Question

 

Q1. Discuss the tools to measure central tendency?

 

 

Q2. I need new and unique answers, please.

a) Discuss parametric and nonparametric test used for    hypothesis testing.

b) In a cross sectional study on coronary heart disease (CHD), the smoking and CHD status is summarized below. Use appropriate statistical test to conclude smoking plays any role in CHD.

Smoking	Cardiovascular Diseases		Total
	Yes	No
Yes	10	90	100
No	26	74	`100

Answer 1

1)

The three most important measures of central tendency are Mean, Median and Mode.

Mean is the sum of observations divided by the total number of observations.

Median is the value that divides the data into 2 equal halves.

Mode is the value which occurs most frequently in the data.

2)

a)

Parametric tests assume the form of statistical distributions of the data.

For example, Student’s t-test for two independent samples provides meaningful results only if each the data is normally distributed and if sample variances are homogeneous.

Non-parametric tests do not assume a statistical distribution for the data. They can be used even if conditions for parametric tests are not met.

Example: Kruskal Wallis test, Mann-Whitney test

b)

The null and alternate hypothesis are:

H0: Smoking and CHD are independent.

Ha: Smoking and CHD are not independent.

Observed frequencies (Oi):

Smoking / CHD	Yes	No	TOTAL
Yes	10	90	100
No	26	74	100
TOTAL	36	164	200

Now, Expected frequency = [(Row total) x (Column total)] / Table total

Expected frequencies (Ei):

Smoking / CHD	Yes	No	TOTAL
Yes		82	100
No	18	82	100
TOTAL	36	164	200

Test statistic value =

Let the level of significance be

The critical value is given by:

Since the test statistic value is greater than the critical value, so we have sufficient evidence to reject null hypothesis H0.

Thus, we can say that Smoking and CHD are not independent.