A scientist has read that the mean birth weight μ of babies born at full term...

A scientist has read that the mean birth weight μ of babies born at full term is 7.3 pounds. The scientist, believing that the mean birth weight of babies born at full term is less than this value, plans to perform a statistical test. She selects a random sample of 50 birth weights of babies born at full term. Suppose that the population of birth weights of babies born at full term has a standard deviation of 1.7 pounds and that the scientist performs her hypothesis test using the 0.01 level of significance.

Based on this information, answer the questions below. Carry your intermediate computations to at least four decimal places, and round your responses as indicated.

(If necessary, consult a list of formulas.)

What are the null and alternative hypotheses that the scientist should use for the test?	H0:μ is		less than, less than or equal to, greater than, greater than or equal to, not equal to, equal to	7.3, 50, 1.7, 6.50
	H1:μ is		less than, less than or equal to, greater than, greater than or equal to, not equal to, equal to	7.3, 50, 1.7, 6.50
Assuming that the actual value of µ is 6.50 pounds, what is the probability that the scientist rejects the null hypothesis? Round your response to at least two decimal places.
What is the probability that the scientist rejects the null hypothesis when, in fact, it is true? Round your response to at least two decimal places.
Suppose that the scientist decides to perform another statistical test using the same population, the same null and alternative hypotheses, and the same sample size, but for this second test the scientist uses a significance level of 0.05 instead of a significance level of 0.01. Assuming that the actual value of µ is 6.50 pounds, how does the probability that the scientist commits a Type II error in this second test compare to the probability that the scientist commits a Type II error in the original test?		The probability of committing a Type II error in the second test is greater
		The probability of committing a Type II error in the second test is less
		The probabilities of committing a Type II error are equal

Expert Solution

milcah answered 1 year ago

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