The document discusses the application of statistical methods using SPSS to analyze data from a competition and academic tests. It includes various analyses such as calculating frequencies, central tendency measures, hypothesis testing, and regression analysis to assess relationships between variables. Additionally, it explores probability problems related to defective items from suppliers.

1. gkhan.a.06@gmail.com & gkhanayrancioglu@gmail.com
Gökhan AYRANCIOGLU | a50236
Estela Vilhena
Statistical Package for the Social Sciences
SPSS

2. Questions & Answer
1. The table bellow includes the data related
with one competition

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1.1 Insert the data in one SPSS file and save it with
the name Grupo4. (Codify accordingly the variables
that you find necessary).

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1.2 Obtain one plot and one table of frequencies for the variable Team.
Scatter Plot

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Table of frequencies for the variable Team.
Frequency : Contains the raw number results for how many people of team.

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has greater percentage of individual.
• The «Percent» column represents the percentage of all cases, including the missing cases,
constituted by each category
• «Valid Percent» category presents the percentage of only the non-missing cases falling into
each category.
• The «cumulative percent», expresses an ongoing sum of the valid percents.

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1.2.2 What is the mode for the Team variable ?

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1.2.2 What is the mode for the Team variable ?
Mode is ‘1.00’ (Team A)
for Team veriable.
Mean The mean is the total of the numbers
divided by how many numbers there
are.
Median The median is the middle value.
Mode The mode is the value that appears the
most.

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1.2.3 What is the frequency of the individuals from Team D ?
Team D
Frequency Percent Valid Percent Cumulative Percent
3 15,0 15,0 100,00

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1.3. Characterize the game score, calculating the value of the central tendency measurements. Interpret the results in
the context of the problem . What is the standard deviation? Get also a histogram for the variable in question.

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You can see groupings of various types of statistics like
central tendency and dispersion.
Standard deviation is a measure of the
spread of data around the mean value.

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Histogram
The purpose is probability distribution of a given variable by depicting the
frequencies of observations occurring in certain ranges of values

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Histogram for Score veriable

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1.4 Create in the way that you find more adequate , a new variable, ‘duraçãoemclasses’, based on the
variable duration of the game,
Creatinig the follow in groups:
[150, 160 [, [ 160, 170[, [170, 180[, [ 180, 190[ e [ 19 0, 20 0[.

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Creatinig the follow in groups:
[150, 160 [, [ 160, 170[, [170, 180[, [ 180, 190[ e [ 19 0, 20 0[.

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1.4 Create in the way that you find more adequate , a new variable, ‘duraçãoemclasses’, based on the
variable duration of the game,
Creatinig the follow in groups:
[150, 160 [, [ 160, 170[, [170, 180[, [ 180, 190[ e [ 19 0, 20 0[.

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1.4.1 . Build a table of frequencies and indicate the number of games
with duration smaller than 180 minutes ?
Indicate The number of games with duration smaller than 180 minutes :

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1.4.2 What is the percentage o f mess with the duration equal or higher than 160, but
lower than 190 minutes?
The percentage of mess with the duration equal or higher than 160, but lower than
190 minutes :

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2. The file "Inqueritos.sav" contains 200 observations related to tests performed to students from
higher education .

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2.1 Verify if you can consider that the grades of the reading and writing tests come from a Normal
population. Properly justify your answer.

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2.1 Verify if you can consider that the grades of the reading and writing tests come from a Normal
population. Properly justify your answer.

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2.1 Verify if you can consider that the grades of the reading and writing tests come from a Normal
population. Properly justify your answer.

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Descriptives for
writing score and
reading score

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Description
This is a sample text here.
Insert your desired text
here. This is a sample text.

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2.1 Perform a hypothesis test in order to as certain whether there is sufficient evidence to consider
that the math average grade in the population is ignificantly different from 50, at a significance level
of 5 %.
One sample t-test is a statistical procedure often performed for testing the
mean value of a distribution.

27. 2.1 Perform a hypothesis test in order to as certain whether there is sufficient evidence to consider
that the math average grade in the population is ignificantly different from 50, at a significance level
of 5 %.

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2.3 Check that the average scores of all disciplines vary with the type of school. List all necessary
steps, properly justifying your answer.
The independent-samples t-test (or independent t-test, for short)
compares the means between two unrelated groups on the same
continuous, dependent variable.

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2.3 Check that the average scores of all disciplines vary with the type of school. List all necessary
steps, properly justifying your answer.
Group Statistics table provides useful descriptive statistics for the two
groups that you compared, including the mean and standard deviation.

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Independent Samples Test Table
This table provides the actual results from the independent t-test.

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2.4 Create a variable that reflects the average of the grades obtained in all tests, justifying your
answer.

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3 . A and B are supplyers from an article to a processor company, that stores them in a container. It is
known that 5% of the articles of A and 9% of items of B are defective, which is why the articles supplyed
from company A are four times the articles suplyed by company B. It was chosen at random one of the
articles of the container.
A useful way of investigating probability problems is to use what are known as tree diagrams. Tree iagrams
are a useful way of mapping out all possible outcomes for a given scenario. They are widely used in
probability and are often referred to as probability trees. They are also used in decision analysis where they
are referred to as decision trees. In the context of decision theory a complex series of choices are available
with various different outcomes and we are looking for the bets of these under a given performance
criterion such as maximising profit or minimising cost.
Tree Diagrams
References : Glasgow Caledonian University

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3.1 What is the probability that the article is defective?
References : Glasgow Caledonian University

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References : Glasgow Caledonian University
3.2 Knowing that the article is defective, what is the probability of being supplied by company A?

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5. Certain company, dedicated to the commercialization and repair of computers expressed an interest in studying
the relationship between the duration of a repair service and the number of electronic components to be repaired
or replaced on a computer. This company has been registering computer repair times (in minutes) and the
respective number of failed components. The obtained data collection is in repararxls.

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5.1. Export the data to SPSS and code correctly the study variables. Build a scatter diagram which allows relating
both variables with the intention to identify a possible linear relationship. Comment the respective chart.

38. 5.1. Export the data to SPSS and code correctly the study variables. Build a scatter diagram which allows relating
both variables with the intention to identify a possible linear relationship. Comment the respective chart.

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5.1. Export the data to SPSS and code correctly the study variables. Build a scatter diagram which allows relating
both variables with the intention to identify a possible linear relationship. Comment the respective chart.

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5.2. Establish the model to fit the data.

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Explanation
5.2. Establish the model to fit the data.
Model Summary
This section shows you the relationship between the two variables (R).

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5.2. Establish the model to fit the data.
This section shows you the p-value (“sig” for “significance”) of the predictors effect on
the criterion variable. P-values less than .05 are generally considered “statistically significant.”
Explanation

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5.2. Establish the model to fit the data.
• This section shows you the beta coefficients for the actual regression equation.
Usually, you want the “unstandardized coefficients,” because this section includes a
y-intercept term (beta zero) as well as a slope term (beta one).
• The “standardized coefficients” are based on a re-scaling of the variables so that
the y-intercept is equal to zero.
Explanation

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5.3 Based on the obtained results, answer to the following questions:
5.3.1. Which are the estimates of b1 and b0 of the regression line? What is the equation of the regression line?
Estimates of b1 =

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5.3.1. Which are the estimates of b1 and b0 of the regression line? What is the equation of the regression line?
Explanation
The Coefficients part of the output gives us the values that we need in order to write the regression equation.
The regression equation will take the form:
Predicted variable (dependent variable) = slope * independent variable + intercept
15,509 * 1 + 4,162 =

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5.3.2. The value of the coefficients are significantly different from 0, with a significance level of 5%? Write for the
two coefficients the hypothesis indicating the value of p-value from the respective test and respective conclusion.

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5.4. Indicate and interpret, justifying properly, the determination coefficient.

48. Description
5.1. Export the data to
SPSS and code correctly
the study variables. Build
a scatter diagram which
allows relating both
variables with the
intention to identify a
possible linear
relationship. Comment
the respective chart.
Output
REGRESSION
STATISTICS
Multiple R 0,993699
R square 0,987437
Adjusted R
square
0,98639
Standart
Error
0,345466
Observatio
ns
14
ANOVA
df SS MS F Significance F
Regression 1 112,5678 112,5678 943,2009 8,92E-13
Residual 12 1,432159 0,119347
Total 13 114
Coefficient Standart Error t Stat P-Value Lower %95 Upper %95 Lower 95,0% Upper 95,0%
Intercept -0,18959 0,221682 -0,85525 0,409163 -0,6726 0,29341 -0,6726 0,29341
X Value 1 0,06367 0,002073 30,71158 8,92E-13 0,059153 0,068187 0,059153 0,068187

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R square :
• This is r2, the Coefficient of Determination. It tells you how many points fall on the
regression line.
• The coefficient of determination, with respect to correlation, is the proportion of
the variance that is shared by both variables. It gives a measure of the amount of
variation that can be explained by the model (the correlation is the model).
REGRESSION STATISTICS
Multiple R 0,993699
R square 0,987437
Adjusted R
square 0,98639
Standart Error 0,345466
Observations 14
Coefficient of
Determination
0,987437

50. Tank You! Obrigado!
Teşekkür Ederim !
Estela Vilhena
Applied Statistic Method
Gökhan AYRANCIOGLU | a50236