| Tag | Value |
|---|---|
| file | Inferential_Statistics_vufsw-width-1233-en_vufsw-width-1233-en |
| name | vufsw-width-1233-en |
| section | inferential statistics/confidence intervals/width |
| type | schoice |
| solution | FALSE, FALSE, TRUE, FALSE |
| Type | conceptual |
| Program | NA |
| Language | English |
| Level | statistical literacy |
If you increase the sample size by a factor of four, the width of the confidence interval will……
The answer: increase by a factor of two is wrong. It is true that the factor is 2, but increasing the sample size decreases the width of confidence intervals because it decreases the standard error. The standard error for a population percentage has the square root of the sample size in the denominator.
The answer: increase by a factor of 4 is wrong. Increasing the sample size decreases the width of confidence intervals because it decreases the standard error. Also, the standard error for a population percentage has the square root of the sample size in the denominator. Hence, increasing the sample size by a factor of 4 (i.e., multiplying it by 4) is equivalent to multiplying the standard error by 1/2.
The answer: decrease by a factor of two is correct. The standard error for a population percentage has the square root of the sample size in the denominator. Hence, increasing the sample size by a factor of 4 (i.e., multiplying it by 4) is equivalent to multiplying the standard error by 1/2. Hence, the interval will be half as wide.
The answer: decrease by a factor of 4 is wrong. It is true that it decreases but not by a factor of 4. The standard error for a population percentage has the square root of the sample size in the denominator. Hence, increasing the sample size by a factor of 4 (i.e., multiplying it by 4) is equivalent to multiplying the standard error by 1/2. Hence, the interval will be half as wide.
If you would like to know more about sample sizes watch this clip.
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Nederlands
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