Identifying binomial data A researcher interested in the transition from middle

Question

Identifying binomial data A researcher interested in the transition from middle school to high school surveys a random sample of 500 eighth-grade students. Which of the following statistics are computed using binomial data? The number of students who play in the school band The average distance the students travel from home to school The instruments played by students in the sample The total number of languages spoken by students in the sample Suppose that the researcher wants to conduct a hypothesis test about the proportion of her sample who live with a grandparent. For the researcher to appropriately use the normal approximation to the binomial distribution, the proportion of students in the population of eighth-grade students who live with a grandparent must be at least _____ and not greater than _____. Suppose that the actual proportion of students in the population of eighth-grade students who live with a grandparent is 0.15. Then the number of students in a sample of 500 eighth-grade students who live with a grandparent is approximately normal, with mean _____ and standard deviation _____.

Explanation / Answer

at least 0.05 and not great than 0.95

mean = np = 500*0.15 = 75

stdev = sqrt(np(1-p))=sqrt(500*0.15*0.85)=7.984

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