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1 Statistical Formulae: 95% CI: 1.96 / : 1 95% CI: / : 1 95% CI: : 2 95% CI: 112 : 2 95% CI: : 1 : 11 ...

Course

STAT1250

Subject

Statistics

University

Macquarie University

Season

Spring

GEOG 2251 Quantitative Methods in Geography

Question

Answered

Question:

Question 1

Steps of quantitative research process

Problem identification. This involves identifying a research problem and developing research questions.

Literature review. Once the problem is identified, the research learns about the topic under investigation. This is done in order to provide foundational knowledge in the topic.

Clarity of the problem. Often the identified problem is broad. Once existing literature is reviewed, the researcher narrows study scope by identifying gaps in the existing literature.

Development of hypothesis and instrumental plan. Based on the gaps in the literature, the researcher develops hypothesis to be tested including quantitative variables to be used. A means of quantifying the variables is then developed.

Data collection. The data is then collected based on the defined instrumentation plan.

Processing data. The collected data is then cleansed for analysis by removing outliers and any other components that do not meet inclusion criteria

Data analysis. The processed data is then subjected to statistical analysis

Findings and conclusion. The analysed data is then interpreted to derive conclusions based on the research questions.

Question 2

Statistics

INFANT DEATH RATE* 

N

Valid

19

Missing

2

Mean

30.00

Median

7.00

Mode

4

Skewness

2.479

Std. Error of Skewness

.524

Kurtosis

6.995

Std. Error of Kurtosis

1.014

Minimum

3

Maximum

182

Percentiles

25

4.00

50

7.00

75

45.00

Mean=30.0

Mode=4.0

Median=7.00

The distribution is right skewed since skewness (2.479>+1)

Five number summary

Minimum=3.0

Q1=4.0

Median=7

Q3 =45

Max=182

Question 3

Tobler’s first law of geography - states that "everything is related to everything else, but near things are more related than distant things.”

Measures of central tendency – this is the measure of central location in a set of data which the measures are mean, median and mode.

Five number summary – this provides a concise summary of the distributions of the observations (minimum, 1st quartile, median, 3rd quartile and maximum).

Box plot –A graphical depiction of a group of numerical data through their quartiles with lines showing variability outside the upper and lower quartiles

Histogram –this is a graph that provide visual interpretation of data by indicating data points it lies within a range of values.

Normal distribution – arrangement in statistical data where most values cluster in the middle of the range with few others at the ends.

Non-normality- data follows specific type of non-normal distribution like bacterial growth which is exponential.

Empirical rule – states that in a normal data set, virtually every piece of data will fall within three standard deviations.

Stratified sample –a sample from dividing population into strata and drawing from them.

Standard normal distribution –normal distribution with a mean of \(0\) and standard deviation of \(1\).

Using Standard normal distribution

  1. P(Z < z) = 0.01   (Z is unknown)

 From normal distribution table, , z = -2.3263

Now, -2.3263 = (X-1200)/120

Hence, X = 920.844 hours

  1. P(Z < z) = 0.5

From normal distribution table, z = 0

Hence, 0 = (X-1200)/120

X = 1200 hours

  1. P(Z < z) = 0.95

From normal distribution table, z = 1.6449

Now, 1.6449 = (X-1200)/120

Hence, X = 1397.388 hours

Correlation Coefficient for Bivariate Data

Correlations

 

 

Freedom to make life choices

 

Social support

 

Freedom to make life choices

Pearson Correlation

1

.418**

Sig. (2-tailed)

 

.000

Sum of Squares and Cross-products

32.392

11.125

Covariance

.021

.007

N

1533

1526

 

Social support

Pearson Correlation

.418**

1

Sig. (2-tailed)

.000

 

Sum of Squares and Cross-products

11.125

22.058

Covariance

.007

.014

N

1526

1549

Correlation is significant at the 0.01 level (2-tailed).

The correlation coefficient =+0.418 indicating a weak positive linear relationship between freedom to make life choices and social support.

One-Sample Statistics

 

N

Mean

Std. Deviation

Std. Error Mean

Number of older siblings

38

1.26

1.005

.163

 

One-Sample Statistics

 

N

Mean

Std. Deviation

Std. Error Mean

Number of older siblings

38

1.26

1.005

.163

  1. Mean =1.26
  2. The hypothesis is tested at 95% significance level. Since this is a 1 tailed test, in SPSS, significance is changed to 90% in order to cater for one tail test.

The t-value =1.614

t-critical =1.687

Therefore p>0.05

Hypothesis

Since p>0.05, do not reject the null hypothesis that says that

Group Statistics

 

Gender

N

Mean

Std. Deviation

Std. Error Mean

Number of older siblings

female

28

1.18

.905

.171

male

10

1.50

1.269

.401

 

Independent Samples Test

 

Levene's Test for Equality of Variances

t-test for Equality of Means

F

Sig.

t

df

Sig. (2-tailed)

Mean Difference

Std. Error Difference

95% Confidence Interval of the Difference

Lower

Upper

Number of older siblings

Equal variances assumed

1.657

.206

-.865

36

.393

-.321

.371

-1.075

.432

Equal variances not assumed

 

 

-.737

12.427

.475

-.321

.436

-1.268

.626

  1. The p-value of Levene’s test =0.206 which is >0.05 therefore we cannot reject the null hypothesis
  2. The results reveal that there is no statistically significant difference between the number of older siblings and gender.

GEOG 2251 Quantitative Methods in Geography

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