AP Stats Nit

Mrs. Chevron shows her class a box filled with black and white beads. When she filled the box, 42% of the box consisted of black beads and the rest were white beads. She selected an SRS of 50 beads, and 19 of the 50, or 38%, were black. Which of the following is the correct representation of the percentage of black beads in the box as well the percentage of black beads in her sample?

• p = 42%, p = 38%, both are parameters

• p = 42%, p-hat = 38%, 42% is a parameter, 38% is a statistic

• p-hat = 42%, p = 38%, 42% is a statistic, 38% is a parameter

• p-hat = 42%, p-hat = 38%, both are statistics

There is a belief that the proportion of heads landing face up is greater than 50% when the coins are stood up on their edge and the table is shaken slightly to knock them over. Out of 100 pennies, 60% land on heads. 100 SRS's of size n = 100 were simulated and the proportion of heads are represented in the dotplot. Is there convincing evidence that the proportion of times a penny lands heads up when stood on its edge is greater than 50%?

• Yes, because getting a proportion of 60% or more heads only occurs 3% of the time, so there is statistical significance.

• No, because getting a proportion of 60% or more heads only occurs 3% of the time, so there is no statistical significance.

• Yes, because the simulated sampling distribution is approximately symmetric and centered about 0.50.

• No, because the simulated sampling distribution is approximately symmetric and centered about 0.50.

Suppose that 73% of residents in a certain city own at least one pet. You select a random sample of 65 city residents. Let p-hat = the proportion of city residents in your sample that own at least one pet. What is the standard deviation of the sampling distribution of p-hat and what does it mean?

• The proportion of residents that own at least one pet in the sample will typically vary by about 0.06 from the true proportion mean of 0.73.

• The proportion of residents that own at least one pet in the sample will typically vary by about 0.73 from the true proportion mean of 0.06.

• The proportion of residents that own at least one pet in the sample will typically vary by about 3.58 from the true proportion mean of 0.73.

• The proportion of residents that own at least one pet in the sample will typically vary by about 3.58 from the true proportion mean of 47.45.

A manufacturer claims that only 3% of their products are defective. A store receives a delivery of 400 items from the manufacturer. Let X = the number of defective items in a sample of 400 items. Assuming the manufacturer is correct that only 3% of their products are defective, what are the mean and standard deviation of the sampling distribution of X?

• The mean is 120 and the standard deviation is 9.17.

• The mean is 12 and the standard deviation is 3.41.

• The mean is 12 and the standard deviation is 0.341.

• The mean is 0.03 and the standard deviation is 0.002.

A company produces a computer part and claims that 99% of the parts produced work properly. A purchaser of these parts is skeptical and decides to select a random sample of 375 parts and test each one to see what proportion of the parts work properly. Based on the sample, is the sampling distribution of p-hat approximately normal? Why?

• Yes, because 250 >= 30 so by the CLT, the sampling distribution of p-hat is a large enough sample that it will be approximately normal.

• Yes, because the value of np is 371.25, which is greater than 10, so the sampling distribution of p-hat is approximately normal.

• No, because the value of n(1 – p) is 3.75, which is not greater than 10, so the sampling distribution of p-hat is not approximately normal.

• No, because the value of p is assumed to be 99%, the distribution of the parts produced will be skewed to the left, so the sampling distribution of p-hat is not approximately normal.

A random sample of 120 students at a certain high school were asked if they spend more than 4 hours per night on homework. Assume the true proportion of students that spend more than 4 hours per night on homework is 15%. Which of the following is closest to the probability that more than 20% of the students in the sample would respond that they spend more than 4 hours per night on homework?

• 0.0475

• 0.0809

• 0.9191

• 0.9375

A random sample of 80 employees at a large grocery store with multiple locations were asked if they spend more than 30 minutes commuting to work. Assume the true proportion of employees that spend more than 30 minutes commuting to work is 35%. Which of the following is closest to the probability that fewer than 24 of the employees in the sample would respond that they spend more than 30 minutes commuting to work each day?

• 0.0280

• 0.1736

• 0.8258

• 0.9720

A random sample of 100 students at a local high school were asked if they carpool to school. Assume the true proportion of students that carpool to school is 40%. Which of the following is closest to the probability that more than 49% of the students in the sample would respond that they carpool to school each day?

• 0.0359

• 0.0406

• 0.9594

• 0.9794

Historical data has shown that students at Waynesburg High School have, on average, 2.2 siblings and a standard deviation of 1.4 siblings. Suppose we select a random sample of 40 Waynesburg High School students. Let x-bar = the sample mean number of siblings for students in your sample. What is the standard deviation of the sampling distribution of and what does it mean?

• The sample mean number of siblings in the sample typically varies by about 6.32 from the true average of 2.2 siblings

• The sample mean number of siblings in the sample typically varies by about 1.4 from the true average of 2.2 siblings

• The sample mean number of siblings in the sample typically varies by about 0.22 from the true average of 2.2 siblings

• The sample mean number of siblings in the sample typically varies by about 0.035 from the true average of 2.2 siblings

A sample of 100 residents was selected from all of the residents in a large city to estimate the average number of pets they own. The sample mean, x-bar, was 1.91 pets. Suppose μ, the true mean number of pets owned by residents in the city, is 1.75 pets with a standard deviation, σ, of 1.1 pets. What is the mean and the standard deviation of the sampling distribution of x-bar?

• The mean is 1.91 pets and the standard deviation is 1.1 pets.

• The mean is 1.91 pets and the standard deviation is 0.11 pets.

• The mean is 1.75 pets and the standard deviation is 1.1 pets.

• The mean is 1.75 pets and the standard deviation is 0.11 pets.