High School

Based on data from a random sample of 50 U.S. adults, we are 95% confident that the mean shoulder girth for this population falls between 105.25 and 111.15 centimeters. The margin of error is 2.95 centimeters.

One sample t-summary confidence interval results:
- Mean of population
- Sample mean: 108.2
- Std. Err.: 1.4665395
- df: 49
- Lower limit: 105.25
- Upper limit: 111.15

Decide if each of the following interpretations is valid or invalid:

1. For shoulder girth, 95% of the sample means fall between 105.25 and 111.15 centimeters when the sample size is 50. [Select]

2. For shoulder girth, 95% of the population means fall between 105.25 and 111.15 centimeters. [Select]

3. 95% of the time, the mean shoulder girth for the population will fall between 105.25 and 111.15 centimeters when the sample size is 50. [Select]

4. 95% of the time, the confidence interval from a random sample of 50 U.S. adults will contain the true mean shoulder girth in the population of U.S. adults. [Select]

5. 95% of the time, the confidence interval from a random sample of 50 U.S. adults will estimate the true mean shoulder girth in the population of U.S. adults within a margin of error of 2.95 centimeters. [Select]

Answer :

Valid interpretations:

For shoulder girth, 95% of the sample means fall between 105.25 and 111.15 centimeters when the sample size is 50.

95% of the time, the confidence interval from a random sample of 50 U.S. adults will contain the true mean shoulder girth in the population of U.S. adults.

95% of the time, the confidence interval from a random sample of 50 U.S. adults will estimate the true mean shoulder girth in the population of U.S. adults within a margin of error of 2.95 centimeters.

Invalid interpretations:

For shoulder girth, 95% of the population means fall between 105.25 and 111.15 centimeters. (This is not directly supported by the given information.)

95% of the time, the mean shoulder girth for the population will fall between 105.25 and 111.15 centimeters when the sample size is 50. (This statement is not supported by the given information.)

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