An engineer has designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 4.1 pounds/square inch. The valve was tested on 26 engines and the mean pressure was 4.3 pounds/square inch with a variance of 0.25. Is there evidence at the 0.01 level that the valve performs above the specifications? Assume the population distribution is approximately normal. Step 1 of 5: State the null and alternative hypotheses. Step 2 of 5: Find the value of the test statistic. Round your answer to three decimal places. Step 3 of 5: Specify if the test is one-tailed or two-tailed. Step 4 of 5: Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places. Step 5 of 5: Make the decision to reject or fail to reject the null hypothesis

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 438.0 gram setting. It is believed that the machine is underfilling the bags. A 46 bag sample had a mean of 436.0 grams. A level of significance of 0.05 will be used. Determine the decision rule. Assume the variance is known to be 400.00. Enter the decision rule.

A manufacturing company produces steel rods. The length of these rods is critical to their customers. The company aims to manufacture rods with a mean length of 150 cm. However, due to variability in the manufacturing process, the lengths of the rods follow a normal distribution. The company's quality control department samples 30 rods and finds that they have a mean length of 151 cm and a standard deviation of 2 cm. Calculate the Process Capability Index (Cp) and the Process Performance Index (Ppk) for this process. Assume the customer's specification limits are 147 cm and 153 cm for the length of the rods.

A Brisbane warehouse buys pre-packed bulk bags of Bundaberg Sugar with an advertised mean weight of 20 kilograms. To determine the validity of the advertised claim, the warehouse manager took a random sample of 55 packets from the latest shipment and found an average weight of the packets of 20.011 kilograms. Bundaberg Sugar know, from analysing data over many years, that their 20kg bulk bag packing process results in a standard deviation of 45 grams. 1. State the direction of the alternative hypothesis used to test the advertised claim. Type the letters gt (greater than), ge (greater than or equal to), lt (less than), le (less than or equal to) or ne (not equal to) as appropriate in the box. 2. Use the tables in the text to determine the critical value used to conduct the test, assuming a 10% level of significance. If there are two critical values, state only the positive value. 3. Calculate the test statistic, reporting your answer to two decimal places 4. Is the null hypothesis…

How many ppm defective parts would be expected in a +/- 4 sigma normally distributed unstable process? Assume the mean shifted by +/- 1.5σ from the target.

What is the meaning of x ~ N (50, 20)?   1. Sampling distribution of x is distributed with a mean of 20 and a standard deviation of 50   2. x-bar is normally distributed with a mean of 20 and a standard deviation of 50   3. x is normally distributed with a mean of 50 and a standard deviation of 20   4. Sampling distribution of x is distributed with a mean of  50 and a standard deviation of 20

A metal fabricator produces connecting rods with an outer diameter that has a 1± 0.02 inch specification. A machine operator takes several sample measurements over time and determines the sample mean outer diameter to be 1.005 inches with a standard deviation of 0.003 inch. Calculate the process capability index for this example. Note: Round your answer to 3 decimal places. Process capability index

The director of research and development is testing a new drug. She wants to know if there is evidence at the 0.02 level that the drug stays in the system for less than 368 minutes. For a sample of 78 patients, the mean time the drug stayed in the system was 363 minutes. Assume the variance is known to be 529.   State the null and alternative hypotheses for the above scenario.

Linda Boardman, Inc., an equipment manufacturer in Boston, has submitted a sample cutoff valve to improve your manufacturing process. Your process engineering department has conducted experiments and found that the valve has a mean (u) of 12.00 and a standard deviation (a) of 0.04. Your desired performance is μ = 12.00 +3 standard deviations, where a = 0.045. For the given information, the process capability index (Cpk) - (round your response to three decimal places).

A manufacturer is selling pharmaceuticals that have a weight specification 199.8 to 200.2 mg, with a target value of 200 mg. Before sending its next shipment, the company collects a large sample of product and determines the mean weight of the sample is 199.89 mg, with a standard deviation of 0.035 mg. The process capability index for the current process is ____. Round to three decimal places.