Question

The null and alternate hypotheses are:

H₀ : μ₁ = μ₂
H₁ : μ₁ ≠ μ₂

A random sample of 10 observations from one population revealed a sample mean of 23 and a sample standard deviation of 3.5. A random sample of 4 observations from another population revealed a sample mean of 27 and a sample standard deviation of 3.6.

At the 0.01 significance level, is there a difference between the population means?

1. State the decision rule. (Negative values should be indicated by a minus sign. Round your answers to 3 decimal places.)

2. Compute the pooled estimate of the population variance. (Round your answer to 3 decimal places.)

3. Compute the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)

Answer 1

a.

Two Tailed test:

Given Significance Level : = 0.01

/2 = 0.01/2=0.005

n1: Sample Size of Sample 1	10
n2 : Sample Size of Sample 2	4
: Sample Mean of Sample 1	23
: Sample Mean of Sample 2	27
s1: Sample Standard Deviation of Sample 1	3.5
s2: Sample Standard Deviation of Sample 2	3.6
Level of Significance	0.01
Degrees of freedom : ( n1+n2-2=10+4-2=12)	12

For two tailed test :

Critical values are : -t/2, t/2 : -t0.005 ,t0.005

For 12 degrees of freedom : t0.005 = 3.0545

Reject the null hypothesis if test statistic is < -3.0545 or test statistic > 3.0545

Fail to reject the null hypothesis if -3.0545 < test statistic < 3.0545

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a. Pooled estimate of population variance = pooled sample variance

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a. Test Statistic

Pooled Standard deviation :

Test Statistic = -1.918

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As Calculated Value is with in the Critical Values i.e.( -3.0545 < -1.9179 < 3.0545 )Fail To Reject Null Hypothesis

There is not sufficient evidence to conclude that there is a difference between the population means