Statistics Homework

Statistics 112: Homework 1 Answer to Question 1:

Variable that is dependent:

Position on women's rights,

Age, gender, and degree of education are independent variables.

Variable\sType\sScale

Attitudes concerning women's rights

Numerical\sInterval

Respondent's age in years

Numerical\sRatio

Degree of Education Categorical Variable Gender Categorical Variable

To be utilized plot

Attitudes concerning women's rights

Histogram and boxplot of respondent's age in years

Histogram,\sGender

Pie and bar graphs

Education Level

Graph with bars

To demonstrate the relationship in question, we can utilize a side by side boxplot.

To demonstrate the relationship in question, we can utilize a side by side bar chart.We can use line chart to exhibit the relationship in question.

Solution to Question Two:

The command in “R” to read the csv file:

Figure 1: Boxplot of Ethnicity

Here is the code and output for the problem:

The code for drawing histogram:

Histogram:

The code for drawing boxplot:

Figure 2: Boxplot for Education Level

e. The required codes are as follows:

Solution to Question Three:

a) Given data: 3, 5, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 10, 11, 13, 15, 44

Mean = = = 10

The data are arranged in ascending order and there are even number of elements (20 data). So, the average of 10th and 11th data will give the median.

Median = = = 8

The first quartile, Q1 will be the average of the 5th and 6th element, which is equal to = 7.

The third quartile, Q3 will be the average of the 15th and 16th element, which is equal to = 9.5.

Inter Quartile Range (IQR) = (9.5–7) = 2.5.

Variance = = …

= 67.5

Standard Deviation = √variance = √ 67.5 = 8.215

(b) Here, Q3 + 1.5 IQR = 9.5 + 1.5×2.5 = 13.5 and Q1–1.5IQR = 3.25

We have 3 values i.e. 3, 15, and 44, which falls outside this range and are outliers.

(c) The modified data without outliers is: 5, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 10, 11, 13

Mean = = = 8.11

The data are arranged in ascending order and there are odd number of elements (17 data). So, the 9th data will give the median.

Median = 8

The first quartile, Q1 will be the 5th element = 7.

The third quartile, Q3 will be the 13th , which is equal to = 9

Inter Quartile Range (IQR) = (9–7) = 2

Variance = = …

= 7.05

In the absence of the outliers, the statistical parameters can predict the central tendency more accurately i.e. they are truer representative of their actual data.

Solution to Question Four:

(a) Z-score = = -1.25; the value of critical value of z from the z-table is = 0.11.

Which means John falls within the 10% percentile.

(b) The required R code to estimate percentile for John:

The percentile value for John is 0.1, which means that John falls within the 10% of the population, who have IQ higher than or equal to 80.

Solution to Question Five:

(a) The required R code and output is given below:

(b) 8.5 Kg

Solution to Question Six:

The R code for plotting histogram is given below:

(b) The required R code:

(c) The required R code is given below:

Solution to Question Seven:

(a) Watching educational short film 🡪 Independent Variable

Attitude of policemen and policewomen toward treating minority 🡪 Dependent variable.

(b) Showing or not showing short film, attitude of policemen and policewomen toward treating minority

(c) He should use a survey based research design

(d) Experimental group 🡪 Those who watched film, Control Group 🡪 Those who did not.

(e) Yes.

(f) Whether education short film has influence on the attitude of policemen and policewomen.