Question

A scientist has read that the mean birth weight of babies bom at full term is 75 pounds. The scientist, believing that the mean birth weight of babies bornet full term is less than this value, plans to perform a statistical test. She selects a random sample of 125 bath weights of babies bom at full term. Suppose that the population of birth weights of babies bom at full term has a standard deviation of 16 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. necessary, consulta list of formulas) 2.5 Assuming that the actual value of wis 7.15 pounds, what is the probability that the scientist com Type II error Round your response to at leaste cimal What is the probability that these Round your response to t ype the deca The power of the second test is greater than the power of the ono natest Suppose that the scientist decides to perform another statistical test using the same population, the same nu and alternative hypotheses, and the same level of significance, but for this second test the scientist chooses random sample of a 150 tead of a random sample 123. Assuming that the actual value of 3.15 pounds, how does the power of the second est compare the power of the ongest The power of the second testless than the power of the

Answer 1

a)

null hypothesis:Ho		μ	is greater than or equal to	7.5
Alternate Hypothesis:Ha		μ	is less than	7.5

b)

7.5 7.15 Hypothesized mean true mean standard deviation 1.6 sample size 125 standard error of mean Fox 0.1431 for 0.01 level and left tailed test critival value Za -2.33 rejection region: X <=u+Za*ox or <= 7.1671 type Il error =probability of not rejecting B = P(Z >17.1671- ua)/ox)) = P(Z >0.12) = 0.4522

probability of type II error =0.45

c)

type I error =0.01

d)

the power of 2nd test is greater,,,,,,,,