A sample of 20 yields a mean of 32.4. Test the two-sided hypothesis that the sample was

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A sample of 20 yields a mean of 32.4. Test the two-sided hypothesis that the sample was drawn from a population with a mean of 35 for the following cases:

(a) if the variance of the population is 33; and

(b) if the variance of the population is unknown, but the sample variance is 33. Use a level of significance of 5%.

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