# statistics-as-necessary-round-all-work-to-two-or-three-decimal-places

As necessary, round all work to two or three
decimal places.

1) Is the gender of a nurse related to the
specialty he or she chooses?? A hospital
administrator counted the number of nurses by gender in three different nursing
specialties within her health system. Perform
the appropriate hypothesis test to answer this question (atα =0.05), showing all necessary parts of the hypothesis test. (30
points)

 Gender Nursing specialty ICU ER Pediatrics Male 16 20 38 Female 24 38 116

2) A professor used data from last
semester’s statistics class to create a regression that predicts how students
will do on the final exam. The equation
is.0/msohtmlclip1/01/clip_image002.png”>,
where X1 is the number of
hours studied for the exam and X2
is the number of sleep interruptions the night before the exam. What is the predicted score of:

a) a student who studied for 10 hours and
had 2 sleep interruptions? (3 points)

b) a student who studied for 6 hours and
had no sleep interruptions? (3 points)

3) An ER nurse notices that when she and
her colleagues are asked to work overtime, they seem to get less sleep (rather
than just having less free time). She
collects data from all of the nurses on her shift on the number of hours of
overtime worked on their last shift and the amount of sleep they got that
evening.

 Hours of overtime Hours of sleep 3 6 0 9 1 7 5 4 4 6

a) Create a scatterplot for these data. (5
points)

b) Calculate the correlation coefficient.
(10 points)

c) Perform a hypothesis test to determine
if there is a significant correlation (α =0.05) between
number of hours of overtime worked and hours of sleep. (15 points)

4) An OB office nurse hears about the data
collected by the ER nurse in problem #3 and wants to see if the same
relationship holds true for her office.
She collects data from her coworkers and finds the following data:

 Hours of overtime Hours of sleep Mean 1.9 8.9 SD 0.7 1.4

r =
-0.734

a) Which correlation shows a stronger
relationship, the ER nurse’s correlation in #3 or the OB nurse’s correlation in
#4? Why? (4 points)

b) Using the data from the OB office, generate
a regression equation predicting number of hours of sleep from number of hours
of overtime worked. (15 points)

c) Interpret the meaning of the slope from
the equation you created in problem #4b. (3 points)

5) A winery owner wants to determine if one
type of her wine is significantly more popular than another. She records the number of bottles of each
type of her wine sold during a month.

 Merlot Pinot Noir Riesling Chardonnay Bottles sold 31 10 47 32

a) What kind of statistic should you use to
test this hypothesis? (2 points)

b) Write the set of hypotheses you would
use to test this hypothesis. (2 points)

c) What are the df and critical value for this hypothesis test? (3 points)

d) Calculate the expected frequencies for
these data. (5 points)

Extra Credit 1: If two variables are
correlated, can we assume that one caused the other? Please explain, using an example. (3 points)

Extra Credit 2: If r = 0.6, what is the proportionate reduction in error gained by
using regression over the mean of Y
for the prediction of Y values? (2
points)

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