# Central Limit Theorem and single sample hypothesis test

A medical research study showed that the average weight of a newborn twin in 1988 was 5.1 lb. To determine if this year's average exceeds the 1988 mean of 5.1 lb., we would test the hypothesis;

Ho (null hypothesis): mu = 5.1 lb.

Ha (alternative hypothesis): mu > 5.1 lb.

Where mu is the actual mean weight of newborn twins born this year.

Suppose you take a random sample of 36 newborn twins. Assuming that the null hypothesis is true, find the probability of getting a sample mean of 5.5 lb. or greater. (use 1.00 lb. as the population standard deviation)

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This problem deals with the distribution of the sample mean. I have attached a Word document explaining how the ...

#### Solution Summary

In this problem, we use the central limit theorem to find the distribution of a sample mean. Then we use that distribution to find the probability that the sample mean from a random sample exceeds a particular value. The probability we find is converted into the p-value then used to test the hypothesis of interest.