The recommended daily allowance of iron for adult femalesunder age 51 is 18 mg.

Question

The recommended daily allowance of iron for adult femalesunder age 51 is 18 mg. To test whether the mean daily intake ofiron among all such women is less than 18 mg, a medical researchermeasured the daily iron intakes for 20 randomly selected women, andobtained a sample mean of 15.7 mg and a sample standard deviationof 4.2 mg. The test is performed at the 1% level ofsignificance. 1. Find the value of the standardozed test statistic. 2. Find the critical value and make the decision. The recommended daily allowance of iron for adult femalesunder age 51 is 18 mg. To test whether the mean daily intake ofiron among all such women is less than 18 mg, a medical researchermeasured the daily iron intakes for 20 randomly selected women, andobtained a sample mean of 15.7 mg and a sample standard deviationof 4.2 mg. The test is performed at the 1% level ofsignificance. 1. Find the value of the standardozed test statistic. 2. Find the critical value and make the decision.

Explanation / Answer

Ho:=18 Ha:<18 Sample size is n=29; =.01;   Since we donot know the population value of we must use a one tailedt-test with 19 degrees of freedom. Therefore the critical valuewill be t.1(19)=-2.54 The standardized test statistic is given by t=(Xbar-)/(/n) t=(15.7-18)/(4.2/20)=-2.45 Since   -2.54<-2.45 we cannot reject thenull hypothesis that =18.

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