Question

1- Which of the following statements is true?

I. For a certain confidence level, you get a higher margin of error if you reduce your sample size.

II. For a given sample size, increasing the margin of error will mean higher confidence.

III. For a fixed margin of error, smaller samples will mean lower confidence.

I only

II only

III only

II and III only

All of them

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2- Which must be true about a 90% confidence interval based on a given sample?

I. The interval contains 90% of the population.

II. The interval is narrower than a 95% confidence interval would be.

III. The interval is wider than a 95% confidence interval would be.

I only

II only

III only

I and II only

I and III only

Answer 1

1)

margin of error = criitcal value*σ/√n

since, margin of error is inversely proportional to sample size,

so, statement I is true

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for a given sample , if confidence level will increase, then critical value will increase and hence, margin of error increase,

so, statement II is also true

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a smaller sample size increases the the std error(σ/√n) of sample proportion ,which for a fixed margin of error decreases the critical value

so, statement III is also true

hence answer is ALL of them

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2)

The interval is narrower than a 95% confidence interval would be because smaller confidence level, smaller critical value, so smaller the margin of error, hence, interval is narrower.

so, answer is III only