Let \(\hat{P}\) be the random variable that represents the sample proportion of households in a given suburb that have solar panels installed.
From a sample of randomly selected households in a given suburb, an approximate 95% confidence interval for the proportion \(p\) of households having solar panels installed was determined to be (0.04, 0.16).
- Find the value of \(\hat{P}\) that was used to obtain this approximate 95% confidence interval. (1 mark)
Use \(z=2\) to approximate the 95% confidence interval.
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- Find the size of the sample from which this 95% confidence interval was obtained. (2 marks)
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- A larger sample of households is selected, with a sample size four times the original sample.
The sample proportion of households having solar panels installed is found to be the same.
By what factor will the increased sample size affect the width of the confidence interval? (1 mark)--- 3 WORK AREA LINES (style=lined) ---