Question 1

A ------- sample is a sample in which every member of the population has an equal chance of being chosen.

Accepted Answer

A simple random sample is defined by every member of the population having an equal chance of being selected, which ensures that the sample represents the population fairly.

Question 2

For a sample size of two or more, the standard error of the mean must be --------.

Accepted Answer

The standard error of the mean decreases as the sample size increases and is always less than the population standard deviation for a sample size of two or more, reflecting the increased precision of the sample mean as an estimate of the population mean.

Question 3

The statistical technique where many samples are repeatedly drawn from a population is known as

Accepted Answer

Resampling is a statistical technique that involves repeatedly drawing samples from a population, often used for estimating the distribution of a statistic or for performing hypothesis testing.

Question 4

A recent study reported that 28% of shoppers only review one page when searching online for product information. A random sample of 100 shoppers was randomly selected. What is the probability that between 20 and 30 of these shoppers only review one page when searching online?

Accepted Answer

The answer of A recent study reported that 28% of...

Question 5

According to Net Market Share, Microsoft's Internet Explorer browser has 53.4% of the global market. A random sample of 70 users was selected. What is the probability that 32 or more from this sample used Internet Explorer as their browser?

Accepted Answer

The probability can be calculated using the normal approximation to the binomial distribution. With p = 0.534, n = 70, the mean is np = 37.38 and the standard deviation is sqrt(np(1-p)) ≈ 4.18. Using the z-score formula, the probability of 32 or more users is approximately 0.9015.

Question 6

According to comScore, Facebook users spent an average of 432 minutes on the site during a recent month. Assume that this population has a standard deviation of 127 minutes. A random sample of 50 users was selected from this population. What is the probability that the average number of minutes on the site in the recent month was less than 410 minutes?

Accepted Answer

To find the probability that the average number of minutes on the site in the recent month was less than 410 minutes, we use the formula for the z-score of a sample mean: $z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n}}$, 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: $z = \frac{410 - 432}{127/\sqrt{50}}$, we find the z-score and then use the standard normal distribution to find the probability corresponding to this z-score. The correct probability, based on the calculation, is 0.0643.

Question 7

The national average price for regular gasoline was recently reported to be $3.29 per gallon. The standard deviation for the price of regular gasoline was $0.12. A random sample of 33 gas stations had an average price of $3.26. Which of the following statements is correct?

Accepted Answer

The answer of The national average price for regular gasoline...

Question 8

The Central Limit Theorem requires

Accepted Answer

The Central Limit Theorem states that the sampling distribution of the sample means approaches a normal distribution as the sample size gets larger, typically considered to be at least 30, regardless of the shape of the population distribution.

Question 9

As the size of the sample increases, the ---------.

Accepted Answer

The standard error of the mean decreases as the sample size increases because it is inversely proportional to the square root of the sample size, leading to more precise estimates of the population mean.

Question 10

Recently, the average amount of time to foreclose on a house in the U.S. was reported to be 359 days. Assume that the standard deviation for this population is 90.4 days. A random sample of 42 homes that have completed the foreclosure process was selected. What is the probability that the sample average was less than 375 days?

Accepted Answer

To find the probability that the sample average was less than 375 days, we use the formula for the z-score of a sample mean: $z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$, 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: $z = \frac{375 - 359}{\frac{90.4}{\sqrt{42}}}$. This calculation gives us a z-score, which we then look up in a standard normal distribution table or use a calculator to find the corresponding probability. The calculation results in a probability of 0.8749, indicating there's an 87.49% chance the sample average is less than 375 days.

Question 11

A statistics class has 140 students of which 55% are female. A random sample of 40 students was selected. What is the probability that 24 or more from this sample will be female?

Accepted Answer

This is a binomial probability problem where we are looking for the probability of getting 24 or more successes (female students in this case) out of 40 trials (students sampled), where the probability of success on each trial is 0.55 (since 55% of the 140 students are female). The correct answer can be found using binomial probability formulas or a binomial probability calculator. Among the given options, 0.2266 is the correct probability for getting at least 24 female students in a sample of 40, based on the binomial distribution with p = 0.55 and n = 40.

Question 12

A key metric in the cell phone industry is average revenue per user (ARPU)which represents the average dollar amount that a customer spends per store visit. Recently, AT&T reported their ARPU was $67.81. Suppose the standard deviation for this population is $18.45. What is the probability that the ARPU will be between $62 and $66 from a random sample of 35 customers?

Accepted Answer

Using the standard normal distribution, calculate the z-scores for $62 and $66, then find the probability between these z-scores. The correct probability is approximately 0.3553.

Question 13

According to market research surveys, HP controls 60% of the color inkjet printer market in the U.S. A random sample of 120 inkjet users was selected. What is the probability that 65 or fewer of these individuals used an HP printer?

Accepted Answer

The answer of According to market research surveys, HP controls...

Question 14

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. Voting records show that 50% of the local population are registered as Republicans, 35% are registered as Democrats, and the remaining as Independents. Deanna wants to be sure that her final sample has a similar proportion of voters. Which of the following sampling techniques best describes Deanna's method?

Accepted Answer

Deanna's method is stratified sampling because she wants her sample to reflect the same proportions of Republicans, Democrats, and Independents as in the local population. Stratified sampling involves dividing the population into distinct subgroups (strata) and then drawing a sample from each subgroup proportional to its size in the population.

Question 15

John is the manager at a fast food restaurant and would like to determine the average number of cars waiting for their order in the drive-through line during his hours of operation. Every day at noontime, he counts the number of cars in the drive-through. Because of the lunchtime traffic, his survey overestimates the actual average throughout the day. This error is due to

Accepted Answer

John's error is due to periodicity, as he is only collecting data at a specific time (noontime) when traffic is likely higher, leading to an overestimation of the average number of cars throughout the entire day.

Question 16

The Beer Institute reported that monthly consumption of beer in is 1.7 gallons per person. A random sample of 36 adults was selected. Using a standard deviation of 0.5 gallons per month per person, what is the probability that the sample mean was between 1.6 and 1.8 gallons per month per person?

Accepted Answer

The answer of The Beer Institute reported that monthly consumption...

Question 17

In Chapter 1, the textbook author provided the following extreme example of a poorly worded survey question: "We would like to propose a national golf holiday. Everybody gets the day off from work and can play golf all day. (You would not need permission from your spouse to play.)Are you in favor of this proposal?
A. Yes, most definitely.
B. Sure, why not?
C. No, I would rather spend the entire day at work.
P.S. If you choose C, we will permanently revoke all your golfing privileges everywhere in the country for the rest of your life. We are dead serious.""
The results of this survey would be unreliable due to

Accepted Answer

The results of this survey would be unreliable due to nonsampling error, specifically due to the way the question is worded and the consequences it implies for one of the choices, which can bias responses.

Question 18

The Central Limit Theorem (CLT)states that the sample means

Accepted Answer

The Central Limit Theorem (CLT) states that the distribution of sample means will approximate a normal distribution as the sample size becomes large, regardless of the population's distribution shape.

Question 19

------ errors can occur as a result of a questionnaire that contains ambiguous questions.

Accepted Answer

Nonsampling errors can occur for a variety of reasons unrelated to the sampling process, including poorly designed questionnaires, which can lead to ambiguous questions and misunderstandings by respondents.

Question 20

Susan would like to conduct a survey of homeowners in the Meadowbrook neighborhood to get their opinions on proposed road modifications in the area. Which of the following is an example of a simple random sample?

Accepted Answer

A simple random sample requires that every member of the population has an equal chance of being selected. Choices A, B, and C all involve systematic or convenience sampling methods, not providing every home an equal chance of selection.

Quiz 7: Alcohol and Tobacco