A sample of 46 observations is selected from one population with a population standard deviation of 4.1. The sample mean is 102.0. A sample of 48 observations is selected from a second
population with a population standard deviation of 5.8. The sample mean is 100.1. Using the 0.05
significance level, is there a difference between the two samples?

there is no significant evidence to conclude that there is difference between the two samples.

Step-by-step explanation:

Given :

x1 = 102 ; σ1 = 4.1 ; n1 = 46

x2 = 100.1 ; σ2 = 5.8 ; n2 = 48

H0 : μ1 = μ2

H0 : μ1 ≠ μ2

The test statistic :

The test statistic :

(x1 - x2) / sqrt[(σ1²/n1 + σ2²/n2)]

(102 - 100) / sqrt[(4.1²/46 + 5.8²/48)]

2 / 1.0326025

Test statistic = 1.937

The Pvalue from test statistic score ;

Pvalue = 0.052745

Pvalue > α ; Fail to reject the null ; Hence, there is no significant evidence to conclude that there is difference between the two samples.

80%

15 are on the council, so 75-15 = 60 are not on the council. Therefore, 60/75 = 0.80 = 80% of the students aren't on the council.

An alternative way to find this answer is to compute 15/75 = 0.20 = 20% showing that 20% of the students are on the council, so 100% - 20% = 80% are not on the council.