Question

In: Statistics and Probability

<<<<<<<<<<Please USE DATA IN QUESTION #9 TO ANSWER QUESTION 10#. #####please answere question 10 using question...

<<<<<<<<<<Please USE DATA IN QUESTION #9 TO ANSWER QUESTION 10#.

#####please answere question 10 using question 9 .............

9. A company that manufactures bicycles receives steel rods in large shipments from a supplier. From past experience, the manager knows that inches and that the lengths .12 σ = 0 are approximately normally distributed. He takes a random sample of 12 rods. The lengths of the sampled rods are as follows:

12.12 11.90 11.94 12.05 12.07 11.97

12.01 12.08 12.05 12.12 12.14 11.15

The manager wants to estimate the mean length of the latest shipment of rods using a 99 percent confidence interval. Help this manager construct a confidence interval and interpret it.

10. With reference to problem 9 above, the company needs rods with a length of 12 inches in order to assemble the bikes properly. Because too-large and too-small rods are unsuitable, shipments not meeting the requirement are sent back to the supplier. Help this manager determine whether the shipment should be accepted or rejected. Perform a hypothesis testing with . 0% α = 1

Expert Solution

9) Given sample data:

Sample size, n=12

Sample mean = = 12.12+11.90+11.94+12.05+...11.15/12

=11.9667

Given population standard deviation =0.12

Since the lengths are normally distributed and is known, we use Z interval.

Here, for 99% confidence , Z = Z_0.001/2 = Z_0.005 = 2.576

Margin of error E = Z_. = 2.576*0.12/ = 0.0892

Therefore 99% confidence intervel to estimate the true mean leangth is

(+-E)= (11.9667 +- 0.0892) =(11.8775,12.0559) (11.88,12.06)

Interpretation: with 90% confidence we can conclude that the true mean length of rods from the shipment is between 11.88 and 12.06 inches.

10) Let denote the true mean length of rods received in the large shipment.

Hence, we need to test if H₀: =12 inches

H₁: 12 inches

Test statistic: Z= = 11.9667-12/0.12/ =-0.961

Given that = 10%

Critucal values +- Z = +- 1.645, +-1.645 = -1.645, +1.644

Decision: Do not reject H₀

Conclusion: There is sufficient evidence to conclude that the shipment should be accepted.

orchestra answered 1 year ago

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