If all other factors are held constant, increasing the sample size will a. incre

Question

If all other factors are held constant, increasing the sample size will

a. increase the standard error

b. decrease the width of the confidence interval

c. increase the width of the confidence interval

d. None of the other 3 choices is correct.

2. Which combination of factors would definitely reduce the width of a confidence interval?

a. use a larger sample and increase the level of confidence

b. use a smaller sample and increase the level of confidence

c. use a larger sample and decrease the level of confidence

d. use a smaller sample and decrease the level of confidence

3. If all other factors are held constant, which of the following would produce the smallest width of a confidence interval for mu?

a. an 80% confidence interval based on a sample of n = 25

b. a 90 % confidence interval base on a sample of n= 25

c. an 80% confidence interval based on a sample of n=100

c. a 90% confidence interval based on a sample of n =100

Explanation / Answer

1) the standard error is inversely proportion to square root of sample size therefore increasing the sample size will reduce the standard error and hence the witdh of the interval will decrease. therefore option B is coorect

2) in this we have to reduce the width of the interval

in previous part as stated that increasing the sample will decrease the width similarly decreasing the confidence level will also decrease the width

hence option C is correct

3) option c has the highest sample size and the lowest confidence interval therefore the width will be smallest.

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