Is the attached problem a two sample test for a two sample normal means hypothesis test? Not sure how to answer the problem.
Transcribed Image Text:Q-1) In the paper "Persistent Pulmonary Hypertension of the Neonate and Asymmetric Growth
Restriction" (Obstetrics & Gynecology, Vol. 91, No. 3, pp. 336-341), M. Williams et al. reported on a
study of characteristics of neonates. Infants treated for pulmonary hypertension, called the PH group,
were compared with those not so treated, called the control group.
PH
Control
33.9
35.2
33.4
33.4
37.9
34.3
32.5
31.8
36.2
31.5
35.1
35.6
34.5
31.3
31.3
33.1
32.9
34.1
34.1
31.9
36.7
33.5
32.4
35.2
31.9
35.1
35.8
35.1
34.8
32.8
36.0
36.3
33.6
34.5
34.0
a. At a = 0.1 level of significance, do the data provide sufficient evidence to conclude that variation
in head circumferences differs among neonates treated for pulmonary hypertension and those
not so treated?
b. What assumptions about the distribution of head circumference for each group is necessary for
the test you conducted in part (a) to be valid?
c. Conduct an appropriate test to compare the mean head circumference between the two
groups. Report the p-value of this test and state your conclusions.
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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