Statistics Question

1. A. Why isB. How would the mean and standard deviation of a data sample change if a number C
is added to all of the observations.
C. How would the mean and standard deviation of a data sample change if each
observation is multiplied by a number C.
2.
A. Describe the explanatory and response variables for this experiment.
B. Describe the treatments in your experiment
C. one possible confounding variable is the experience levels of the players. Explain how you
would control this variable?
D. Can the results of this experiment be generalized to all male tennis players? Why or why not
full?
3. A researcher surveys 1000 people, asking them if they have been a victim to auto theft. The
responses are yes or no [the variable studied his categorical]. Describe a method for the
researcher to be able to study a quantitative variable.
4. The data in the table at right are from observations taken on Roman coins dating from the first
three centuries AD. Historians believe that different mints might reveal themselves in a different
trace element profiles in the coins; These coins are known to have been minted in Rome. The
technique of atomic absorption spectrometry was used to estimate the percentage by weight of
various elements in these coins, the percentage by weight that is Gold is represented here.
Part A.
A. Calculate the mean
B. Calculate the standard deviation
C. Calculate the median
D. Calculate the interquartile range
Part B
Construct a skeletal box plot for these data.
Part C
Judging from the data and responses in parts A&B would you say this distribution is skewed or
approximately symmetric? Justify your response using appropriate statistical terminology.
5.
b. Find A5 number summary (minimum 𝑄1, median 𝑄3, maxium) for the data.
Locate the mean, median, lower quartile, and upper quartile on the histogram.
c. Describe the distribution of the impairment scores, and note any unusual features.
d. According to the Empirical Rule, apporixmatley 16% of the joint impairment
scores are above what value? Compare this to the actual value. Why would the two
values be different?
6.
b. Write the equation of the least squares line describing the relationship between 𝑥 =
body length and 𝑦 = mean speed.
c.
d.
e. What proportion of variation in the mean speed is explained by the body length?