A recent poll of 124 randomly selected residents of a town with a population of 310 showed that 93 of them are opposed to a new shopping center being built in their town. With a desired confidence of 90%, which has a z-score of 1.645, which statements are true? Check all that apply. E = z The sample size is 93. The sample size is 310. The point estimate of the population proportion is 0.4. The point estimate of the population proportion is 0.75. The margin of error is approximately 4%. The margin of error is approximately 6%.

Question

Answer:

The sample size is 124.
93 of them are opposed to new shopping center.

So,
n = 124
p = [tex] \frac{93}{124}=0.75 [/tex]

The point estimate of the population proportion = p = 0.75
q = 1 - p = 0.25

Margin of error (E) can be calculated by:

[tex]E= Z_{c} \sqrt{ \frac{pq}{n} } [/tex]

Using the values, we get:

[tex]E=1.645 \sqrt{ \frac{0.75*0.25}{124} }=0.06 [/tex]

Therefore, the margin of error is approximately 0.06 or 6%.

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