Prob and Stats

Scores on the SAT math exam followed a normal distribution with mean 515 and standard deviation 114. You choose a SRS of 100 students and calculate a mean math score. Which of the following are the mean and standard deviation of the sampling distribution of the sample means?

• Mean = 515; SD = 114

In a congressional district, 55% of the registered voters are Democrats. Which of the following is closest to the probability of getting less than 50% Democrats in a random sample of size 100?

• 0.157

• 0.496

• 0.504

• 0.843

Below is the population distribution of midterm scores for students in an introductory statistics class. The true mean of the population is \mu=76 and the standard deviation is \sigma=8. Is the shape of the sampling distribution of sample means approximately normal? Justify.

• Yes, because of Large Counts.

• Yes, because the population is more than 30.

• No, because the population is not symmetric and the sample size is more than 30.

• No, because the population is not symmetric and the sample size is NOT more than 30.

The amount that households pay service providers for access to the Internet varies, with a mean monthly fee of $48 and standard deviation of $20. The distribution is not normal. A sample survey asks a SRS of 500 households with Internet access how much they pay per month. Let X-bar be the mean amount paid by the members of the sample. Which type of sampling distribution does this describe?

• Sampling distribution of sample count

• Sampling distribution of sample proportion

• Sampling distribution of sample means

According to government data, 22% of American children under the age of 6 live in households with incomes less than the official poverty level. A study of learning in early childhood chooses an SRS of 300 children. Let X = the number of children in this sample who live in households with incomes less than the official poverty level. Which type of sampling distribution does this describe?

• Sampling distribution of sample count

• Sampling distribution of sample proportion

• Sampling distribution of sample means

According to government data, 22% of American children under the age of 6 live in households with incomes less than the official poverty level. A study of learning in early childhood chooses an SRS of 300 children. Let X = the number of children in this sample who live in households with incomes less than the official poverty level. What is the shape of the sampling distribution of X?

• Approximately Normal by Large Counts

• Not approximately Normal; Large Counts is not met

• Approximately Normal by Central Limit Theorem

• Not approximately Normal; Central Limit Theorem is not met.

According to government data, 22% of American children under the age of 6 live in households with incomes less than the official poverty level. A study of learning in early childhood chooses an SRS of 300 children. Let p-hat = the proportion of children in this sample who live in households with incomes less than the official poverty level. Which type of sampling distribution does this describe?

• Sampling distribution of sample count

• Sampling distribution of sample proportion

• Sampling distribution of sample means

The central limit theorem is important in statistics because it allows us to use the normal distribution to find probabilities involving the sample mean if the

• sample size is reasonably large for any population shape

• sample size is reasonably large AND the population is normally distributed

• population size is reasonably large for any population shape

• population size is reasonably large and the population is normally distributed.