Question

What is the difference between parameters and statistics? 2. Does statistical process control inspect all the items produced after they are finished? 3. The inspector samples five circuit boards at regular intervals and finds the mean solder quality score x for these five boards. Do we expect x to be exactly 100 if the soldering process is functioning properly? 4. If the quality of individual boards varies according to a normal distribution with mean µ = 100 and standard deviation σ = 4 , what will be the distribution of the sample averages, x ? (Recall the sample size is n = 5.) 5. In general, is the mean of several observations more or less variable than single observations from a population? Explain. 6. The distribution of call lengths to a call center is strongly skewed. What does the Central Limit Theorem say about the distribution of the mean call length x from large samples of calls?

Answer 1

1. The parameter refers to the entire population

The statistics refers to a sample

2. only a sample will be inspected

3. No only 99.7%

4. A student t distribution with spread = σ/√n

5. The mean is less variable than single observations from the population

6. The distribution of the mean call length x becomes approximately normal distributed

Explanation:

1. The parameter refers to numbers that summarize the data of the entire population while;

The statistics refers to the numbers that summarize the data for a subset of the population or of a sample

2. No only a sample will be inspected

3. No he expects 99.7% to function within three standard deviations of the mean

4. The distribution of the sample average will be the student t distribution curve with spread = σ/√n

5, The mean comprises a collection of variables from the sample, hence it is less variable than single observations from the population

6. According to the Central Limit Theorem, the distribution of the mean call length x from large samples of calls becomes more and more approximately normal as the size of the sample approaches that of the population.