Answer to Question #189153 in Statistics and Probability for EUGINE HAWEZA

Question

a) Explain how you can determine the Correlation Coefficient in Quantitative Research

(b) Explain how regression equation is used in Quantitative Research

(c) With practical statistical examples, explain how you can calculate and interpret the following:

(i) Mean, mode, median, range, standard deviation and variance for ungrouped data

(ii) Mean, mode, median, range, standard deviation and variance for grouped data

(iii) Probability of an event to occur and Probability of an event not to occur

(iv) Type I and Type II errors

(v) Confidence interval, Anova, and Chi Square 

(vi) Explain all the steps and statistical information involved in testing an hypothesis. 

Answer 1

(a) Correlation coefficient is determined by the following formula-

$r=\dfrac{cov(x,y)}{\sigma_x.\sigma_y}$

(b) Regression equation are used to determine the relationships between the two distributed data and further predict the solution.

(c)

Consider an example we gave set {$x_1,x_2,x_3$ }

(i) Mean$=\dfrac{\text{ sum of observation}}{\text{ Total observation}}=\dfrac{x_1+x_2+x_3}{3}$

Median$=(\dfrac{N+1}{2})^{th} term=\dfrac{3+1}{2}=2^{th}\text{ term }= x_2$

Mode = Highest occuring frequency

Range= Largest value - smallest value

Variance $=\dfrac{\sum(\text{observation-mean})^2}{\text{total observation}}$

Standard deviation $=\sqrt\dfrac{\sum(\text{observation-mean})^2}{\text{total observation}}$

(ii) For grouped data-

Mean $=\dfrac{\sum xf}{\sum f}$

Median$=l+\dfrac{\frac{N}{2}-cf}{f}\times h$

Mode$=l+\dfrac{f_1-f_0}{2f_1-f_0-f_2}\times h$

Range= Largest value - smallest value

Variance $=\dfrac{\sum(x-\bar{x})^2}{N}$

Standard deviation $=\sqrt{\dfrac{\sum(x-\bar{x})^2}{N}}$

(iii) Let probability of event occur be p,

Then , Probability of event not occur =1-p

(iv) a Type I error is the rejection of a true null hypothesis, while a type II error is the non-rejection of a false null hypothesis.

(v) Confidence interval is a type of estimate computed from the statistics of the observed data

ANOVA is used to determine significant relationship between two qualitative variables

chi square the second is used. to determine if the sample data has a particular distribution.

(vi) Procedure involve in testing a hypothesis:

1. Making assumptions
2. Stating the research and null hypotheses and selecting (setting) alpha
3. Selecting the sampling distribution and specifying the test statistic
4. Computing the test statistic
5. Making a decision and interpreting the results