Question

Does pollution increase mean death rate? A researcher sampled 31 “unpolluted” areas greater than 50 km away from industrial plants, and 23 different “polluted” areas near industrial plants. The average mortalities in the unpolluted areas were 3 deaths per day per 100000 people (with a sample standard deviation of 0.4 deaths/day/100000 people), and was 3.3 deaths per day per 100000 people (with a sample standard deviation of 0.5 deaths/day/100000 people) in the polluted area. At the alpha=0.01 level, answer the question does pollution increase average death rate? Show statistical and critical values as appropriate. Assume that variances are equal.

Answer 1

Sample 1 : Unpolluted areas

Sample 2 : Polluted areas

: Population average mortalities in the unpolluted area

: Population average mortalities in the polluted area

Null Hypothesis : H_o : Population average mortalities in the unpolluted area = Population average mortalities in the polluted area; = or - = 0

Alternate Hypothesis : H_a: Pollution increase average death rate; Population average mortalities in the unpolluted area: < Population average mortalities in the polluted area; < ; -<0;(Left Tailed test)

Average mortalities in the '31' sampled unpolluted areas were 3 deaths per day per 100000 people (with a sample standard deviation of 0.4 deaths/day/100000 people

Average mortalities in the '23' sampled polluted area. were 3.3 deaths per day per 100000 people (with a sample standard deviation of 0.5 deaths/day/100000 people)

Given
: Sample Size of Sample 1 : Unpolluted area	31
: Sample Size of Sample 2: Polluted Area	23
: Sample Mean of Sample 1	3
: Sample Mean of Sample 2	3.3
: Sample Standard Deviation of Sample 1	0.4
: Sample Standard Deviation of Sample 2	0.5
Level of Significance : alpha :	0.01
Degrees of freedom : ( -2=31+23-2=52)	52

Calculated value of t : Test statistic: t_stat = -2.4491

For Left Tailed Test : Reject null hypothesis if Calculated value of 't' is less than Critical Value :

Critical value :

As Calculated Value of t is less than Critical Value i.e. ( -2.4491<-2.4002 ); Reject Null Hypothesis

Sufficient evidence to reject that Population average mortalities in the unpolluted area = Population average mortalities in the polluted area

Pollution increase average death rate.

Critical value is computed using excel function : T.INV(0.01,52)

T.INV function

This article describes the formula syntax and usage of the T.INV function in Microsoft Excel.

Returns the left-tailed inverse of the Student's t-distribution.

Syntax

T.INV(probability,deg_freedom)

The T.INV function syntax has the following arguments:

• Probability     Required. The probability associated with the Student's t-distribution.

• Deg_freedom     Required. The number of degrees of freedom with which to characterize the distribution