Problem 2. Let two samples, one of size 15 and the other of 20, be drawn from two normal distributions. The sample means are 4 and 5, respectively. The sample unbiased variances are 1.4 and 2.0, respectively. (i) From prior sampling, it is known that the normal distributions have the sample variance. Test the null hypothesis that the means of the

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Problem 2. Let two samples, one of size 15 and the other of 20, be drawn
from two normal distributions. The sample means are 4 and 5, respectively.
The sample unbiased variances are 1.4 and 2.0, respectively.
(i) From prior sampling, it is known that the normal distributions have
the sample variance. Test the null hypothesis that the means of the
two distributions are identical against the alternative hypothesis that
they are not identical. The test is to be carried out at a significance
level of 0.05.
(ii) How would your conclusion differ from that in part (i) if you had used
the pooled sample variance and the Central Limit Theorem? Give
relevant justifications.
Transcribed Image Text:Problem 2. Let two samples, one of size 15 and the other of 20, be drawn from two normal distributions. The sample means are 4 and 5, respectively. The sample unbiased variances are 1.4 and 2.0, respectively. (i) From prior sampling, it is known that the normal distributions have the sample variance. Test the null hypothesis that the means of the two distributions are identical against the alternative hypothesis that they are not identical. The test is to be carried out at a significance level of 0.05. (ii) How would your conclusion differ from that in part (i) if you had used the pooled sample variance and the Central Limit Theorem? Give relevant justifications.
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