Question

Population 1 has an estimated mean of 50 and a sample standard deviation of 3 while population 2 has a sample mean of 48 and a sample standard deviation of 4. A sample of size 16 is taken for each population.

With the null being equality of means and the alternative being that the means are not equal, the conclusion as to the equality of means at the 90% level of confidence would be:

A. Accept the null of no difference.

B. Reject the null of no difference.

With the null being equality of means and the alternative being that the mean of population 1 exceeds the mean of population 2, the critical value of t would be?

With the null being equality of means and the alternative being that the mean of population 1 exceeds the mean of population 2, the conclusion as to the equality of means at the 90% level of confidence would be:

A. Accept the null of no difference.

B. Reject the null of no difference.

Answer 1

With the null being equality of means and the alternative being that the means are not equal, the conclusion as to the equality of means

i.e Two tailed test :

Given
n1 : Sample Size of sample 1	16
n2 : Sample Size of Sample 2	16
: Sample Mean of Sample 1	50
: Sample Mean of Sample 2	48
s1: Sample Standard Deviation of sample 1	3
s2 : Sample Standard Deviation of Sample 2	4
Confidence level	90%
Level of Significance : (100-90)100	0.10

For Two tailed test :

for degrees of freedom : 27 ; P(t>1.6) = 0.0606

As P-Value i.e. is greater than Level of significance i.e (P-value:0.1212 > 0.1:Level of significance); Fail to Reject Null Hypothesis

Ans :

A. Accept the null of no difference.

With the null being equality of means and the alternative being that the mean of population 1 exceeds the mean of population 2

i.e. Right tailed test :

For Right Tailed test :

As P-Value i.e. is less than Level of significance i.e (P-value:0.0606 < 0.1:Level of significance); Reject Null Hypothesis

Ans :

B. Reject the null of no difference.