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You measure 36 randomly selected textbooks' weights, and find they have a mean weight of 38 ounces. Assume the population standard deviation is 6.2 ounces. Based on this, construct a 95% confidence interval for the true population mean textbook weight.

User Marnina
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1 Answer

4 votes

Final answer:

A 95% confidence interval for the true population mean textbook weight with a sample mean of 38 ounces, population standard deviation of 6.2 ounces, and a sample size of 36 is calculated to be approximately 35.9752 to 40.0248 ounces.

Step-by-step explanation:

The subject of this question is Mathematics, and the grade level appears to be College as it deals with constructing confidence intervals, which is typically a topic covered in college-level statistics courses.

To construct a 95% confidence interval for the true population mean textbook weight when the population standard deviation is known, we use the formula for the confidence interval for a population mean, which is:

Mean ± (Z-score * (Population standard deviation/sqrt(n)))

Where:

  • The sample mean is 38 ounces.
  • The Z-score for a 95% confidence level is approximately 1.96.
  • The population standard deviation is 6.2 ounces.
  • The sample size (n) is 36.

Plugging the numbers into the formula gives:

38 ± (1.96 * (6.2/sqrt(36)))

38 ± (1.96 * 1.033)

38 ± 2.0248

The 95% confidence interval is then 35.9752 to 40.0248 ounces.

User Guillaume Ponce
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