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Exam 7: Sampling Distributions

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Question 51

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

A) It has a normal distribution with the same mean and standard deviation as the population.
B) It has a normal distribution with the same mean as the population but with a smaller standard deviation.
C) It has the same shape,mean,and standard deviation as the population.
D) It has the same shape and mean as the population,but has a smaller standard deviation.

E) A) and B)
F) A) and C)

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Question 52

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Australian football salaries averaged $150,000 with a standard deviation of $80,000 in a recent year.Suppose a sample of 100 football players was taken.What was the standard error for the sample mean salary?

A) $8,000
B) $800,000
C) $8 million
D) $150,000

E) A) and B)
F) B) and C)

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Question 53

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

If a simple random sample is chosen with replacement,each individual has the same chance of selection on every draw.

The amount of bleach a machine pours into bottles has a mean of 1080 grams with a standard deviation of 4.5 grams.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 4.5.

For sample size 16,the sampling distribution of the mean will be approximately normally distributed

Instruction 7-2 The mean selling price of new homes in a country town over a year was $115,000.The population standard deviation was $25,000.A random sample of 100 new home sales from this town was taken. -Referring to Instruction 7-2,what is the probability that the sample mean selling price was more than $110,000?

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

The question "Is your household income last year somewhere in between $25,000 and $35,000?" will most likely result in coverage error.

The amount of time it takes to complete an examination has a skewed-left distribution with a mean of 65 minutes and a standard deviation of 8 minutes.If 64 students were randomly sampled,the probability that the sample mean of the sampled students exceeds 71 minutes is approximately 0.

The amount of pyridoxine (in grams)per multiple vitamin is normally distributed with μ = 110 grams and σ = 25 grams.A sample of 25 vitamins is to be selected.What is the probability that the sample mean will be greater than 100 grams?

Coverage error results in a ________.

Instruction 7-7 Online customer service is a key element to successful online retailing.According to a marketing survey,37.5% of online customers take advantage of the online customer service.Random samples of 200 customers are selected. -Referring to Instruction 7-7,________% of the samples are likely to have between 35% and 40% who take advantage of online customer service.

Instruction 7-4 According to a survey,only 15% of customers who visited the web site of a major retail store made a purchase.Random samples of size 50 are selected. -Referring to Instruction 7-4,the average of all the sample proportions of customers who will make a purchase after visiting the web site is ________.

The lecturer of a business statistics class wanted to find out the average amount of time per week her students spent studying for the class.She divided the students into the left,right and centre groups according to the location they sat in the class that day.One of these 3 groups was randomly selected and everyone in the group was asked the average amount of time per week he/she spent studying for the class.This is an example of a cluster sample.

Sampling distributions describe the probability distribution of

The amount of bleach a machine pours into bottles has a mean of 1080 grams with a standard deviation of 4.5 grams.Suppose we take a random sample of 36 bottles filled by this machine.The probability that the mean of the sample exceeds 1080.3 grams is ________.

A study at a university in New South Wales reveals that,historically,45% of their students are minority students.If a random sample of size 75 is selected,the probability is ________ that between 30% and 50% of the students in the sample will be minority students.

The amount of time required for an oil and filter change on a car 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 probability that the sample mean will be between 39 and 48 minutes?

The sampling process begins by locating appropriate data sources called ________.