# Statistical Analysis Case Solution & Answer

Statistical Analysis

### Question 3

#### Hypotheses

A hypothesis is the predictions concerning what the investigation will reveal are expressed in a theory. It is a hypothetical conditional answer to the exploration inquiry. It might need to write several hypotheses for some research projects in order to address different facets of the research question.

Hypotheses purpose at least two components are connected, according to theories. Something the expert alters or manages is a free component. A dependent variable is something the expert observes and gauges.

#### Statistical technique

The kind of statistical technique appropriate for testing the hypothesis is Descriptive. Descriptive statistics are used to summarize the data, while inferential measurements are used to summarize the results for the population as a whole.

#### Part (c)

##### Reasons
• To provide basic information about variable in dataset.
• To highlights potential relationship between variables.

#### Part (d)

The interquartile range determines how widely the information is spread out. It is the attempt to reach the middle of the example. Use the IQR to determine the range in which the bulk of the attributes are concentrated. Larger characteristics demonstrate that the information’s central theme has spread out further.

#### Part (e)

Interquartile range in r×0 is 40.13 and r×1 is 12.73 which describe the spread of the data. Figures r0 and r1 reveal that half of the values in the dataset had a spread of 41.13 millimeters of mercury and 12.7 millimeters respectively.

#### Part (f)

An unknown population parameter’s range of possible values is known as a confidence interval. A 95 % confidence interval is a set of values that encompass the population’s actual mean. The confidence interval of r×0 is 141.78 < µ > 160.53 which means the population mean lies between these two bounds and contain true mean. This test does not include zero which means the test is statistically significant.

#### Part (g)

The skewness talks about the direction of outliers. The table shows the skewness value of r×0 is -0.124. As the value of skewness is in negative sign and less than 1, it means the distribution is left skewed.

#### Part (h)

The reason behind having almost similar values of mean and median in r×1 is the symmetrical distribution of the data. The variable’s value occurs at the same point and at regular frequencies.

### Question 1

#### Part (a)

Case processing summary shows the included and excluded values for the given data. Here it indicates no missing value in the data.

#### Part (b)

The mean of mother is 163.8 and the mean height of daughter is 163.78.

#### Part (c)

The name of the diagram in figure 3 is Box plot.

#### Part (d)

The height of the mother shows a boxplot of a normal distribution with no outliers. The image 3 represents a symmetrical distribution of data. The distribution of data for the height of daughter is negatively skewed as the median is closer to the top of the box. The distribution of the data in image 5 shows the height of mother on x axis and the height of daughter on y axis. The scatter plot diagram represent that the distribution of the data is liner with strong positive correlation between the variables.

#### Part (e)

There is a linear relationship between the height of mother and height of daughter. We use the correlation coefficient to describe the degree of linear relationship between two variables.

#### Part (f)

Image 5 shows a scatter plot graph, which shows the relation between the two variables. Here in part (e), we concluded that the data is linear with positive correlation. We test the relationship by checking the plot points as the y variable is tend to increase with respect to increase in variable x.

#### Part (g)

Assumption 1: Both the variable must be measured in inches as the height of the mother and daughter is given.

Assumption 2: To check linearity relationship between both the variables

Assumption 3: There should be no significant outliers.

Assumption 4: Both the variables must be normally distributed.

#### Part (h)

The r value shows the strength of linear relationship as the value of r is greater than 0.8 i.e., 0.807 it means having a very strong linear relationship between both variables. The p value is less than 0.05 i.e., p < 0.001 is shows statistically significant.

### Question 2

#### Part (a)

Ho: There is not a significant impact of year of working on score of burnouts.

H1: There is a significant impact of years of working on score of burnouts.

#### Part (c)

The distribution of the data in the above graph shows the years of working on x axis and the score of burnouts on y axis. The scatter plot diagram represent that the distribution of the data is liner with strong positive correlation between the variables.

#### Part (d)

The correlation coefficient r is 0.768 which indicates strong positive correlation. The correlation is significance as the sig value is less than 0.05.

#### Part (e)

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