Problem 24 Historical data reveals that 47% of all adult women think they do not

Question

Problem 24 Historical data reveals that 47% of all adult women think they do not get enough time for themselves. A recent opinion poll interviews 1025 randomly chosen women and records the sample proportion of women who do not feel that they get enough time for themselves. This statistic will vary from sample to sample if the pol is repeated. Suppose the true population proportion is 0.47. In what range will the middle 68% of all sample results fall for samples of size 1025? (a) 0.314 to 0.626 (b) -1 to +1 (c) 0.548 to 0.822 (d) 0.454 to 0.486 (e) 0.439 to 0.501

Explanation / Answer

Here population proportion p = 0.47

sample size = 1025

standard error of proportion = sqrt (0.47 * 0.53/1025) = 0.0156

68% of all sample results = 0.47 +- 1 * 0.0156 = (0.454, 0.486)

Option d is correct here.

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