Working only with multiples of 0.01 (e.g., 0.60 comma 0.61 comma 0.62 comma Numb

Question

Working only with multiples of 0.01 (e.g., 0.60 comma 0.61 comma 0.62 comma Number . . .), determine and list all potential values of the population proportion pi for which the observed sample proportion 0.69 falls within two standard deviations of pi in the sampling distribution. Enter your answers in increasing order. The potential values of pi are between and because they fall within 2 standard deviations of 0.69.

f. Summarize your findings in part e in terms of which numbers are plausible values for the proportion of the population who planned to give out Halloween treats from the doors of their homes in 1999 based on this observed sample result. The plausible values for the percentage of the population who planned to give out Halloween treats from the door of their homes in 1999 was between % and % inclusive.

Explanation / Answer

Solution:

Sample proportion = 0.69

Standard deviation  = sqrt(pq/n) = sqrt(0.69 *0.31/1005) = 0.0146

So, Values that lies between two standard deviation

= (0.69 - 0.0146, 0.69 + 0.0146)

= (0.6754, 0.7046)

So, The potential values will be 0.67, 0.68, 0.69, 0.70

f) The plausible values for the percentage of the population who planned to give out Halloween treats from the door of their homes in 1999 was between 67 % and 70 % inclusive

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