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STAT 250-004 Data Analysis Assignment 4

Solved assignment for STAT 250-004, covering data analysis techniques.

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    1 Priscilla Bo ngungu STAT 250 - 004 Professor: K. Strazzeri D ata Analysis Assignment 4 Problem 1 : Got Milk According to the U.S. Department of Agriculture, 58.8% of males between 20 and 39 years old consume the minimum daily requirement of calcium. After an aggressive “Got milk” advertising campaign, the USDA conducted a survey of 55 randomly selected males between the ages of 20 and 39 and found that 36 of them consume the recommended daily allowance of calcium. a) Construct a 90 % confidence interval for the above data. Show your work using the formulas and verify your work using Stat Crunch .          Given proportion of males consume calcium =58.8% =0.588; sample size 55 no.of males consume recommended = 36 ˆ sample proportion = 36/55=0.654545 10% 0.1 ˆ ˆ 1 0.654545 1 0.654545 0.064119 55 P n p given p p SE n              ˆ ˆ 1 ˆ 90% confidence interval is * z critical value at 90% confidence is 1.64485 90% confidence interval is 0.54908,0.760011 p p p z n    b) At the  = 0.01, is there evidence to conclude that the percentage of males between the ages of 20 and 39 who consume the recommended daily allowance of calcium has increased? Conduct a full hypothesis test by following the steps below.

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    2 i. State the null and alternative hypotheses. Null hypothesis: The percentage of males between the ages of 20 and 39 who consume the recommended daily allowance of calcium is 58.8%, 0 p =58.8% Alternative hypothesis: The percentage of males between the ages of 20 and 39 who consume the recommended daily allowance of calcium has increased . i.e 0 p > 58.8% ii. State the significance level for this problem. The level of significance is  = 0.01 iii. Check the conditions that allow you to use the test statistic, and, if appropriate, calculate the test statistic. The conditions to use the test statistic is 1. Samples should be drawn at random. For using normal approximation, np>=10 and nq>=10 Here np = 36 and nq=19 The test statistic is   n p p p p z 0 0 0 1 ˆ        0 0 0 ˆ 0.654545 0.588 1.00268 1 0.588 1 0.588 55 p p z p p n        iv. Calculate the p - value and include the probability notation statement. p - value is P(z > 1.00268) = 1 - P(Z<=1.002 68)=1 - 0.842=0.158 v. State whether you reject or do not reject the null hypothesis. Since the p - value (0.158) is greater 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 who consume the recommended daily allowance of calcium is 58.8%

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