It is claim that the proportion of defective items produced by a particular machine is more...

It is claim that the proportion of defective items produced by a particular machine is more than 0.1

Letting π represents the proportion of defective items produced by a particular machine, set up the null and alternative hypotheses needed to provide evidence supporting the claim.
By using the significance level of α = 0.05, show the rejection area for the test statistics.
A random sample of 100 items is inspected and found to contain 15 defective items. Calculate the test statistics, Z, to test the claim.
Make a conclusion on the claim made.
Suppose that, for a sample of size n = 50 measurements, we find that x = 12. Assuming that  equals 6, construct a 99% confidence interval for the population mean µ. Interpret the answer.

Expert Solution

orchestra answered 2 years ago

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.

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 number of defective items produced by a machine (Y) is known to be linearly related...

The number of defective items produced by a machine (Y) is known to be linearly related to the speed setting of the machine (X). Data is provided below. a) (3) Fit a linear regression function by ordinary least squares; obtain the residuals and plot the residuals against X. What does the residual plot suggest? b) (3) Plot the absolute value of the residuals and the squared residuals vs. X. Which plot has a better line? c) (4) Perform a weighted...

2a. When a new machine is functioning properly, only 5% of the items produced are defective....

2a. When a new machine is functioning properly, only 5% of the items produced are defective. Assume that we will randomly select two parts produced on the machine and that we are interested in the number of defective parts found. Compute the probabilities associated with finding exactly one defect. 2b.When a new machine is functioning properly, only 5% of the items produced are defective. Assume that we will randomly select two parts produced on the machine and that we are...

When a new machine is functioning properly, only 3% of the items produced are defective. Assume...

When a new machine is functioning properly, only 3% of the items produced are defective. Assume that we will randomly select ten parts produced on the machine and that we are interested in the number of defective parts found. Compute the probability associated with: a. [4 points] No defective parts b. [6 points] At least 1 defective parts. 2. [12 points] Over 500 million tweets are sent per day (Digital Marketing Ramblings website, December 15, 2014). Bob receives on average...

a. Suppose that 5 % of the items produced by a factory are defective. If 5...

a. Suppose that 5 % of the items produced by a factory are defective. If 5 items are chosen at random, what is the probability that none of the items are defective? Write your answer as a decimal accurate to three decimal places. b. Suppose that 7.9 % of the items produced by a second factory are defective. If 5 items are chosen at random from the second factory, what is the probability that exactly one of the items is...

Suppose that the proportion θ of defective items in a large shipment is unknown, and that...

Suppose that the proportion θ of defective items in a large shipment is unknown, and that the prior distribution of θ is a beta distribution for which the parameters are α = 2 and β = 200. If 100 items are selected at random from the shipment and if three of these items are found to be defective, what is the posterior distribution of θ?

A manufacturer wants to estimate the proportion of defective items in production. However, 18 of the...

A manufacturer wants to estimate the proportion of defective items in production. However, 18 of the 8,000 items in a random sample were found to be defective. (a) Establish a 99% confidence interval for the proportion of defective items. (b) If a confidence interval for the proportion of non-defective items had been constructed from of the same data, would you have gotten a larger margin of error? (c) A proportion of defective items of 3/1000 is considered acceptable. Are we...

(a) The probability of a defective item produced by a machine is 0.20. Find the probability...

(a) The probability of a defective item produced by a machine is 0.20. Find the probability that at least 3 of the 5 next items produced by a machine will be in this defective. (b) Analyze skewness of the following data with formula and diagram. 1,2,5,2,3,1,3,1.

A factory tests all its products. The proportion of defective items is 0.02. The probability that...

A factory tests all its products. The proportion of defective items is 0.02. The probability that the test will catch a defective product is 0.95. The test will also reject nondefective products with probability 0.01. (a) Given that a product passes the test, what is the probability that it is defective? (b) Given that the product does not pass the test, what is the probability that the product is defective?

Question