Educational Research

1. The Mental Development Index (MDI) for infant development is a standardized measure used in longitudinal

follow-up of high risk infants. The MDI scores are known to be normally distributed with mean 100 and variance
256. For a study of infants, a random sample of size 400 is selected.

(a) find the standard error of the mean MDI originating from this sample.

(b) find the percentage of the mean MDI score from this sample that

(i) will be greater than 101.6
(ii) will be less than 98.4
(iii) will be between 98.4 and 101.6

(c) find the number of additional subjects needed for the study, in order to double the precision of this sample
estimate of the population parameter.

2. After the third 2012 presidential debate between Obama and Romney, CNN conducted a survey of 475 debate
watchers to find out who won the debate and obtained the following percentages:
Obama 54%
Romney 46%
a. Compute the standard error and the 95% confidence margin of error of this estimation.

b. Based on the findings from this survey, political analyst, John argued that the performance of the two
candidates was a tie while Candy concluded that Obama had won. Assuming you did not watch the debate and only
obtained this information, who of the two political analysts (John or Candy) is correct and why?

 
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