STAT 250-004 Data Analysis Assignment 4

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1Priscilla BongunguSTAT 250-004Professor: K. StrazzeriData Analysis Assignment 4Problem1: Got MilkAccording to the U.S. Department of Agriculture, 58.8% of males between 20 and 39 years oldconsume the minimum daily requirement ofcalcium. After an aggressive “Got milk” advertisingcampaign, the USDA conducted a survey of 55 randomly selected males betweenthe ages of 20and 39 and foundthat 36 of them consume the recommended daily allowance of calcium.a)Construct a 90% confidence interval for the above data. Show your work using theformulas and verify your work usingStat Crunch.Givenproportion of males consume calcium=58.8% =0.588;sample size55no.of males consume recommended = 36ˆsample proportion= 36/55=0.65454510%0.1ˆˆ10.65454510.6545450.06411955PnpgivenppSEnˆˆ1ˆ90% confidence interval is*z critical value at 90% confidence is 1.6448590% confidence interval is0.54908,0.760011pppznb)At the=0.01, is there evidence to conclude that the percentage of males between theages of 20 and 39 who consume the recommended daily allowance of calcium hasincreased?Conduct a full hypothesis test by following the steps below.

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2i.State the null and alternative hypotheses.Null hypothesis: The percentage of males between the ages of 20 and 39 who consume therecommended daily allowance of calcium is 58.8%,0p=58.8%Alternative hypothesis:The percentage of males between the ages of 20 and 39 who consume therecommended daily allowance of calcium has increased . i.e0p> 58.8%ii.State the significance level for this problem.The level of significance is=0.01iii.Check the conditions that allow you to use the test statistic, and, ifappropriate, calculate the test statistic.The conditions to use the test statistic is1. Samples should be drawn at random.For using normal approximation, np>=10 and nq>=10Here np = 36 and nq=19The test statistic isnppppz0001ˆ000ˆ0.6545450.5881.0026810.588 10.58855ppzppniv.Calculate thep-value and include the probability notation statement.p-value is P(z > 1.00268) = 1-P(Z<=1.00268)=1-0.842=0.158v.State whether you reject or do not reject the null hypothesis.Since the p-value (0.158) isgreater than 0.01 we accept the null hypothesis.vi.State your conclusion in context of the problem (i.e. interpret your results).We conclude that the percentage of males between the ages of 20 and 39 whoconsume the recommended dailyallowance of calcium is 58.8%

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