when estimating a population mean, are you more likely to be correct when you use a point estimate or an interval estimate? explain your reasoning.
choose the correct answer below.
a. you are more likely to be correct using an interval estimate because it is unlikely that a point estimate will exactly equal the population mean.
b. if n ≤ 30 an interval estimate is more accurate. if n 30 a point estimate is more accurate.
c. you are more likely to be correct using a point estimate because an interval estimate is too broad and contains many possible values.
d. there is no difference between an interval estimate and a point estimate in terms of accuracy.

Question

when estimating a population mean, are you more likely to be correct when you use a point estimate or an interval estimate? explain your reasoning.
choose the correct answer below.
a. you are more likely to be correct using an interval estimate because it is unlikely that a point estimate will exactly equal the population mean.
b. if n ≤ 30 an interval estimate is more accurate. if n > 30 a point estimate is more accurate.
c. you are more likely to be correct using a point estimate because an interval estimate is too broad and contains many possible values.
d. there is no difference between an interval estimate and a point estimate in terms of accuracy.

Accepted Answer

# Brief Explanations:
A point estimate is a single value. The probability that this single - value (point estimate) exactly equals the population mean is extremely low. An interval estimate, on the other hand, gives a range of values. Since the population mean is more likely to lie within a range (interval) rather than being exactly equal to a single point, an interval estimate is more likely to be correct.
- Option B is incorrect because the sample size $n$ does not make a point estimate more accurate than an interval estimate in the way described. A larger sample size ($n>30$) is used to justify using certain distributions (like the normal distribution) for interval - estimate calculations, but it doesn't make the point estimate more accurate.
- Option C is incorrect. While an interval estimate contains many values, the purpose of an interval estimate is to provide a range within which the population parameter (mean, in this case) is likely to fall. It is not a drawback in terms of being correct (i.e., containing the population mean).
- Option D is incorrect. There is a difference; an interval estimate provides a range and is more likely to contain the population mean than a single - value point estimate.

# Answer:
A. You are more likely to be correct using an interval estimate because it is unlikely that a point estimate will exactly equal the population mean.

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