Statistics Projects for High School Students

Two scatterplots are shown below.
Scatterplot 1
A scatterplot has 14 points.
The horizontal axis is labeled "x" and has values from 30 to 110.
The vertical axis is labeled "y" and has values from 30 to 110.
The points are plotted from approximately (55, 60) up and right to approximately (95, 85).
The points are somewhat scattered.
Scatterplot 2
A scatterplot has 10 points.
The horizontal axis is labeled "x" and has values from 30 to 110.
The vertical axis is labeled "y" and has values from 30 to 110.
The points are plotted from approximately (55, 55) steeply up and right to approximately (70, 90), and then steeply down and right to approximately (85, 60).
The points are somewhat scattered.
Explain why it makes sense to use the least-squares line to summarize the relationship between x and y for one of these data sets but not the other.
Scatterplot 1 seems to show a relationship between x and y, while Scatterplot 2 shows a relationship between the two variables. So it makes sense to use the least squares line to summarize the relationship between x and y for the data set in , but not for the data set in .

What is a frequency distribution of qualitative data and why is it useful?

A researcher is conducting a study to examine the effects of cognitive behavior therapy for the treatment of social anxiety in a sample of 16 participants. He measures the social anxiety scores of participants before the tratment and then again after treatment and the resulting data is as follows:
$n=16,M_0=5,s=4$
a) What type of design is this study (single-sample, independent measures, repeated measures)
b)State the null and alternate hypotheses
c) Using an ${\displaystyle \alpha levelof.05(\alpha =.05)}$, identify the critical values of t for a 2-tailed test.

To state:A factor that could affect the value of the response variable that is fixed at a set level.

Which of these shows the strongest correlation?

Examine the two-way frequency table below.
$\begin{array}{|cccc|}\hline & \text{Score: 90-100}& \text{Score: 70-89 }& \text{Score:0-69}\\ \text{Math Test}& 20& 40& 7\\ \text{Science Test}& 15& 35& 5\\ \hline\end{array}$
Which percentage of students took the math test and received a grade of 90 or above?
a)29.85%
b)57.14%
c)28.69%
d)16.39%

What mathematician was instrumental in the creation of the normal distribution? What application prompted this person to create the normal distribution?

is Bivariate normal distributions an assumption for the Pearson Correlation ?

Regarding observational studies and designed experiments:
a. Describe each type of statistical study.
b. With respect to possible conclusions, what important difference exists between these two types of statistical studies?

Do Left-Handers Die Earlier? According to a study published in the Journal of the American Public Health Association, lefthanded people do not die at an earlier age than right-handed people, contrary to the conclusion of a highly publicized report done 2 years earlier. The investigation involved a 6-year study of 3800 people in East Boston older than age 65. Researchers at Harvard University and the National Institute of Aging found that the “lefties” and “righties” died at exactly the same rate. “There was no difference, period,” said Dr. J. Guralnik, an epidemiologist at the institute and one of the coauthors of the report.

For a variable that is normally distributed with a mean of 50 and a standard deviation of 5, approximately _? of the scores are between _?.
A)95%, 45 and 55
B)95%, 40 and 60
C)68%, 40 and 60
D)95%, 35 and 65
E)99%, 40 and 60

Sketch a scatterplot in which the presence of an outlier decreases the observed correlation between the response and explanatory variables. Indicate on your plot which point is the outlier.

Basic Computation:$\hat{p}$ Distribution Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.
(c) Suppose $n=48$ and $p=0.15$. Can we approximate the $\hat{p}$ distribution by a normal distribution? Why? What are the values of ${\mu }_{hatp}$ and ${\sigma }_p$.?

We have to explain the relationship between employee performance 01 and employee performance 02 using the scater plot

An investigator wants to test whether exposure to secondhand smoke before 1 year of life is associated with development of childhood asthma (defined as asthma diagnosed before 5 years of age). Give two possible study designs.

1.An investigator wants to assess whether the use of a specific medication given to infants born prematurely is associated with developmental delay. Infants who were born prematurely are recruited and followed for 2-years.
Some of the infants were given the medication at birth and others were not. All infants will undergo extensive testing at age 2 to assess various aspects of development.
What type of study design: The Case Report/Case Series, The Cross-Sectional Survey, The Cohort Study, The Case Control Study, The Nested Case-Control Study, The Randomized Controlled Trial or The Crossover Trial?

Answer true or false to each statement. Explain your answers.
a. Two normal distributions that have the same mean are centered at the same place, regardless of the relationship between their standard deviations.
b. Two normal distributions that have the same standard deviation have the same spread, regardless of the relationship between their means.

The value of s alone doesn't reveal information about the form of an association. Sketch a scatterplot showing a nonlinear association with a small value of s and a second scatterplot showing a linear association with a large value of s.

Sketch a scatterplot showing data for which the correlation is [r = -1].