Statistics: Unit 2 Sampling Distributions

A student would like to estimate the mean length of words in a book report he just finished writing. He selects a random sample of 20 words and determines the mean length to be 4 characters. Later, he discovers how to use a built-in function of his word-processing program that reveals that the mean length of all words in his book report is 4.3 characters. Which of the following describes the number, 4.3?

parameter

A teacher knows that scores on one of her tests are heavily left skewed, with a mean score of 78 and a standard deviation of 18. She randomly selects 15 grades and records the mean score. What is the shape of the distribution of the sample mean for all possible random samples of size 15 from this population?

skewed left

The prices of pants at a large clothing store chain are skewed left with a mean of $32 and a standard deviation of $20. The manager at one of the stores randomly selects 10 pairs of pants. Which of the following best describes the sampling distribution of all possible samples of size 10?

skewed left with a mean of 32 and standard deviation of 6.32

A fair six-sided number cube is rolled 60 times. What is the probability that fewer than 10% of the rolls are a five?

0.082

The agent wants to randomly select 2 of the 4 homes to show in an open house this coming weekend. This means the agent may show home A and B, A and C, A and D, B and C, B and D, or C and D. If homes A and B are selected, what is the sample mean listing price for this particular selection?

$200,000

Agriculturists in a certain state claim that 43% of the residents in the northern portion of the state prefer flour tortillas over corn tortillas, while 59% of the residents in the southern portion of the state prefer flour tortillas over corn tortillas. Suppose random samples of 33 northerners and 41 southerners are selected. Let and be the sample proportions of northern and southern residents of this state, respectively, who would prefer flour tortillas over corn tortillas. Which of the following is the mean of the sampling distribution of ?

-0.16

Alex's times for running a mile are Normally distributed with a mean time of 5.28 minutes and a standard deviation of 0.38 seconds. Chris's times for running a mile are Normally distributed with a mean time of 5.45 seconds and a standard deviation of 0.2 seconds. Ten of Alex's times and 15 of Chris's times are randomly selected. Let represent the difference in the mean times for Alex and Chris. Which of the following represents the mean of the sampling distribution for ?

-0.17

The times a musician spends performing a rock song and a country song are approximately Normally distributed. The rock song has a mean time of 133 seconds with a standard deviation of 3.5 seconds, and the country song has a mean time of 126 seconds with a standard deviation of 3.3 seconds. If the musician randomly selects 4 times the rock song is played and 3 times the country song is played, what is the probability that the mean time for the rock song is less than the mean time for the country song?

0.0034

A course for a snail race has times that are skewed right with a mean of 5.18 minutes and a standard deviation of 2.34 minutes. If a random sample of 38 snails is selected, what is the probability that the mean race time is less than 4.3 minutes?

0.0102

The number of pieces of cat food in a one-cup scoop is approximately Normally distributed with a mean of 344 pieces and a standard deviation of 16 pieces. If a random sample of 28 scoops of cat food is selected, what is the probability that the mean number of pieces will be more than 350 pieces?

0.0236

Hans has two route options to drive to work. When he travels Hampton Road, the distribution of times is approximately Normal with a mean of 23.9 minutes and a standard deviation of 3.1 minutes. When Hans travels Route 8, the distribution of times is approximately Normal with a mean of 20.8 minutes and a standard deviation of 5.4 minutes. Hans randomly selects 11 times he drove Hampton Road and 11 different times that he drove Route 8. What is the probability the mean time of the Hampton Road trips will be less than the mean of the Route 8 trips?

0.0493

King, a golden retriever, can find a tennis ball hidden in his yard 89% of the time, while Tessa, a Labrador mix, can find a tennis ball hidden in her yard 94% of the time. Suppose King's owner hides a tennis ball in his yard 100 times and Tessa's owner hides a tennis ball in her yard 150 times. Let K = the proportion of times King finds the tennis ball and T = the proportion of times Tessa finds the tennis ball. What is the probability that the proportion of tennis balls King finds is greater than the proportion Tessa finds?

0.088

The total number of forks dropped by customers per day at a busy restaurant is multimodal with a mean of 24.5 and a standard deviation of 3.3. If a random sample of 80 days is selected, what is the probability that the mean number of forks dropped during those days will be more than 25?

0.088

The time needed for passengers to board the Twisting Thunder roller coaster is skewed right with a mean of 49 seconds and a standard deviation of 7.1 seconds. The time to board the Spiral Wonder roller coaster is skewed left with a mean of 44.8 seconds and a standard deviation of 3.7 seconds. What is the probability in a random sample of 32 times loading Twisting Thunder and 36 times loading Spiral Wonder that the mean time for Twisting Thunder is less than that of Spiral Wonder?

0.1416

The volume of liquid soap in containers labeled as 7 oz is approximately Normally distributed and has a mean of 7.15 oz and a standard deviation of 0.11 oz. If 8 bottles of the soap are randomly selected, what is the probability that the mean is less than 7.11 oz?

0.1519

The monthly cost for cell phones for plan Amazing has a mean of $39.17 with a standard deviation of $13.58, while the monthly cost for plan Best has a mean cost of $41.16 with a standard deviation of $7.18. A random sample of 37 phones is selected from plan Amazing, and a random sample of 40 phones is selected from plan Best. What is the probability that the mean cost for plan Amazing will be more than the mean cost for plan Best?

0.2134

In a certain town, 62% of the residents enjoy riding roller coasters. Alfred takes a sample of 75 residents from this town. What is the probability that fewer than 58% of the residents in the sample enjoy riding roller coasters?

0.238

A coin is bent so that, when tossed, "heads" appears two-thirds of the time. What is the probability that more than 70% of 100 tosses result in "heads"?

0.239

On any given day, 34% of sales at Ruby's jewelry store are from necklaces, while 28% of sales at Nugget Jewels are from necklaces. Suppose Ruby's has 50 customers and Nugget Jewels has 60 customers on a randomly selected day. Let R = the proportion of sales that are from necklaces at Ruby's and N = the proportion of sales that are from necklaces at Nugget Jewels. What is the probability that the proportion of sales from necklaces at Ruby's will be less than the proportion of sales from necklaces at Nugget Jewels?

0.250

In a large local high school, 19% of freshmen have had their wisdom teeth removed and 24% of seniors have had their wisdom teeth removed. Suppose that a random sample of 60 freshmen and 50 seniors is selected. Let F = the proportion of freshmen who have had their wisdom teeth removed and S = the proportion of seniors who have had their wisdom teeth removed. What is the probability that the proportion of freshmen who have had their wisdom teeth removed is greater than the proportion of seniors?

0.263

In a beach town, 13% of the residents own boats. A random sample of 100 residents was selected. What is the probability that less than 11% of the residents in the sample own boats?

0.276

The weights of bunches of bananas in the grocery store are Normally distributed with a mean weight of 3.54 pounds and a standard deviation of 0.64 pounds. A random sample of four bunches is taken and the mean weight is recorded. Which of the following is the standard deviation of the sampling distribution for the mean of all possible samples of size four?

0.32

In a large urban high school, 68% of the students take public transportation to and from school. Annette takes a random sample of 75 students from this school. What is the probability that more than 70% of the students in the sample take public transportation to and from school?

0.356

Ricardo and Tammy practice putting golf balls. Ricardo makes 47% of his putts and Tammy makes 51% of her putts. Suppose that Ricardo attempts 25 putts and Tammy attempts 30 putts. Let R = the proportion of putts Ricardo makes and T = the proportion of putts Tammy makes. What is the probability that Ricardo makes a higher proportion of putts than Tammy?

0.384

Carol and Diane are axe throwers. Carol hits the board on 44% of her throws, while Diane hits the board on 42% of her throws. Suppose that Carol throws 25 axes at the board and Diane throws 28. Let C = the proportion of axes that hit the board when Carol throws and D = the proportion of axes that hit the board when Diane throws. What is the probability that Diane's proportion of axes hitting the board is higher than Carol's?

0.442

The heights of five-year-olds are Normally distributed with a mean of 42.5 inches and a standard deviation of 2.5 inches. A random sample of 16 five-year-olds is taken and the mean height is recorded. What would be the standard deviation of the sampling distribution of all possible samples of size 16?

0.63

The distribution of tips given by customers who buy only a cup of coffee is bimodal with a mean of $0.29 and a standard deviation of $0.116. The distribution of tips given by customers who buy only a salad is approximately Normally distributed with a mean of $2.89 and a standard deviation of $1.18. If a random sample of 35 tips from customers who buy only a cup of coffee is selected and a random sample of 20 customers who buy only a salad is selected, what is the probability of a sample mean being at least $2.50 more for customers who buy only a salad than for those who buy only a cup of coffee?

0.6781

Driving instructors Mr. Adams and Mr. Bateman teach class independently of each other. Among Mr. Adams's students, 68% pass the driving test on the first try, while 74% of Mr. Bateman's students pass the driving test on the first try. Suppose there are 40 students in Mr. Adams's class and 50 students in Mr. Bateman's class. Let A = the proportion of students who pass the driving test on the first try from Mr. Adams's class and B = the proportion of students who pass the driving test on the first try from Mr. Bateman's class. What is the probability that Mr. Bateman's class has more students who pass on the first try?

0.734

A statistics teacher has a large container of beads that she says contains 60% blue beads. A student randomly selects 50 beads. Let p = the true proportion of blue beads in the container. If the true proportion of blue beads is 0.60, which value of is least likely to occur?

0.80

The distribution of the number of items washed in a standard load of laundry is skewed left with a mean of 41 items and a standard deviation of 7.7 items. What is the probability that 50 randomly selected loads of laundry have a mean of more than 39.5 items?

0.9158

Latisha owns two spas, one in Pine township and the other in Adams township. Each spa offers a 30-minute face, head, and neck massage to reduce muscle tension. However, therapists first ask each patient questions about their type of tension and stop about five minutes before the end of the 30 minutes to have time to prepare for the next patient. The number of minutes each therapist massages the patients at both spas is approximately Normally distributed, with the Pine spa having a mean of 22.6 minutes and a standard deviation of 1.7 minutes and the Adams spa having a mean of 21.0 minutes and a standard deviation of 2.8 minutes. If Latisha randomly selects 8 massage times from Pine and 9 from Adams, what is the probability that the mean time for Pine is longer than the mean time for Adams?

0.9252

A catering company provides packages for weddings and for showers. The cost per person for small groups is approximately Normally distributed for both weddings and showers. The mean cost for weddings is $82.30 with a standard deviation of $18.20, while the mean cost for showers is $65 with a standard deviation of $17.73. If 9 weddings and 6 showers are randomly selected, what is the probability the mean cost of the weddings is more than the mean cost of the showers?

0.9665

The distribution of the number of blocks a young child can stack before their tower falls is approximately Normally distributed with a mean of 12.7 blocks and a standard deviation of 1.4 blocks. If 6 of the child's towers are randomly selected, what is the probability that the mean number of blocks is more than 11 blocks?

0.9985

The president of the company wants to randomly select 2 of the 5 vice presidents to send to a conference. How many distinct groups of 2 vice presidents can be selected without replacement from this small population of 5 vice presidents?

10

A random sample of 40 seniors reveals that 10% of those sampled have assigned parking spaces in the high school's main lot. This is surprising because, according to the main office of a large high school, 45% of seniors have assigned parking spaces in the high school's main lot. Which of the following statements is true?

10% is a statistic and 45% is a parameter.

A farmer determines that, on average, his chickens lay a total of 16 eggs each day. A random sample of 10 days was taken, and the mean number of eggs was determined. Let μ = the true mean number of eggs the chickens lay each day. Which of the following values for the sample mean is the least likely to occur?

18

The owner of an apple orchard knows that the average weight of Granny Smith apples is 380 grams. Which of the following sample sizes would have the greatest variability?

20

A random sample of 50 bottles is selected from the production line of a large manufacturing company. The mean of the contents of the 50 bottles is 20.25 ounces. The manager of the company requests that the machines be recalibrated because bottles coming off the production line are supposed to contain 20 ounces. Which of the following statements is true?

20 is a parameter and 20.25 is a statistic.

A bottled water company bottles varying sizes of water, from 8-ounce to 1-gallon containers. The company has determined that the mean quantity in their 20-ounce bottles is 20.8 ounces with a standard deviation of 0.6 ounces. The bottling plant manager believes his machines are overfilling the bottles. A random sample of 30 bottles is taken, and the mean number of ounces of water is recorded. Which of the following values of the mean of the sample is most likely to occur if the true mean number of ounces is 20.8?

20.9

The weights of bunches of bananas in the grocery store are Normally distributed with a mean weight of 3.54 pounds and a standard deviation of 0.64 pounds. A random sample of four bunches is taken and the mean weight is recorded. Which of the following is the mean of the sampling distribution for the mean of all possible samples of size four?

3.54

The owner of an apple orchard knows that the average weight of Granny Smith apples is 380 grams. A random sample of 40 apples was selected and the mean weight was calculated. Let μ = the true mean weight of the Granny Smith apples in the orchard. Which of the following means is least likely to occur if the true mean weight is 380 grams?

300 grams

A student wants to investigate the proportion of students who would support a fundraiser at a large high school. Which of the following sample sizes would have the least variability?

35

The daily temperatures for the winter months in Virginia are Normally distributed with a mean of 59°F and a standard deviation of 10°F. The daily temperatures for the winter months in California are Normally distributed with a mean of 64°F and a standard deviation of 12°F. Random samples of 10 temperatures are taken from the winter months for both Virginia and California. The mean temperature is recorded for both samples. Let represent the difference in the mean temperatures for the winter months in Virginia and California. Which of the following represents the standard deviation of the sampling distribution for ?

4.9

The heights of five-year-olds are Normally distributed with a mean of 42.5 inches and a standard deviation of 2.5 inches. A random sample of 16 five-year-olds is taken and the mean height is recorded. What would be the mean of the sampling distribution of all possible samples of size 16?

42.5

The times to pop a regular bag of microwave popcorn without burning it are Normally distributed with a mean time of 140 seconds and a standard deviation of 20 seconds. The times to pop a mini bag of microwave popcorn without burning it are Normally distributed with a mean time of 90 seconds and a standard deviation of 15 seconds. Suppose two independent random samples, 25 of each, are taken and the mean popping times are calculated. Let R = the popping time of a randomly selected regular-sized bag and M = the popping time of a mini-sized bag. Which of the following best describes the standard deviation of the sampling distribution of ?

5 seconds

A professional tennis player has a serve-return rate of p = 0.71. A random sample of 55 serve returns is selected. Which of the following is the mean of the sampling distribution of ?

A

The proportion of twins born in a town is p = 0.12. Suppose we randomly select 100 women from this town who give birth in the next year. Which of the following is the mean of the sampling distribution of ?

A

Which of the following gives the correct order of the graphs of the population distribution, distribution of a single sample, and sampling distribution, respectively?

A, C, B

The agent wants to randomly select 2 of the 4 homes to show in an open house this coming weekend. Which of the following gives a complete list of all possible samples of size 2 selected from this population of 4 homes without replacement?

AB, AC, AD, BC, BD, CD

A conference consists of 5 sessions: A, B, C, D, and E. Here are the costs of the sessions. Session A: $50Session B: $50Session C: $100Session D: $150Session E: $200 A participant plans to attend 3 sessions. Which of the following gives a complete list of all possible samples of size 3 from this population of 5 sessions, selected without replacement?

ABC, ABD, ABE, ACD, ACE, ADE, BCD, BCE, BDE, CDE

A real estate agent has 4 homes for sale: A, B, C, and D. Here are the listing prices. Home A: $150,000Home B: $250,000Home C: $190,000Home D: $550,000 The agent wants to randomly select 2 of the 4 homes to show in an open house this coming weekend. This means the agent may show home A and B, A and C, A and D, B and C, B and D, or C and D. Which of the following gives the sampling distribution of the sample mean listing price for all possible samples of size 2 from this population of 4 homes?

B

The proportion of twins born in a town is p = 0.12. Suppose we randomly select 100 women from this town who give birth in the next year. Which of the following is the correct calculation and interpretation of the standard deviation of the sampling distribution of ?

B

A professional tennis player has a serve-return rate of p = 0.71. A random sample of 55 serve returns is selected. Which of the following is the correct calculation and interpretation of the standard deviation of the sampling distribution of ?

C

The president of the company wants to select 2 of the 5 vice presidents randomly to send to a conference. Which of the following gives a correct list of all possible samples of size 2 selected from this population of 5 vice presidents without replacement?

C) (Andrew, Beth), (Andrew, Charles), (Andrew, Diane), (Andrew, Eric), (Beth, Charles), (Beth, Diane), (Beth, Eric), (Charles, Diane), (Charles, Eric), (Diane, Eric)

A bottled water company bottles varying sizes of water, from 8-ounce to 1-gallon containers. The company has determined that the mean quantity in their 20-ounce bottles is 20.8 ounces with a standard deviation of 0.6 ounces. The bottling plant manager believes his machines are overfilling the bottles. A random sample of 30 bottles is taken, and the mean number of ounces of water is determined to be 21. Under the assumption that the true mean ounces of water is 20.8, 100 simulated means for samples of size 30 are shown in the dotplot What does the dot above 21 represent?

In one simulated random sample of 30 bottles of water, the mean number of ounces was 21.

The owner of an apple orchard knows that the average weight of Granny Smith apples is 380 grams. A random sample of 40 apples was selected, and the mean weight was 390 grams. Let μ = the true mean weight of the Granny Smith apples in the orchard. Under the assumption that the true mean weight of Granny Smith apples is 380 grams, 100 simulated means for samples of size 40 are shown in the dotplot. What does the dot above 371 represent?

In one simulated random sample of 40 Granny Smith apples, the mean weight of the sample was 371 grams.

A statistics teacher has a large container of beads that she says contains 60% blue beads. A student randomly selects 50 beads. Let p = the true proportion of blue beads in the container. Under the assumption that the true proportion is 0.60, the student generated 200 values of . What does the dot above 0.74 represent?

In one simulated sample of 50 beads the proportion of blue beads is 0.74.

A student decides to spin a dime and determine the proportion of times it lands on heads. The student spins the dime 25 times and records that it lands on heads 17 times. Let p = the true proportion of times the dime would land on heads when spun. If the true proportion is 0.5, which of the following sample proportions is the least likely to occur?

NOT A

The distribution of the number of blocks a young child can stack before their tower falls is approximately Normally distributed with a mean of 12.7 blocks and a standard deviation of 1.4 blocks. If 6 of the child's towers are randomly selected, what is the probability that the mean number of blocks is more than 11 blocks?

NOT A

A student would like to know what proportion of the text messages she sends are to her best friend. She selects a random sample of 50 text messages she sent and determines the proportion of those messages that are sent to her best friend. Which of the following statements is true?

NOT A and B

At a certain high school, 38% of freshmen and 31% of sophomores walk to school. Suppose that random samples of 40 freshmen and 45 sophomores are chosen. Let S = the proportion of sophomores who walk to school and F = the proportion of freshmen who walk to school. What is the probability that the proportion of sophomores who walk to school is greater than the proportion of freshmen?

NOT B

The daily temperatures for the winter months in Virginia are Normally distributed with a mean of 59°F and a standard deviation of 10°F. A random sample of 10 temperatures is taken from the winter months and the mean temperature is recorded. What is the mean of the sampling distribution of the sample mean for all possible random samples of size 10 from this population?

NOT B

A random sample of 100 cartons of eggs is selected from a grocery store, and it is discovered that 2% of the selected cartons contain at least one broken egg. A separate random sample of 100 cartons of eggs is selected from a club store and it is found that 5% of the selected cartons contain at least one broken egg. Which of the following statements is true?

NOT C

A statistics teacher has a large container of beads that she says contains 60% blue beads. A student randomly selects 50 beads, and 25 of them were blue. Let p = the true proportion of blue beads in the container. Under the assumption that the true proportion is 0.60, the student generated 200 values of . Is there evidence that the true proportion of blue beads in the container is less than 0.60?

NOT C

According to records at the guidance office, the mean GPA of all juniors is 3.45 and the mean GPA of all seniors is 3.62. Which of the following statements is true?

NOT C and A

The president of the company wants to select 2 of the 5 vice presidents to send to a conference. The 10 possible samples of size 2 that can be selected from this population without replacement are (Andrew, Beth), (Andrew, Charles), (Andrew, Diane), (Andrew, Eric), (Beth, Charles), (Beth, Diane), (Beth, Eric), (Charles, Diane), (Charles, Eric), and (Diane, Eric). Which of the following gives the sampling distribution of the sample proportion of east regional responsibility for all possible samples of size 2 from this population?

NOT C and D

The salaries of professional baseball players are heavily skewed right with a mean of $3.2 million and a standard deviation of $2 million. The salaries of professional football players are also heavily skewed right with a mean of $1.9 million and a standard deviation of $1.5 million. A random sample of 40 baseball players' salaries and 35 football players' salaries is selected. The mean salary is determined for both samples. Let represent the difference in the mean salaries for baseball and football players. Which of the following represents the mean of the sampling distribution for ?

NOT D

The prices of houses in the US are strongly skewed to the right with a mean of $383,500 and a standard deviation of $289,321. A real estate agent takes a random sample of 10 houses and records the mean price. What is the shape of the distribution of the sample mean for all possible random samples of size 10 from this population?

NOT D and C

A random sample of 50 bottles is selected from the production line of a large manufacturing company. The mean weight of the contents of the 50 bottles is 20.25 ounces. The manager of the company requests that the machines be recalibrated because bottles coming off the production line are supposed to contain 20 ounces. Which of the following statements is true?

NOT D) The population is the 50 bottles that were selected and the population is all bottles in the production line.

The distribution of time spent brushing teeth for the 1,200 students in a school is multimodal with a mean of 43 seconds and a standard deviation of 8.99 seconds. If a random sample of 9 students is selected, is it appropriate to calculate the probability of the sample mean being less than 30 seconds using an approximately Normal model?

No, it is not appropriate to estimate the probability using an approximately Normal model because the population is not Normal, and the sample size is small.

An air-conditioning repair technician claims to complete 67% of repairs in under an hour. A random sample of 31 repairs was chosen, and 22 of those were completed in under an hour. Let = the proportion of the random sample that were completed in under an hour. The probability that 71% or more of this technician's repairs were completed in under an hour is 0.317. Does this result provide convincing evidence against the technician's claim?

No, the difference between the sample result and what is expected is not extreme enough. The probability of it occurring by chance alone is not unlikely.

The ages of the 5 officers for a school club are 18, 18, 17, 16, and 15. The median of the ages of the officers is 17.0. The table displays all possible samples of size 2 and the corresponding median for each sample. Using the medians in the table, is the sample median an unbiased estimator?

No, the mean of the sample medians is 16.8, which is not the same as the median age of the officers.

The ages of the 5 officers for a school club are 18, 18, 17, 16, and 15. The minimum of the ages of the officers is 15. The table displays all possible samples of size 2 and the corresponding minimum for each sample. Using the minimums in the table, is the sample minimum an unbiased estimator?

No, the mean of the sampling distribution of the sample minimums is 16, which is not 15.

Alex's times for running a mile are Normally distributed with a mean time of 5.28 minutes and a standard deviation of 0.38 seconds. Chris's times for running a mile are Normally distributed with a mean time of 5.45 seconds and a standard deviation of 0.2 seconds. Ten of Alex's times and 15 of Chris's times are randomly selected. Let represent the difference in the mean times for Alex and Chris. Which of the following represents the shape of the sampling distribution for ?

Normal, because both population distributions are Normal.

A student decides to spin a dime and determine the proportion of times it lands on heads. The student spins the dime 25 times and records that it lands on heads 17 times. He decides to spin the dime again and spins it 100 times. Which of the following is a correct statement about the variability of the sampling distribution?

Since the sample size is increased, the variability will decrease.

Movie critics claim that 68% of adults and 79% of teenagers would recommend seeing the newest action movie. Suppose a random sample of 43 adults and 52 teenagers is selected. Let and be the sample proportions of adult and teenage moviegoers, respectively, who would recommend this movie. Which of the following is the correct calculation and interpretation of the standard deviation of the sampling distribution of ?

The difference (adult - teenager) in the sample proportions of those who would recommend this action movie varies about 0.091 from the true difference in proportions.

At a large, rural high school, 21% of sophomores have an allergy to ragweed, while 17% of seniors have one. Let and be the sample proportions of sophomores and seniors, respectively, who have an allergy to ragweed. Suppose 50 sophomores and 62 seniors from this school are selected at random and asked if they have an allergy to ragweed. Which of the following is the correct calculation and interpretation of the standard deviation of the sampling distribution of ?

The difference (sophomores - seniors) in the sample proportions of those who have an allergy to ragweed typically varies about 0.075 from the true difference in proportions.

At a large university, 68% of the students have a laptop, while only 43% of professors have one. Let and be the sample proportions of students and professors, respectively, who have a laptop. Suppose 56 students and 31 professors from this university are selected at random and asked if they have a laptop. Which of the following is the correct calculation and interpretation of the standard deviation of the sampling distribution of ?

The difference (student - professor) in the sample proportions of those who have a laptop typically varies about 0.109 from the true difference in proportions.

At a university, 34% of undergraduate students love spicy food, while 45% of graduate students love spicy food. Let and be the sample proportions of undergraduate and graduate students at this university, respectively, who love spicy food. Suppose 35 undergraduate students and 28 graduate students from this university are selected at random and asked if they love spicy food. Which of the following is the correct calculation and interpretation of the standard deviation of the sampling distribution of ?

The difference (undergraduate students - graduate students) in the sample proportions of those who love spicy food typically varies about 0.123 from the true difference in proportions.

A random sample of 40 seniors reveals that 10% of those sampled have assigned parking spaces in the high school's main lot. This is surprising because, according to the main office of the large high school, 45% of seniors have assigned parking spaces in the high school's main lot. Which of the following statements is true?

The population is all seniors and the sample is the 40 seniors who were randomly selected.

A student would like to estimate the mean length of words in a book report he just finished writing. He selects a random sample of 20 words and determines the mean length to be 4 characters. Later, he discovers how to use a built-in function of his word-processing program that reveals that the mean length of all words in his book report is 4.3 characters. Which of the following statements is true?

The population is all words in the book report and the sample is the random sample of 20 words.

The manager of a large grocery store wants to inspect an incoming shipment of oranges to determine the proportion of blemishes. One inspector, Mary, takes a random sample of 25 oranges, and another inspector, Pat, takes a random sample of 50 oranges. Which of the following statements about variability of the sample proportion is correct?

The variability of the proportion of blemishes for Mary's sample will be greater than the variability of Pat's.

Students in a large district's two high schools are offered a "Second Breakfast" program after their first-period class. The district's nutrition manager is interested in determining if the program is effective. He takes two independent random samples of days from the previous years, 20 from high school A and 15 from high school B, and calculates the mean amount of money, in dollars spent, for the program. Which of the following statements concerning the variability of the sampling distribution of the sample mean is correct?

The variability of the sample mean amount of dollars spent for high school A will be less than the variability of high school B.

A farmer determines that, on average, his chickens lay a total of 16 eggs each day. A random sample of 10 days was taken, and the mean number of eggs was 15.1 eggs. Let μ = the true mean number of eggs the chickens lay each day. Under the assumption that the true mean number of eggs is 16, 100 simulated means for samples of size 10 are shown in the dotplot. Using the dotplot, is there evidence that the chickens are laying fewer than 16 eggs?

Yes, since a sample mean number of eggs of 15.1 eggs or less only occurred twice in simulated values, there is evidence that the true mean number of eggs is less than 16.

The owner of an apple orchard knows that the average weight of Granny Smith apples is 380 grams. A random sample of 40 apples was selected, and the mean weight was 390 grams. Let μ = the true mean weight of the Granny Smith apples in the orchard. Under the assumption that the true mean weight of Granny Smith apples is 380 grams, 100 simulated means for samples of size 40 are shown in the dotplot. Using the dotplot, is there evidence that the true mean weight of Granny Smith apples is greater than 380 grams?

Yes, since a sample mean weight of 390 grams or more only occurred once in 100 simulated values, there is evidence that the true mean weight is greater than 380 grams.

The ages of the 5 officers for a school club are 18, 18, 17, 16, and 15. The mean of the ages of the officers is 16.8. The table displays all possible samples of size 2 and the corresponding mean for each sample. Using the means in the table, is the sample mean an unbiased estimator?

Yes, the mean of the sample means is 16.8, which is the same as the mean age of the officers.

The probability that 94% or fewer of these gel pens can write more than 10,000 words is 0.0115. Does this result provide convincing evidence against the producer of the gel pens?

Yes, the probability of seeing the sample result is so far from what is expected that the probability of it occurring by chance alone is very unlikely (0.0115 < 0.05).

The probability that 60% or fewer graduates land a major acting role within one year of graduating from this school is 0.043. Does this result provide convincing evidence against the school's claim?

Yes, the probability of seeing the sample result is so far from what is expected that the probability of it occurring by chance alone is very unlikely (0.043 < 0.05).

The number of marshmallows an adult can fit in their mouth is skewed right with a mean of 6.5 and a standard deviation of 0.58. What is the probability that a random sample of 40 adults would have a mean of at least 7 marshmallows?

approximately 0

The daily temperatures for the winter months in Virginia are Normally distributed with a mean of 59°F and a standard deviation of 10°F. A random sample of 10 temperatures is taken from the winter months and the mean temperature is recorded. What is the shape of the distribution of the sample mean for all possible random samples of size 10 from this population?

approximately Normal

The prices of pants at a large clothing store chain are skewed left with a mean of $32 and a standard deviation of $20. The manager at one of the stores randomly selects 30 pairs of pants. What is the shape of the distribution of the sample mean for all possible random samples of size 30 from this population?

approximately Normal

The proportion of twins born in a town is p = 0.12. Suppose we randomly select 100 women from this town who give birth in the next year. Which is the best description of the shape for the sampling distribution of ?

approximately Normal

The weights of gala apples follow a Normal distribution with a mean of 140 grams and a standard deviation of 12 grams. The owner of an apple orchard randomly selects 5 apples from the harvest and records the mean weight. What is the shape of the distribution of the sample mean for all possible random samples of size 5 from this population?

approximately Normal

Movie critics claim that 68% of adults and 79% of teenagers would recommend seeing the newest action movie. Suppose random samples of 43 adults and 52 teenagers are selected. Let and be the sample proportions of adult and teenage moviegoers, respectively, who would recommend this movie. Which of the following is the correct shape and justification of the sampling distribution of ?

approximately Normal because the expected numbers of successes and failures for each sample are all at least 10

The salaries of professional baseball players are heavily skewed right with a mean of $3.2 million and a standard deviation of $2 million. A baseball analyst randomly selects 40 athletes and records the mean salary. Which of the following best describes the sampling distribution of all possible samples of size 40?

approximately Normal with a mean of 3.2 million and a standard deviation of 0.32 million

The prices of houses in the US is strongly skewed to the right with a mean of $383,500 and a standard deviation of $289,321. A real estate agent takes a random sample of 30 houses and records the mean price. What is the best description for the sampling distribution?

approximately Normal with a mean of 383,500 and a standard deviation of 52,823