A scientist has read that the mean birth weight ? of babies bornat full term is 7.3 pounds. The scientist, believing that the meanbirth weight of babies born at full term is less than this value,plans to perform a statistical test. She selects a random sample of50 birth weights of babies born at full term. Suppose that thepopulation of birth weights of babies born at full term has astandard deviation of 1.7 pounds and that the scientist performsher hypothesis test using the 0.01 level of significance.
Based on this information, answer the questions below. Carryyour intermediate computations to at least four decimal places, andround your responses as indicated.
(If necessary, consult a list of formulas.)
| What are the nulland alternative hypotheses that the scientist should use for thetest? | H0:? is | lessthan, less than or equal to, greater than, greater than or equalto, not equal to, equal to | 7.3, 50,1.7, 6.50 | H1:? is | lessthan, less than or equal to, greater than, greater than or equalto, not equal to, equal to | 7.3, 50,1.7, 6.50 | | Assumingthat the actual value of µ is 6.50 pounds, what is the probabilitythat the scientist rejects the null hypothesis? Round your responseto at least two decimal places. | | | What isthe probability that the scientist rejects the null hypothesiswhen, in fact, it is true? Round your response to at least twodecimal places. | | | Suppose that thescientist decides to perform another statistical test using thesame population, the same null and alternative hypotheses, and thesame sample size, but for this second test the scientist uses asignificance 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 theprobability that the scientist commits a Type II error in thissecond test compare to the probability that the scientist commits aType II error in the original test? | | The probability ofcommitting a Type II error in the second test is greater | | The probability ofcommitting a Type II error in the second test is less | | The probabilitiesof committing a Type II error are equal |
|
