Exam 7: Sampling Distributions

The cause of a change in a process variable being monitored is regarded as random variation if it can be found and corrected.

Which of the following is the standard error of a statistic used as an estimator of a population parameter?

The standard deviation of the sampling distribution of the proportion is denoted by SE .

A producer of brass rivets randomly samples 500 rivets each hour and calculates the proportion of defectives in the sample. The mean sample proportion calculated from 250 samples was equal to 0.025. Calculate the upper and lower control limits for a control chart for the proportion of defectives in samples of 500 rivets. Explain how the control chart can be of value to a manager.

A population with a large standard deviation will have a sampling distribution that is more spread out for a given sample size than a similar population with a small standard deviation.

Content Composition Analysis Narrative A well-known juice manufacturer claims that its citrus punch contains 15% real orange juice. A random sample of 150 cans of the citrus punch is selected and analyzed for content composition. -Refer to Content Composition Analysis Narrative. Completely describe the sampling distribution of the sample proportion.

The shape of the normal distribution is determined by its mean, , and its standard deviation, .

Canadian Cancer Society Survey Narrative A recent nationwide survey by the Canadian Cancer Society found the percentage of women who smoke has increased to 30%. That seemed a little low for your province, so you sampled 500 women from your province and found that 180 of them smoke. -Refer to Canadian Cancer Society Survey Narrative. Based on your answer to the previous question, what might you conclude about the Canadian Cancer Society's claim that p = 0.30?

The Central Limit Theorem indicates that the sampling distribution of the sample proportion can be approximated by a normal distribution if np > 5 and nq > 5.

The sample standard deviation measures the variability of all possible sample mean, , values that might be obtained.

Random samples of size 36 each are taken from a large population whose mean is 120 and standard deviation is 39. In this case, which of the following are the values of the mean and the standard error, respectively, of the sampling distribution of the sample mean?

Salaries of Professors Narrative Suppose that college faculty with the rank of professor at four-year institutions earn an average of $72,500 per year with a standard deviation of $4,500. In an attempt to verify this salary level, a random sample of 60 professors was selected from a personnel database for all four-year institutions in Canada. -Refer to Salaries of Professors Narrative. Within what limits would you expect the sample average to be, with probability 0.95?

Weights of Candy Bars Narrative A candy bar company is interested in reducing the percentage of defective candy bars made, where a defective candy bar is one that has too few almonds by weight. The company randomly samples 100 candy bars a day for 5 days and finds the percentage of the defective bars to be 0.0200, 0.0125, 0.0225, 0.0100, and 0.0150, respectively. The company wants to construct a control chart for the proportion defective in samples of size n = 100. -Refer to Weights of Candy Bars Narrative. How are these control limits used?

The population of pop cans filled by a particular machine is known to be normally distributed with a mean of 340 mL and a standard deviation of 4.5 mL. Given this information, the sampling distribution of the sample mean, , for a random sample of 16 cans will also be normally distributed with a mean equal to

Sixty samples of size 600 each were drawn from a manufacturing process and the number of defectives in each sample was counted. The average sample proportion was 0.04. What would be the lower control limit for the p chart?

Lab Mice Experiments Narrative In a learning experiment, untrained mice are placed in a maze and the time required for each mouse to exit the maze is recorded. The average time for untrained mice to exit the maze is $\mu$ = 50 seconds and the standard deviation of their times is $\sigma$ = 16 seconds. Suppose that a sample of 64 randomly selected untrained mice are placed in the maze and the time necessary to exit the maze is recorded for each. -Refer to Lab Mice Experiments Narrative. What is the probability that the sample mean differs from the population mean by more than 3?

A sampling distribution is the distribution of the values that are included in a sample selected randomly from the population.

Statistical process control (SPC) methodology was developed to monitor, control, and improve products and services.

College Football Division Narrative A student government representative at a local university claims that 60% of the undergraduate students favour a move to Division I in college football. A random sample of 250 undergraduate students is selected. -Refer to College Football Division Narrative. Completely describe the sampling distribution of the sample proportion.

Battery Lifetime Narrative The lifetime of a particular type of battery is normally distributed with a mean of 1100 days and a standard deviation of 80 days. The manufacturer randomly selects 400 batteries of this type and ships them to a tire retailer. -Refer to Battery Lifetime Narrative. What is the probability the average lifetime of these 400 batteries is between 1097 and 1104 days?