Math Problem Statement

A batch containing a very large number of reels of synthetic fibers has arrived at the rope makers. The fibers are required to have a mean breaking strain of at least 500g. To check whether the batch is acceptable, a piece was cut from each of 10 reels and the breaking strain was measured. The resulting data were normally distributed. To form a confidence interval for the mean breaking strain of the batch, the number of degrees of freedom for the required t-distribution is:

Solution

This problem relates to forming a confidence interval using a t-distribution. When using a t-distribution, the degrees of freedom (df) are calculated as:

df=n1df = n - 1

Where:

  • nn is the sample size.

In the problem, 10 reels were used, so the sample size n=10n = 10. Therefore, the degrees of freedom are:

df=101=9df = 10 - 1 = 9

So, the correct answer is E) 9.

Would you like more details on this concept or have any other questions?

Related Questions:

  1. How do you calculate confidence intervals for a population mean?
  2. Why is the t-distribution used instead of the z-distribution in small samples?
  3. What assumptions must be met for using the t-distribution in hypothesis testing?
  4. How does the sample size affect the degrees of freedom in a t-test?
  5. How does the shape of the t-distribution change as the degrees of freedom increase?

Tip:

Remember, as the sample size increases, the t-distribution approaches the normal distribution (z-distribution). This is why larger samples often use z-scores for confidence intervals.

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Math Problem Analysis

Mathematical Concepts

Statistics
t-Distribution
Degrees of Freedom
Confidence Interval

Formulas

df = n - 1

Theorems

t-distribution

Suitable Grade Level

Grades 10-12