Past experience has indicated that the breaking strength of yarn used in manufacturing drapery material is normally distributed. A random sample of 8 specimens is tested, and the breaking strength for each specimen is recorded. Assuming known population standard deviation, the width of a 95 percent confidence interval was found to be 2.694. What was the value of population standard deviation used in calculating the confidence interval?

Question

Mathematics

Chris Daugherty

13 November, 08:10

Past experience has indicated that the breaking strength of yarn used in manufacturing drapery material is normally distributed. A random sample of 8 specimens is tested, and the breaking strength for each specimen is recorded. Assuming known population standard deviation, the width of a 95 percent confidence interval was found to be 2.694. What was the value of population standard deviation used in calculating the confidence interval?

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Agustin Bruce · Answer 1

Answer: the value of population standard deviation is 3.87

Step-by-step explanation:

From the information given,

Number of sample, n = 8

For a confidence level of 95%, the corresponding z value is 1.96. This is determined from the normal distribution table.

We will apply the formula

Confidence interval

= mean ± z * standard deviation/√n

Since confidence interval = 2.694,

It becomes

2.694 = 1.96 * standard deviation/√8

Dividing both sides of the equation by 1.96, it becomes

1.37 = standard deviation/√8

Standard deviation = 1.37 * √8

Standard deviation = 3.87