Exam 7: Sampling and Sampling Distributions

The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 25 grams. A sample of 25 cans is to be selected. What is the probability that the sample mean will be greater than 100 grams?

The only way one can eliminate sampling error is to take the whole population as the sample.

When dealing with human surveys, we are usually interested in sampling with replacement.

The standard error of the mean for a sample of 100 is 30. In order to cut the standard error of the mean to 15, we would

If the amount of gasoline purchased per car at a large service station has a population mean of 15 gallons and a population standard deviation of 4 gallons and a random sample of 64 cars is selected, there is approximately a 95.44% chance that the sample mean will be between 14 and 16 gallons.

As the size of the sample is increased, the standard deviation of the sampling distribution of the sample mean for a normally distributed population will stay the same.

As the sample size increases, the effect of an extreme value on the sample mean becomes smaller.

An electronic appliance chain gathered customer opinions on their services using the customer feedback forms that are attached to the product registration forms. This is an example of a convenience sample.

TABLE 7-6 According to an article, 19% of the entire population in a developing country have high-speed access to the Internet. Random samples of size 200 are selected from the country's population. -Referring to Table 7-6, among all the random samples of size 200, ________ % will have between 14% and 24% who have high-speed access to the Internet.

The Central Limit Theorem ensures that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases.

The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. The probability that the mean of the sample is between 35.94 and 36.06 oz. is ________.

The fact that the sample means are less variable than the population data can be observed from the standard error of the mean.

For distributions such as the normal distribution, the arithmetic mean is considered more stable from sample to sample than other measures of central tendency.

In inferential statistics, the standard error of the sample mean assesses the uncertainty or error of estimation.

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. If a sample of 25 fish yields a mean of 3.6 pounds, what is the Z-score for this observation?

The standard deviation of the sampling distribution of a sample proportion is where $\sqrt{\frac{\pi(1-\pi)}{n}}$ π is the population proportion.

The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample of 16 cars is selected. 90% of the sample means will be greater than what value?