Sampling Distribution Basics

The Gallup Poll asked a random sample of 1785 adults whether they attended church during the past week.  We will count the number of people in the sample who attended church.  A newspaper report claims that 40% of all U.S. adults went to church last week.  What type of analysis would we do?

• Proportion

• Means

28% of all Woodrow students believe Monday will be snow day. You take a sample of 50 students and find that 15 of them believe Monday will be a snow day. What symbol would we use to represent 15?

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30% of all dogs in a city are micro-chipped. In a sample of 500 dogs, what is the probability that less than 32% of dogs are micro-chipped? In order to do this problem, you would use the formulas for...

• proportions

• means

According to the Center for Disease Control, 93% of children entering kindergarten in the U.S. are vaccinated. A school district has 180 incoming kindergarten children.

Which of the following is true concerning the shape of the sampling distribution?

• The sampling distribution is normal because n > 30

• The sampling distribution is not normal because nq is < 30

• The sampling distribution is normal because 93% of 180 is > 10

• The sampling distribution is normal because np and n(1-p) are both > 10

Knowing that the result of flipping a coin is equally likely (that means, 50/50 chance of observing either outcome). If you flip a coin 500 times, approximate the probability that at least 51% of them will be Tails.

In order to do this problem, you would need to use the formulas for...

• proportions

• means

Your mail-order company advertises that it ships 90% of its orders within three working days. You select an SRS of 100 of the 5000 orders received in the past week for an audit.

What symbol would you use for the mean of the sample?

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The average speed of 1500 vehicles traveling on a stretch of highway one particular day is 67 miles per hour with a standard deviation of 3.5 miles per hour. If 100 vehicles are randomly selected as samples, what would be the mean of the resulting sampling distribution of sample means?

In order to do this problem, you would need to use the formulas for...

• proportions

• means

Answer explanation

The Central Limit Theorem kicks in here since the sample size is greater than 30. The sampling distribution would be skewed right for samples less than 30

The amount of fuel used by jumbo jets to take off is normally distributed with a mean of 4000 gallons and a standard deviation of 125 gallons. What is the shape, mean and standard deviation of the distribution of sample means from samples of size n = 81.

This would be a problem dealing with...

• Proportions

• Means

Suppose the teenagers that attend public high schools get an average of 5.7 hours of sleep each night with a standard deviation of 1.7 hours. The distribution of sleep time is skewed to the left. What is the shape, mean, and standard deviation of the distribution of sample means from samples of size n = 400?

This is a ____ question.

• Proportions

• Means