Question

# 1- Which of the following statements is true? I. For a certain confidence level, you get...

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

----------------------------------

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

#### Homework Answers

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

---------------

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

------------------------------------------------

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

===================================================================

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

Know the answer?
Your Answer:

#### Post as a guest

Your Name:

What's your source?

#### Earn Coins

Coins can be redeemed for fabulous gifts.

##### Not the answer you're looking for?
Ask your own homework help question
ADVERTISEMENT
##### Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

ADVERTISEMENT