In: Statistics and Probability

In the following study a sample of n=933 men and women age 25 to 64 who have recently suffered severe back pain, where selected. the objective of the study is to determine the factor that have greatest influence of the severity back pain. Each subject has given questionaries and scores on a scale of 0-100 as to serenity of their back pain disability. in addition to age and sex, measurements where take on height,weight,height/weight ratio and lifetime participation rate in physical activities( active and inactive) on each of the n=933 subjects, discuss the possible way to analyze data. what short of problem one can expect on your analysis.

As it has been told in the problem, the objective of the study is to determine the factors that have greatest influence on the severity of back pain.

The recorded variables are –

Severity of back pain : (categorical, ordinal) *but as
recorded on scale of 0-100, can be considered as quantitative data
for practical purpose.*

Gender : (categorical, binary) male, female.

Age : (quantitative)

Height: (quantitative)

Weight: (quantitative)

Height/weight ratio: (quantitative)

Lifetime participation: (categorical, binary) active, inactive.

For the analysis, sample of n=933 patients are available.

This is essentially a multiple regression problem with ‘severity of back pain’ as dependent/response variable and all other variables are independent/predictor variables.

The most significant factors of back pain will be the variables
that will enter in selected final regression model. i.e. set of
only those predictors whose modeling and predicting ability
altogether, is optimal in some sense. (We can use different
criterion for optimality here like – R^{2}, adj
R^{2}, Mallow’s C_{p}, AIC, BIC etc.)

**Problem that may arise:**

Multicollinearity, which means near linear association among predictor variables may arise in this problem. As one of the predictor (height/weight ratio) is actually function of other two predictors – height and weight. There are ways to diagnose model for multicollinearity, e.g. eigenvalue analysis. And multicollinearity can be dealt with available techniques like – ridge regression, LASSO regression.

A study was conducted on the number of hours slept by men and
women. A sample of 18 men slept an average of 6.1 hours a day with
a sample standard deviation of 2.1 hours, whereas a sample of 21
women slept an average of 6.4 hours a day with a sample standard
deviation of 1.7 hours. Use a 0.05 significance level to test the
claim that the average number of hours that there is a difference
between the average...

A university conducted a study of whether running is healthy
for men and women over age 50. During the first eight years of the
study, 1.9% of the 457 members of a fitness association died. We
are interested in the proportion of people over 50 who ran and died
in the same eight-year period.
NOTE: If you are using a Student's t-distribution, you may
assume that the underlying population is normally distributed. (In
general, you must first prove that assumption,...

17. Height of Men and Women in the U.S. Women: μ= 64 inches , σ
= 3.5 Men: μ= 70 inches , σ = 4
a. calculate the z score that corresponds to a women height of
68 inches.
b. state the percentile ranking for that score.
c. for both women and men in the US, calculate the z score and
raw score (in inches) that separates the tallest 2.5% from the
97.5% of scores below.
d. for both women...

A recent study was done comparing the IQ scores of women and
men. In a sample of 22 women, the average IQ score was 100.6 with a
sample standard deviation of 7.3, and for a sample of 13 men, the
average IQ score was 101.3 with a sample standard deviation of 9.8.
Use a 0.01 level of significance to test the claim that the average
IQ score for women and men is the same.

We have a sample of 9254 participants, 4557 men and 4697 women.
The mean age of the sample is 34.33 years; men mean age is 34.12
(Variance= 663.063). The Variance in the women's group is 637.5625.
Can you calculate women mean age? If so, is there a
statistically significant difference between men and women
mean age?

We have a sample of 9254 participants, 4557 men and 4697 women.
The mean age of the sample is 34.33 years; men mean age is 34.12
(Variance= 663.063). The Variance in the women's group is 637.5625.
Can you calculate women mean age? If so, is there a
statistically significant difference between men and women
mean age?

A recent study focused on the number of times men and women who
live alone buy take-out dinners in a month. The information is
summarized below.
Statistic
Men
Women
Sample mean
25.0
21.2
Sample standard deviation
4.5
3.9
Sample size
110
110
At the .05 significance level, can we claim that men order
take-out dinners more often than women?

A recent study focused on the number of times men and women who
live alone buy take-out dinner in a month. Assume that the
distributions follow the normal probability distribution and the
population standard deviations are equal. The information is
summarized below. Statistic Men Women Sample mean 23.81 21.97
Sample standard deviation 5.67 4.61 Sample size 32 36 At the 0.01
significance level, is there a difference in the mean number of
times men and women order take-out dinners in...

A recent study focused on the number of times men and women who
live alone buy take-out dinner in a month. Assume that the
distributions follow the normal probability distribution and the
population standard deviations are equal but unknown. The
information is summarized below,
Sample Mean
Sample Standard Deviation
Sample Size
Men
25
6
20
Women
23
4
22
At the 0.05 significance level, is there a difference in the
mean number of times men and women order take-out dinners...

A recent study focused on the number of times men and women who
live alone buy take-out dinner in a month. Assume that the
distributions follow the normal probability distribution and the
population standard deviations are equal. The information is
summarized below.
Statistic
Men
Women
Sample mean
24.85
21.33
Sample standard deviation
5.54
4.93
Sample size
34
36
At the 0.01 significance level, is there a difference in the
mean number of times men and women order take-out dinners in...

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