Exam 7: Sampling Distributions

Suppose a sample of n = 50 items is selected from a population of manufactured products and the weight, X, of each item is recorded.Prior experience has shown that the weight has a probabilitydistribution with $\mu$ = 6 ounces and $\sigma$ = 2.5 ounces.Which of the following is true about thesampling distribution of the sample mean if a sample of size 15 is selected?

Suppose the ages of students in Statistics 101 follow a right skewed distribution with a mean of23 years and a standard deviation of 3 years.If we randomly sampled 100 students, which of the following statements about the sampling distribution of the sample mean age is incorrect?

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 sampling distribution of the sample mean has a standard error of 0.15.

SCENARIO 7-3 The lifetimes of a certain brand of light bulbs are known to be normally distributed with a mean of 1,600 hours and a standard deviation of 400 hours.A random sample of 64 of these light bulbs is taken. -Referring to Scenario 7-3, the probability is 0.20 that the sample mean lifetime differs from the population mean lifetime by at least how many hours?

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 exceeds 36.01 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.

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 it is assumed that the amount of gasoline purchased per car is symmetric, there is approximately a 68.26% chance that a random sample of 16 cars will have a sample mean between 14 and 16 gallons.

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.What is the standard error of the mean?

Which of the following is true regarding the sampling distribution of the mean for a large sample size?

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?

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

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

The sample mean is an unbiased estimate of the population mean.

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 4 cars is selected, there is approximately a 68.26% chance that the sample mean will be between 13 and 17 gallons.

At a computer manufacturing company, the actual size of a computer chip is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter.A random sample of 12 computer chips is taken.What is the probability that the sample mean will be between 0.99 and1.01 centimeters?

If the population distribution is skewed, in most cases the sampling distribution of the mean can be approximated by the normal distribution if the samples contain at least 30 observations.

The amount of tea leaves in a can from a production line is normally distributed with $\mu = 110$ grams and $\sigma = 25$ grams.A sample of 25 cans is to be selected.So, the middle 70% of allsample means will fall between what two values?

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past.Suppose a sample of 100 major league players was taken.Find the approximate probability that the mean salary of the 100 players was less than $2.5 million.

The sample proportion is an unbiased estimator for the population proportion.

A manufacturer of power tools claims that the mean amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes.Suppose a random sample of 64 purchasers of this table saw is taken.The probability that the sample mean will be greater than 88 minutes is .