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The width of a confidence interval is defined to be the upper bound of the confidence interval minus the lower bound of the confidence interval. For example, if a confidence interval is (−2.34,9.87), then the width of this confidence interval is 9.87−(−2.34)=12.21. Assume that we are estimating the mean of a population. Assuming that the confidence coefficient, the sample mean and sample standard deviation stay the same, if we decrease the the sample size of a confidence interval from 100 to 50, then the width of that confidence interval will also decrease.True or False?

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Answer:

False

Step-by-step explanation:

Steps in calculating confidence Interval are

  1. Calculate degree of freedom by subtracting 1 from sample size that is df=sample size -1
  2. find α by subtracting confidence interval level from 1 and divide by 2
  3. Use value ot α and df to determine t from t-distribution table. From table it can be seen that the value of t increases as value of df decreases
  4. Divide standard distribution by square root of sample size. As sample size decreases this value will increase
  5. Multiple step 3 by step 4. We can say, if sample size is decreased this value will increase.
  6. For lower end , subtract step 5 from sample mean and for upper end add step 5 to sample mean.

If sample size is decrased, step 3 and step 4 will increase. As a result result obtained from step 5 will also increase. Hence, confidence interval will increase if sample size is decreased

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