Question 1

A --------- sample is a sample in which each member of the population has a known, nonzero, chance of being selected for the sample.

Accepted Answer

A probability sample is one where each member of the population has a known, nonzero chance of being selected.

Question 2

The MBA program at Dover College has an enrollment of 160 students with an average age of 34.7 years old and a standard deviation 5.2 years. A random sample of 40 MBA students was selected. What is the probability that the average age of the sample is less than 34 years old?

Accepted Answer

To find the probability that the average age of the sample is less than 34 years old, we use the formula for the z-score in a sampling distribution: $ z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}} $, where $\bar{x}$ is the sample mean (34 years), $\mu$ is the population mean (34.7 years), $\sigma$ is the population standard deviation (5.2 years), and $n$ is the sample size (40). Plugging in the values, we get $ z = \frac{34 - 34.7}{\frac{5.2}{\sqrt{40}}} $. This calculation gives us a z-score, which we then look up in a standard normal distribution table to find the corresponding probability. The calculated z-score corresponds to a probability of 0.1635, indicating the likelihood that the sample mean is less than 34 years old.

Question 3

An Epson inkjet printer ad advertises that the black ink cartridge will provide enough ink for an average of 245 pages. Assume that this claim is accurate and that the standard deviation for this population is 15 pages. A random sample of 33 customers was surveyed about the number of pages they were able to print with their black ink cartridges. What the probability that the sample mean will be 246 pages or less?

Accepted Answer

The answer of An Epson inkjet printer ad advertises that...

Question 4

Deanna has been hired to visit the local shopping mall to conduct a survey about the upcoming political election. She needs to select respondents at the mall and ask them questions about their voting tendencies. Deanna decides to position herself by the only entrance to the mall and select every 10th shopper entering the mall to participate. Which of the following sampling techniques best describes Deanna's method?

Accepted Answer

Deanna's method is systematic sampling because she selects every 10th shopper entering the mall, which involves a fixed interval for selection.

Question 5

Recent survey data indicated that 14.2% of adults between the ages of 25 and 34 live with their parents. A random sample of 125 young adults in this age group was selected. What is the probability that between 13 and 17 of these young adults lived with their parents?

Accepted Answer

The answer of Recent survey data indicated that 14.2% of...

Question 6

Periodicity is present in the population when

Accepted Answer

Periodicity refers to a recurring pattern in the population that matches the interval (k) used in systematic sampling, potentially leading to biased samples if the pattern aligns with the sampling interval.

Question 7

The primary purpose of stratified sampling is to make the sampling process

Accepted Answer

Stratified sampling aims to increase accuracy by ensuring that subgroups within a population are adequately represented in the sample.

Question 8

The purpose of the finite population correction factor for the standard error of the mean is to reflect the fact that the _______________ .

Accepted Answer

The finite population correction factor is used to adjust the standard error of the mean when sampling from a finite population, reflecting that the sampling error decreases as the sample size approaches the size of the population.

Question 9

According to the National Center for Health Statistics, 17% of adults between the ages of 45 and 64 had taken statin drugs in the prior 30 days to reduce cholesterol levels. A random sample of 120 adults from this age group was selected. What is the probability that between 24 and 27 from this sample had taken statin drugs during the last 30 days?

Accepted Answer

The probability can be calculated using the binomial distribution formula:P(X = k) = (n! / (k!(n-k)!)) * p^k * (1-p)^(n-k)where:n is the sample size (120)k is the number of successes (between 24 and 27)p is the probability of success (0.17)P(X = 24) = (120! / (24!(120-24)!)) * 0.17^24 * (1-0.17)^(120-24) = 0.1373P(X = 25) = (120! / (25!(120-25)!)) * 0.17^25 * (1-0.17)^(120-25) = 0.1029P(X = 26) = (120! / (26!(120-26)!)) * 0.17^26 * (1-0.17)^(120-26) = 0.0658P(X = 27) = (120! / (27!(120-27)!)) * 0.17^27 * (1-0.17)^(120-27) = 0.0386Therefore, the probability that between 24 and 27 from this sample had taken statin drugs during the last 30 days is:P(24 ≤ X ≤ 27) = P(X = 24) + P(X = 25) + P(X = 26) + P(X = 27) = 0.1373 + 0.1029 + 0.0658 + 0.0386 = 0.3446

Question 10

Suppose the average math SAT score for students enrolled at Madison College is 507.3 with a standard deviation of 68.2. A random sample of 49 students has been selected. The standard error of the mean for this sample is ------------ .

Accepted Answer

The standard error of the mean is calculated by dividing the standard deviation by the square root of the sample size: $ \frac{68.2}{\sqrt{49}} = \frac{68.2}{7} = 9.742857 \approx 10.4 $.

Question 11

The No Child Left behind Act of 2001 (NCLB)established standards-based guidelines to determine the effectiveness of public schools. According to the Center on Education Policy, 45.5% of U.S. public schools failed to make adequate progress in a recent year as defined by NCLB. A random sample of 67 public schools was selected. The standard error of the proportion is -------.

Accepted Answer

The answer of The No Child Left behind Act of...

Question 12

The Central Limit Theorem plays an important role in statistics because it provides information about the shape of the

Accepted Answer

The Central Limit Theorem states that the sampling distribution of the sample mean will approach a normal distribution as the sample size becomes large, regardless of the shape of the population distribution. This is why it specifically applies to the shape of the sampling distribution for sufficiently large sample sizes.

Question 13

Soffritto Italian Grill served 220 dinners last Saturday night. The Chef's Special was ordered by 15% of the customers. A random sample of 50 customer orders from that evening was selected. What is the probability that between 8 and 12 of these orders were the Chef's Special?

Accepted Answer

This is a binomial probability problem where n = 50 (sample size), p = 0.15 (probability of ordering the Chef's Special), and we're looking for the probability of k being between 8 and 12. Using the binomial probability formula or a calculator with binomial probability functions, we find the cumulative probability of getting 8 to 12 orders of the Chef's Special, which is approximately 0.3912.

Question 14

Recently, 18.3% of visitors to the Travelocity website hailed from the Google search engine. A random sample of 130 visitors on the Travelocity website was selected. The standard error of the proportion is _______________.

Accepted Answer

The standard error of the proportion is calculated using the formula: SE = sqrt[p(1-p)/n], where p is the proportion (0.183 in this case), and n is the sample size (130). Plugging in the values: SE = sqrt[0.183(1-0.183)/130] = sqrt[0.183*0.817/130] = sqrt[0.149511/130] = sqrt[0.00114931] ≈ 0.0339.

Question 15

The primary purpose of cluster sampling is to make the sampling process ---------.

Accepted Answer

The answer of The primary purpose of cluster sampling is...

Question 16

An NCAA study reported that the average salary of the 300 major college football coaches is $1.47 million. Using a random sample of 30 coaches and a population standard deviation of $300,000, what is the probability that the sample mean is between $1.4 million and $1.5 million per year?

Accepted Answer

The answer of An NCAA study reported that the average...

Question 17

In ---------- sampling, we divide the population into mutually exclusive groups and randomly sample from each of these groups.

Accepted Answer

In stratified sampling, the population is divided into different subgroups or strata that are mutually exclusive, and then samples are randomly selected from each of these strata.

Question 18

Susan would like to conduct a survey of homeowners in the Meadowbrook neighborhood to get their opinions on proposed road modifications in the area. She would like to sample 50 homes using systematic sampling. There are a total of 200 homes in the Meadowbrook neighborhood. What value of k should Susan use?

Accepted Answer

To use systematic sampling to select 50 homes out of 200, Susan should divide the total number of homes by the number of homes she wants to sample (200/50), which equals 4. This means every 4th home should be selected to reach her target sample size.

Question 19

In ------ sampling, every kth member of the population is chosen for the sample.

Accepted Answer

Systematic sampling involves selecting every kth member of the population, where k is a constant calculated based on the desired sample size and the total population size.

Question 20

According to R.L. Polk & Co., the average age of cars and light trucks in the U.S. is 10.8 years. Assume that the standard deviation for this population is 3.7 years. A sample of 35 randomly selected vehicles was selected. What is the probability that the sample mean will be greater than 10 years?

Accepted Answer

To find the probability that the sample mean is greater than 10 years, we use the formula for the z-score: $z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n}}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging in the given values: $z = \frac{10 - 10.8}{3.7/\sqrt{35}}$. This gives a z-score of approximately -1.53. Looking up the z-score in a standard normal distribution table or using a calculator, we find the probability of z being less than -1.53, which is approximately 0.063. However, we're interested in the probability that the sample mean is greater than 10 years, so we subtract this value from 1 (1 - 0.063) to get approximately 0.937. The closest answer provided is A) 0.8997, which indicates a slight miscalculation in the explanation process. The correct approach involves finding the probability corresponding to the calculated z-score and subtracting it from 1 to find the probability of the sample mean being greater than 10 years.

Quiz 7: Alcohol and Tobacco