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Exam 8: Sampling Distributions

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Question 21

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In an effort to identify the true proportion of shoplifters who are under age 18,a random sample of 300 shoplifting cases was taken.One hundred and twenty of those cases involved persons under age 18.What value would be used to estimate the true proportion of under age 18 shoplifters?

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Question 22

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Vehicles Four families live on a cul-de-sac represent a very small population.The number of vehicles owned by each family is shown below: $\begin{array} { | c | c | } \hline \text { Family } & \boldsymbol { x } \text { = Number of vehicles } \\\hline \text { Ali } & 1 \\\text { Brown } & 1 \\\text { Cosby } & 2 \\\text { Davis } & 3 \\\hline\end{array}$ -Calculate the population standard deviation.

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Question 23

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In order to estimate the mean salary for a population of 500 employees,the president of a certain company selected at random a sample of 40 employees.If the population standard deviation is $800,compute the standard error both with and without using the finite population correction factor. With correction factor: Without correction factor:

Fifty percent of all college students attend schools within 50 miles of their homes.In a sample of 500 college students,the probability that the sample proportion will be between 0.45 and 0.55 is:

The chairman of a statistics department in a certain college believes that 70% of the department's graduate assistantships are given to international students.A random sample of 50 graduate assistants is taken.Assume that the chairman is correct and that $\pi$ = 0.70.Find the expected value and the standard error of the sampling distribution of p. E(p): SE:

Pets $\begin{array} { | c | c | } \hline \text { Name } & \boldsymbol { x } = \text { Number of Pets } \\\hline \text { Abby } & 2 \\\text { Brenda } & 1 \\\text { Caro1 } & 3 \\\text { David } & 4 \\\text { Ed } & 2 \\\hline\end{array}$ -Calculate the population mean and standard deviation. Mean = ____________________ SD = ____________________

Vehicles Four families live on a cul-de-sac represent a very small population.The number of vehicles owned by each family is shown below: $\begin{array} { | c | c | } \hline \text { Family } & \boldsymbol { x } \text { = Number of vehicles } \\\hline \text { Ali } & 1 \\\text { Brown } & 1 \\\text { Cosby } & 2 \\\text { Davis } & 3 \\\hline\end{array}$ -Calculate the standard deviation of the sample means.

Suppose it is known that 60% of students at a particular college are smokers.A sample of 500 students from the college is selected at random.Approximate the probability that at least 280 of these students are smokers.

State the central limit theorem.

List all possible samples of 2 families that can be selected without replacement from this population.

A population that consists of 500 observations has a mean of 40 and a standard deviation of 15.A sample of size 100 is taken at random from this population.The standard error of the sample mean equals:

The heights of men in the USA are normally distributed with a mean of 68 inches and a standard of 4 inches.What is the probability that the mean height of a random sample of 35 men is greater than 70 inches?

The concept that allows us to draw conclusions about the population based strictly on sample data without having any knowledge about the distribution of the underlying population is

The average SAT score for the 300 students accepted at Tiny College this year is 1050 with a standard deviation of 275.If a random sample of 40 students is selected from this class,what is the probability that the average SAT score will be between 1060 and 1120?

TV Sets The following data give the number of TV sets owned for a population of 4 families: $\begin{array} { | l | l l l l | } \hline \text { Family } & \text { A } & \text { B } & \text { C } & \text { D } \\\hline \text { Number of TV Sets } & 2 & 1 & 4 & 3 \\\hline\end{array}$ Find the mean and the standard deviation for the population. Mean: SD:

Fifty percent of all college students attend schools within 50 miles of their homes.In a sample of 500 college students from a city with 5000 college students,what is the probability that the sample proportion will be between 0.45 and 0.55?

Suppose an actual census showed that 18.4% of the households in California have incomes in excess of $50,000.What is the probability that the sample proportion will be 0.22 or greater for a random sample of 750 households from a city population which totals 10,000?

A producer of a juice drink advertises that it contains 10% real fruit juices.A sample of 75 bottles of the drink is analyzed and the percent of real fruit juices is found to be 6.5%.If the true proportion is actually 0.10,what is the probability that the sample percent will be 6.5% or less?

The average weight of a 4 year old male is 40 lbs with a standard deviation of 6 lbs.What would be the probability that the average weight from a random sample of 50 boys at this age would have be greater than 41 lbs?

If the original population from which the samples were drawn is not normally distributed,then the sampling distribution of the mean will be ____________________ for large sample sizes.