Sampling Distributions – Center and Variability Answers

A large university with over 40,000 students recently took a survey in which 31% of the students claimed to exercise at least 3 times a week. A simple random sample of 250 students was selected. Let = the proportion of students in the sample who claimed to work out at least 3 times a week.What is the shape of the sampling distribution of and why?

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A recent survey of the 1,800 students at a local high school revealed that 12% of the students believe that uniforms should be worn in schools. A simple random sample of 80 students is taken. Use the drop-down menus to complete the statement. Enter all proportions rounded to the hundredths place, starting with 0. The shape would best be described as with a mean of and a standard deviation of approximately .

Approximately 68% of the samples of size 150 will fall between 27% and 35% of the students claiming they exercise at least 3 times a week.The proportion of the sample who work out at least 3 times a week is 0.04.In simple random samples of size 150, the sample proportion of students who exercise at least 3 times a week will typically vary by about 0.04 from the true proportion of 0.31.In simple random samples of size 150, the sample proportion of students who exercise at least 3 times a week will always vary by exactly 0.04 from the true proportion of 0.31.

In the US, 77% of all teens have a TV in their bedrooms, while 59% of all teens in Spain have them. A simple random sample of 500 teens from the US and 300 from Spain are selected and all are asked whether they have a TV in their bedrooms. Let be the difference in the sample proportions of teens with a TV in their bedrooms, where is the sample proportion of US teens with a TV in their bedrooms and is the sample proportion of Spanish teens with a TV in their bedrooms.What is the shape of the sampling distribution of the difference in the two sample proportions?

⇒ 0.18

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In the US, 77% of all teens have a TV in their bedrooms, while 59% of all teens in Spain have them. A simple random sample of 500 teens from the US and 300 from Spain are selected and all are asked whether they have a TV in their bedrooms. Let be the difference in the sample proportions of teens with a TV in their bedrooms, where is the sample proportion of US teens with a TV in their bedrooms and is the sample proportion of Spanish teens with a TV in their bedrooms. The standard deviation of the sampling distribution of the difference in sample proportions is 0.034. Use the drop-down menus to complete the statement. In random samples of size of US and Spanish teens, the will by about 0.034 from the true difference in of 0.18.

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