Answer:
The interval (-0.0199, 0.0510) represents the region of values where the true difference (in population terms now) between the initial proportion of registered voters that favour candidate X and the proportion of registered voters that favour candidate X just before election can take on with a confidence level of 90%.
Step-by-step explanation:
Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence. It is usually obtained from the sample.
p₁ represents the proportion of registered voters that favour candidate X in the initial poll, way before the election.
p₂ represents the proportion of registered voters that favour candidate X in the poll just before the election.
So, for this question the confidence interval for the true difference between the population proportion of registered voters that favour candidate X way before the elections and the population proportion that favour candidate X just before the election lies within (-0.0199, 0.0510) with a confidence interval of 90%.
Confidence interval is calculated mathematically as thus:
Confidence Interval = (Difference in Sample proportion) ± (Margin of error)
Margin of Error is the width of the confidence interval about the difference in the two sample proportions.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error)
Critical value = 1.645 (obtained from the z-tables because the sample size is large enough to ignore that information about the population standard deviation isn't given and t-critical value approximates z-critical value)
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