After a bit of searching, Dr. Jung located a number of earring sets that he would consider purchasing. But he knew the pricing of diamonds varied considerably. To assist in his decision making, Dr. Jung decided to use regression analysis to develop a model to predict the retail price of different sets of round-cut earrings based on their color, clarity, and carat scores. He assembled the data in the file Diamonds.xls for this purpose. Use this data to answer the following questions for Dr. Jung.
1) Prepare scatter plots showing the relationship between the earring prices (Y) and each of the potential independent variables. What sort of relationship does each plot suggest?
2) Let X1, X2, and X3 represent diamond color, clarity, and carats, respectively. If Dr. Jung wanted to build a linear regression model to estimate earring prices using these variables, which variables would you recommend that he use? Why?
3) Suppose Dr. Jung decides to use clarity (X2) and carats (X3) as independent variables in a regression model to predict earring prices. What is the estimated regression equation? What is the value of the R2 and adjusted-R2 statistics?
4) Use the regression equation identified in the previous question to create estimated prices for each of the earring sets in Dr. Jung’s sample. Which sets of earrings appear to be overpriced and which appear to be bargains? Based on this analysis, which set of earrings would you suggest that Dr. Jung purchase?
5) Dr. Jung now remembers that it sometimes helps to perform a square root transformation on the dependent variable in a regression problem. Modify your spreadsheet to include a new dependent variable that is the square root on the earring prices (use Excel’s SQRT( ) function). If Dr. Jung wanted to build a linear regression model to estimate the square root of earring prices using the same independent variables as before, which variables would you recommend that he use? Why?
1
6) Suppose Dr. Jung decides to use clarity (X2) and carats (X3) as independent variables in a regression model to predict the square root of the earring prices. What is the estimated regression equation? What is the value of the R2 and adjusted-R2 statistics?
7) Use the regression equation identified in the previous question to create estimated prices for each of the earring sets in Dr. Jung’s sample. (Remember, your model estimates the square root of the earring prices. So you must actually square the model’s estimates to convert them to price estimates.) Which sets of earring appears to be overpriced and which appear to be bargains? Based on this analysis, which set of earrings would you suggest that Dr. Jung purchase?
8) Dr. Jung now also remembers that it sometimes helps to include interaction terms in a regression model—where you create a new independent variable as the product of two of the original variables. Modify your spreadsheet to include three new independent variables, X4, X5, and X6, representing interaction terms where: X4 = X1 × X2, X5 = X1 × X3, and X6 = X2 × X3. There are now six potential independent variables. If Dr. Jung wanted to build a linear regression model to estimate the square root of earring prices using the same independent variables as before, which variables would you recommend that he use? Why?
9) Suppose Dr. Jung decides to use color (X1), carats (X3) and the interaction terms X4 (color * clarity) and X5 (color * carats) as independent variables in a regression model to predict the square root of the earring prices. What is the estimated regression equation? What is the value of the R2 and adjusted-R2 statistics?
10) Use the regression equation identified in the previous question to create estimated prices for each of the earring sets in Dr. Jung’s sample. (Remember, your model estimates the square root of the earring prices. So you must square the model’s estimates to convert them to actual price estimates.) Which sets of earrings appear to be overpriced and which appear to be bargains? Based on this analysis, which set of earrings would you suggest that Dr. Jung purchase?

A local school has both male and female students Each student either plays a sport or doesnt.

According to Census data, 1950 the population of the U.S amounted to 151.3 million persons, and 13.4% of them were living in the West. In 2000, the population was 281.4 million, and 22.5% of them were living in the West. Is the difference in percentages practically significant? statistically significant? Or do these questions makes sense? Explain briefly.

${\displaystyle \mu =50,\sigma =10}$
Is the range be approximately 60 if it's normal distribution?

Horace keeps track of the amount of time he studies and the score he gets on his quizzes. The data are shown in the table below. Which of the scatter plots below accurately records the data?

Regarding a scatterplot matrix:
a. Identify two of its uses.
b. What property should the scatterplots of the response versus each predictor variable have in order to proceed to obtain the regression plane for the data?

A researcher investigating the association between two variables collected some data and was surprised when he calculated the correlation.
He had expected to find a fairly strong association, yet the correlation was near 0.
Discouraged, he didnt