Exam 10: Sampling and Sampling Distributions

Suppose we want to estimate the mean salary of seven people based on a sample of size 3 . The salaries of the seven people in thousands of dollars are $25,10,19,57,53,55$ , and 63 , so that the population means we want to estimate is $\mu=36.5$ . If the first three of these salaries are those of bank trainees and the other four are salaries of officers in the bank, find $n_{1}$ and $n_{2}$ if the allocation is -proportional.

If we sample with replacement from a finite population, our sample would be random if in each draw all elements of the population _______ and successive draws are _______.

If the population is divided into three strata and $\frac{n_{1}}{N_{1} \sigma_{1}}=\frac{n_{2}}{N_{2} \sigma_{2}}=\frac{n_{3}}{N_{3} \sigma_{3}}$ , then the allocation is called _______

Random samples of size 2 are selected from the finite population which consists of the numbers 4, 7, 10, 13, 16, and 19. -Construct the sampling distribution of the mean for the 15 possible random samples of size 2 from the given finite population. Assign each possible sample a probability of $\frac{1}{15}$ .

An investor considers investing in the stocks of the following companies: IBM, Honeywell, Mobil, Eastman Kodak, and Homestake Mining. -In how many ways can the investor select three stocks to buy?

The weights of ice cream in "one-scoop" cones by an employee of a certain ice cream store is known to have a mean of 4 ounces with a standard deviation of . 6 ounces. What is the probability that in a random sample of 36 "one -scoop" cones the average weight is -between 3.9 and 4.2 ounces?

When we sample from an infinite population, what happens to the standard error of the mean if the sample size is decreased from 225 to 100 ?

When sampling with replacement, the finite population correction factor can be omitted.

A stratified sample of size $n=300$ is to be taken from a population of size $N=30,000$ which consists of four strata for which $N_{1}=10,000, N_{2}=5,000, N_{3}=8,000, N_{4}=7,000, \sigma_{1}=15, \sigma_{2}=25, \sigma_{3}=20$ and $\sigma_{4}=30$ . How large a sample must be taken from each stratum if the allocation is to be -proportional?

The central limit theorem is important since it justifies the use of _______ in solving problems.

When we sample from an infinite population, what happens to the standard error of the mean if the sample size is increased from 64 to 400 ?

Our sample size criterion for applying the central limit theorem if the population may not be normal is

The central limit theorem gives the probability that the will be less than a given number when we use the mean of a sample to estimate the _______.

Suppose we obtain a sample mean of 80 from a sample of size 100 from an infinite population with $\sigma=50$ . Then the probability is 0.75 that the error in estimating the population mean using Chebyshev's theorem is:

A new cure for the common cold has the side effect of producing dizziness in the user for an average of 40 minutes with a standard deviation of 12 minutes. -In a random sample of 64 people who take the drug, find the probability that the average time that a user remains dizzy is between 41 and 45 minutes.

The weights of ice cream in "one-scoop" cones by an employee of a certain ice cream store is known to have a mean of 4 ounces with a standard deviation of . 6 ounces. What is the probability that in a random sample of 36 "one -scoop" cones the average weight is -at least 3.7 ounces?

If the population is divided into relatively small subdivisions and then some of these subdivisions are selected for inclusion in the overall sample, the method is called _______ sampling.

The mean of a random sample of size 49 is used to estimate the mean of a very large population, consisting of the lifetimes of certain stereo components which have a standard deviation of $\sigma=35$ hours. What is the probability that our estimate will be in error by -less than 6 hours?

Using simple random sampling, the probability of selecting any particular sample of size 3 from a population of size 30 is _______.

The error in estimating the mean of a population by using a sample mean is expressed in symbols by _______.