Sampling Distributions Mixed Review

The magazine Sports Illustrated asked a random sample of 750 Division I college athletes, “Do you believe performance-enhancing drugs are a problem in college sports?” Suppose the 30% of all Division I college athlete thinks that these drugs are a problem. Which of the following are the mean and standard deviation of the sampling distribution of p̂

• Mean = 0.30, SD = 0.017

• Mean = 0.30, SD = 0.55

• Mean = 0.30, SD = 0.0003

• Mean = 225, SD = 12.5

• Mean = 225, SD = 157.5

The magazine Sports Illustrated asked a random sample of 750 Division I college athletes, “Do you believe performance-enhancing drugs are a problem in college sports?” Suppose the 30% of all Division I college athlete thinks that these drugs are a problem. The sampling distribution of p̂ is approximately normal because

• There are at least 7500 Division I college athletes

• np = 225 and n(1-p) = 525 are both at least 10

• The athletes’ responses are quantitative

• A random sample was chosen

• The sampling distribution of p̂ always has this shape

The sampling distribution of a statistic is...

• Using repeated samples and finding a probabilitity
• The distribution of values taken by a statistic in all possible samples of the same sample size from the same population
• The way that sample results differe from each other
• the distribution of values in a sample of size n

Increasing the sample size of an opinion poll will reduce the

• bias of the estimates made from the data collected in the poll.
• variability of the estimates made from the data collected in the poll.
• variability of opinions in the sample.
• variability of opinions in the population.

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

A statistic is unbiased if...

• the value of the statistic from any sample is NOT equal to the parameter
• The value of the statistic from any sample IS equal to the parameter
• The mean of the sampling distribution is NOT equal to the true value of the parameter
• The mean of the sampling distribution IS equal to the value of the population mean

A random sample of female college students has a mean height of 64.5 inches, which is greater than the 63 inch mean height of all adult American women. 63 inches is a

• Sample

• Population

• Statistic

• Parameter

Portly Polls asked 1720 first year college students if they say they like the cafeteria food. According to the colleges, 40% of all first year college students say they like the cafeteria food. What is the probability that Portly Polls' random sample will give a result within 2% of the true value?

• 4.54%

• 95.45%

• 90.44%

• 86.35%

How can you check to see if your sample of size n is large enough to apply the Central Limit Theorem?

• n ≤ 10

• n ≤ 30

• n ≥ 10

• n ≥ 30

Tags

CCSS.HSS.ID.A.4

Portly Polls asked 149 fourth year college students on average, how much they spent for lunch. According to the colleges, the average amount they spent for lunch is N(30,10). Portly Polls got less than $30.4 on average. How likely is this result?

• 84.02%

• 68.79%

• 165.5%

• 58.37%

A study of a population of males who smoke at least two packs of cigarettes daily shows that the mean life span is 65.3 years, with a standard deviation of 3.4 years.

Find the probability that from a random sample of 40 males who smokes at least two packs of cigarettes daily, the life span is less than 65 yrs.

• 0.3925

• 0.5416

• 0.7116

• 0.2884