Test the claim that the two samples described below come from populations with t

Question

Test the claim that the two samples described below come from populations with the same mean. Assume that the samples are independent random samples, the populations are normal, and that population variances are equal.
Sample 1: n1=18, x¯¯¯1=12, s1=3n1=18, x¯1=12, s1=3.
Sample 2: n2=26, x¯¯¯2=10, s2=4.5n2=26, x¯2=10, s2=4.5.

(a) The test statistic is

(b) Find the t critical value for a significance level of 0.050.05 for an alternative hypothesis that the first population has a LARGER mean (one-sided test): t0=t0=

(c) The conclusion is

A. There is sufficient evidence to warrant rejection of the claim that the two populations have the same mean and support that the first population has a larger mean.
B. There is not sufficient evidence to warrant rejection of the claim that the two populations have the same mean.

Explanation / Answer

Two-Sample T-Test and CI

Sample N Mean StDev SE Mean
1 18 12.00 3.00 0.71
2 26 10.00 4.50 0.88

Difference = mu (1) - mu (2)
Estimate for difference: 2.00
95% lower bound for difference: 0.10
T-Test of difference = 0 (vs >): T-Value = 1.77 P-Value = 0.042 DF = 41

P-value 0.04 < 0.05 we reject null hypothesis so we conclude that There is sufficient evidence to warrant rejection of the claim that the two populations have the same mean and support that the first population has a larger mean.

Hope this will be helpful. thanks and god Bless you ;-)

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