Question

In: Statistics and Probability

A random sample of 200 printed circuits boards contains 15 defective or nonconforming units. Estimate the...

A random sample of 200 printed circuits boards contains 15 defective or nonconforming units. Estimate the process fraction nonconforming. a. Test the hypothesis that the true fraction nonconforming in this process is 0.10. b. Construct a 95% confidence interval on the true fraction nonconforming in the production process.

Solutions

Expert Solution

a)

H0: p = 0.10

HA: p 0.10

Sample proportion = 15 / 200 = 0.075

Test statistics

z = - p / sqrt(p( 1 - p) / n)

= 0.075 - 0.10 / sqrt( 0.10 * 0.9 / 200)

= -1.18

This is test statistics value.

Critical value at 0.05 level = -1.96 , 1.96

Since test statistics value falls in the non-rejection region, that is falls between -1.96 and 1.96 ,

we do not have sufficient evidence to reject H0.

We conclude that we fail to support the claim.

b)

95% confidence interval for p is

- Z * sqrt( ( 1 - ) / n) < p < + Z * sqrt( ( 1 - ) / n)

0.075 - 1.96 * sqrt(0.075 * 0.925 / 200) < P < 0.075 + 1.96 * sqrt(0.075 * 0.925 / 200)

0.0385 < p < 0.1115

95% CI is ( 0.0385 , 0.1115)


Related Solutions

A company manufactures Printed Circuit Boards (PCBs) expects to have 6 defective units each day. Let...
A company manufactures Printed Circuit Boards (PCBs) expects to have 6 defective units each day. Let Y be a random variable that counts the number of defective units produced each day. A. Which discrete random variable distribution would best model this scenario? B. What is the probability that the number of defective units observed in a dayexceeds the mean number by more than one standard deviation? C. What is the probability that, on two randomly selected days, no defective units...
A shipment contains 200 items of which 50 are defective. A sample of 16 items from the shipment is selected at random without replacement.
 A shipment contains 200 items of which 50 are defective. A sample of 16 items from the shipment is selected at random without replacement. We accept the shipment if at most 3 items in the sample are defective. (a) Write down (but do not evaluate) an exact formula for the probability of acceptance. (b) Use a Table to give the decimal value for the binomial approximation of the probability of acceptance. Show your work. (c) Suppose instead that the shipment contains 500 items of...
Only 4% of items produced by a machine are defective. A random sample of 200 items...
Only 4% of items produced by a machine are defective. A random sample of 200 items is selected and checked for defects. a. Refer to Exhibit 7-1. What is the expected value for ? b. What is the probability that the sample proportion will be within +/-0.03 of the population proportion c.What is the probability that the sample proportion will be between 0.04 and 0.07?
The fraction of defective integrated circuits produced in a photolithography process is being studied. A random...
The fraction of defective integrated circuits produced in a photolithography process is being studied. A random sample of 300 circuits is tested, revealing 15 defectives. (a) Calculate a 95% two-sided confidence interval on the fraction of defective circuits produced by this particular tool. Round the answers to 4 decimal places. Entry field with incorrect answer now contains modified data less-than-or-equal-to p less-than-or-equal-to Entry field with incorrect answer now contains modified data (b) Calculate a 95% upper confidence bound on the...
Assume that 15% of circuit boards used in manufacturing compact displayers are defective. Off a batch...
Assume that 15% of circuit boards used in manufacturing compact displayers are defective. Off a batch of 200 randomly selected such circuit boards, use the normal approximation with the continuity correction to find the probability that at most 30 of these boards are defective. Is your answer approximate or exact. b. find exact probability using R code to compare answer on the previous question?
A production lot of 80 units has 8 defective items. We draw a random sample of...
A production lot of 80 units has 8 defective items. We draw a random sample of 10 units and we want to know: a.- the probability that the sample contains less than 3 defective articles b.- the probability that the sample contains at least 3 good articles c.- the probability that the sample contains more than 6 good articles
A shipment of 13 microwave ovens contains for defective units. A restaurant buys three of these...
A shipment of 13 microwave ovens contains for defective units. A restaurant buys three of these units. What is the probability of the restaurant by at least 2 non defective units? The probability of the restaurant buying at least 2 nondefective units is
A shipment of 1000 radios contains 15 defective ones. a) If an inspector selects 10 to...
A shipment of 1000 radios contains 15 defective ones. a) If an inspector selects 10 to sample, what is the % chance he will detect at least one defect? b) How many radios must be sampled to yield a 50+% chance of detecting a defect?
Suppose that a box contains 6 cameras and that 3 of them are defective. A sample...
Suppose that a box contains 6 cameras and that 3 of them are defective. A sample of 2 cameras is selected at random. Define the random variable XX as the number of defective cameras in the sample. Write the probability distribution for XX. kk P(X=kX=k) What is the expected value of XX?
Of the parts produced by a particular machine, 1% are defective. If a random sample of...
Of the parts produced by a particular machine, 1% are defective. If a random sample of 8 parts produced by this machine contains 2 or more defective parts, the machine is shut down for repairs. Find the probability that the machine will be shut down for repairs based on this sampling plan.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT