LAST KHAN EVER

A newspaper report claims that 30%30%30, percent of all tea-drinkers prefer green tea to black tea. Leo is the office manager at a company with thousands of employees.

...equal to 30%30%30, percent.

Amanda

p=0.1336

The National Sleep Foundation recommends that teenagers aged 141414 to 171717 years old get at least 888 hours of sleep per night for proper health and wellness.

...less than 8 hours.

According to a very large poll in 2015, about 90%90%90, percent of homes in California had access to the internet. Market researchers want to test if that proportion is now higher, so they take a random sample of 100100100 homes in California and find that 969696 of them have access to the internet.

2

A school counselor heard that teenagers sleep an average of 999 hours per night on the weekend. The counselor wants to test if this figure holds true for students at their school, so they take a random sample of students and ask them about their weekend sleep habits.

A

Kellen was testing H0:μ=0H0​:μ=0H, start subscript, 0, end subscript, colon, mu, equals, 0 versus Ha:μ>0Ha​:μ>0H, start subscript, start text, a, end text, end subscript, colon, mu, is greater than, 0 with a sample of 888 observations. Her sample mean was 3.13.13, point, 1and her sample standard deviation was 1.21.21, point, 2. Assume that the conditions for inference were met.

A

A large school district knows that 75%75%75, percent of students in previous years rode the bus to school. Administrators wondered if that figure was still accurate, so they took a random sample of n=80n=80n, equals, 80 students and found that p^=65%p^​=65%p, with, hat, on top, equals, 65, percent of those sampled rode the bus to school.

B

A poll from a previous year showed that 10%10%10, percent of smartphone owners relied on their data plan as their primary form of internet access. Researchers were curious if that had changed, so they tested H0:p=10%H0​:p=10%H, start subscript, 0, end subscript, colon, p, equals, 10, percent versus Ha:p≠10%Ha​:p​=10%H, start subscript, start text, a, end text, end subscript, colon, p, does not equal, 10, percent, where ppp is the proportion of smartphone owners who rely on their data plan as their primary form of internet access.

C

A company that produces cranberries knows that about 7%7%7, percent of its cranberries are bruised in the bagging process. They changed their bagging method, and they were curious if the proportion of cranberries bruised was different.

Yes, because 0.004<0.010.004<0.010, point, 004, is less than, 0, point, 01.

A large university is curious if they should build another cafeteria. They plan to survey a sample of their students to see if there is strong evidence that the proportion interested in a meal plan is higher than 40%40%40, percent, in which case they will consider building a new cafeteria.

c

A manufacturer knows that 2%2%2, percent of its microchips are produced with a certain defect. They decide to change their process to make it more efficient, and they want to test if the new process has the same defect rate or not.

c

Samuel was testing H0:μ=12H0​:μ=12H, start subscript, 0, end subscript, colon, mu, equals, 12 versus Ha:μ>12Ha​:μ>12H, start subscript, start text, a, end text, end subscript, colon, mu, is greater than, 12 with a sample of 888 observations. His test statistic was t=2.411t=2.411t, equals, 2, point, 411. Assume that the conditions for inference were met.

c

Elliot read a report from a previous year saying that 6%6%6, percent of adults in his city biked to work. He wanted to test whether this had changed, so he took a random sample of 240240240 adults in his city to test H0:p=0.06H0​:p=0.06H, start subscript, 0, end subscript, colon, p, equals, 0, point, 06 versus Ha:p≠0.06Ha​:p​=0.06H, start subscript, start text, a, end text, end subscript, colon, p, does not equal, 0, point, 06, where ppp is the proportion of adults in Elliot's city that bike to work.

e

Fay read an article that said 26%26%26, percent of Americans can speak more than one language. She was curious if this figure was higher in her city, so she tested H0:p=0.26H0​:p=0.26H, start subscript, 0, end subscript, colon, p, equals, 0, point, 26 vs. Ha:p>0.26Ha​:p>0.26H, start subscript, start text, a, end text, end subscript, colon, p, is greater than, 0, point, 26, where ppp represents the proportion of people in her city that can speak more than one language.

p=0.0336

A website streams movies and television shows to its subscribers. Employees know that the average time a user spends per session on their website is 222 hours. The website changed its design, and they wanted to know if the average session length was longer than 222 hours. They randomly sampled 505050 users and found that their session lengths had a mean of 2.752.752, point, 75 hours and a standard deviation of 1.551.551, point, 55 hours.

t=2.75-2/1.55

A quality control engineer is testing the battery life of a new smartphone. The company is advertising that the battery lasts 242424 hours on a full-charge, but the engineer suspects that the battery life is actually less than that. They take a random sample of 505050 of these phones to see if their average battery life is significantly less than 2424

​H0​:μ=24 hours Ha​:μ<24 hours​ type ii error-b

Adam is a golfer who thinks that his drives have an average length of more than 200 m200 m200, start text, space, m, end text. He decided to test H0:μ=200 mH0​:μ=200 mstart text, H, end text, start subscript, 0, end subscript, colon, mu, equals, 200, start text, space, m, end text versus Ha:μ>200 mHa​:μ>200 mstart text, H, end text, start subscript, start text, a, end text, end subscript, colon, mu, is greater than, 200, start text, space, m, end text using a sample of 494949 drives. His sample mean distance was 208 m208 m208, start text, space, m, end textand his sample standard deviation was 25 m25 m25, start text, space, m, end text.

2.24

It is commonly said that 10%10%10, percent of people are left-handed, but Lilianna suspected that a higher proportion of art students at her university are left-handed. To test this theory, she took a sample of 150150150 art students and found that p^=14%p^​=14%p, with, hat, on top, equals, 14, percent of the sample was left-handed.

C

Miriam was testing H0:μ=18H0​:μ=18H, start subscript, 0, end subscript, colon, mu, equals, 18 versus Ha:μ<18Ha​:μ<18H, start subscript, start text, a, end text, end subscript, colon, mu, is less than, 18 with a sample of 777 observations. Her test statistic was t=−1.9t=−1.9t, equals, minus, 1, point, 9. Assume that the conditions for inference were met.

C

t is commonly said that 10%10%10, percent of people are left-handed, but Lilianna suspected that a higher proportion of art students at her university are left-handed. To test this theory, she took a sample of 150150150 art students and found that p^=14%p^​=14%p, with, hat, on top, equals, 14, percent of the sample was left-handed.

C

A fair coin should land showing tails with a relative frequency of 50%50%50, percent in a long series of flip

H0​:p=50% Ha​:p>50%​

Fernanda runs a large bowling league. Altogether, members of the league have played thousands of individual games over the course of the season. She suspects that the league average score is greater than 150150150 per game.

a,c

A healthcare provider saw that 48%48%48, percent of their members received their flu shot in a recent year. The healthcare provider tried a new advertising strategy in the following year, and they took a sample of members to test if the proportion who received their flu shot had changed.

​H0​:p=48% Ha​:p​=48%​

Roshanda suspects that teachers in her state, on average, have less than 555 years experience. She wants to take a random sample of teachers to determine if there is convincing evidence to support her suspicion.

​H0​:μ=5 yearsHa​:μ<5 years​

A city had an unemployment rate of 7%7%7, percent. The mayor pledged to lower this figure and supported programs to decrease unemployment

​H0​:p=7% Ha​:p<7%​

According to a large poll in a previous year, about 80%80%80, percent of homes in a certain county had access to high-speed internet. Market researchers wondered if that proportion had changed, so they took a random sample of 646464homes from that county and found that 484848 of them had access to high-speed internet.

-1 p=≈0.0409

Hunter was testing H0:μ=100H0​:μ=100H, start subscript, 0, end subscript, colon, mu, equals, 100 versus Ha:μ<100Ha​:μ<100H, start subscript, start text, a, end text, end subscript, colon, mu, is less than, 100 with a sample of 505050 observations. His sample mean was 103103103 and his sample standard deviation was 555. Assume that the conditions for inference were met.

D-p(t)

Jake heard that spinning—rather than flipping—a penny raises the probability above 50%50%50, percent that the penny lands showing heads. He tests this by spinning 101010 different pennies 101010 times each, so he's willing to treat these spins as a random sample. In his 100100100 spins, the penny landed showing "heads" in 686868 spins. He wants to use these results to test H0:p=0.50H0​:p=0.50H, start subscript, 0, end subscript, colon, p, equals, 0, point, 50 versus Ha:p>0.50Ha​:p>0.50H, start subscript, start text, a, end text, end subscript, colon, p, is greater than, 0, point, 50, where ppp is the true proportion of spins that a penny would land showing "heads".

3.6

A city planner will consider adding electric vehicle charging stations if she is convinced that more than 15%15%15, percent of residents would use them. She will survey a sample of residents to test the hypotheses H0:p≤15%H0​:p≤15%H, start subscript, 0, end subscript, colon, p, is less than or equal to, 15, percent vs. Ha:p>15%Ha​:p>15%H, start subscript, start text, a, end text, end subscript, colon, p, is greater than, 15, percent, where ppp is the true proportion of residents that would use the stations.

A

A restaurant chain wants to hire roughly the same proportion of men and women for entry-level positions. Management took an SRS of 121212 entry-level hires from over 100010001000 entry-level hires in a recent month. They want to use the sample data to test H0:p=0.5H0​:p=0.5H, start subscript, 0, end subscript, colon, p, equals, 0, point, 5 versus Ha:p≠0.5Ha​:p​=0.5H, start subscript, start text, a, end text, end subscript, colon, p, does not equal, 0, point, 5, where ppp is the proportion of all entry-level hires that month who were women.

a,c

Lian read a report claiming that 9%9%9, percent of people in her country were classified as living in poverty. She wonders if this holds true in her large city, so she obtains an SRS of 505050 people from her city. She wants to use the sample data to test H0:p=0.09H0​:p=0.09H, start subscript, 0, end subscript, colon, p, equals, 0, point, 09 versus Ha:p≠0.09Ha​:p​=0.09H, start subscript, start text, a, end text, end subscript, colon, p, does not equal, 0, point, 09, where ppp is the proportion of all people in her city that are classified as living in poverty.

a,c

A campaign manager for a political candidate released a series of advertisements criticizing the opposing candidate in an upcoming election. The opposing candidate previously had the support of 45%45%45, percent of voters, so the manager wants to test H0:p=0.45H0​:p=0.45H, start subscript, 0, end subscript, colon, p, equals, 0, point, 45 versus Ha:p<0.45Ha​:p<0.45H, start subscript, start text, a, end text, end subscript, colon, p, is less than, 0, point, 45, where ppp is the proportion of voters that support the opposing candidate.

b

Aurelia has a coin that she suspects is unfair. She wants to test H0:p=0.5H0​:p=0.5H, start subscript, 0, end subscript, colon, p, equals, 0, point, 5 versus Ha:p≠0.5Ha​:p​=0.5H, start subscript, start text, a, end text, end subscript, colon, p, does not equal, 0, point, 5, where ppp is the proportion of flips that this coin lands showing heads.

c- 2*p(z)

A manufacturer makes chocolate squares that have a target weight of 8 g8 g8, start text, space, g, end text. Quality control engineers sample chocolate squares from a batch to test the hypotheses H0:μ=8 gH0​:μ=8 gH, start subscript, 0, end subscript, colon, mu, equals, 8, start text, space, g, end text vs. Ha:μ≠8 gHa​:μ​=8 gH, start subscript, start text, a, end text, end subscript, colon, mu, does not equal, 8, start text, space, g, end text, where μμmuis the true mean weight of the chocolate squares in that batch.

c-n equals 50

A ketchup company regularly receives large shipments of tomatoes. For quality control purposes, they take a sample of tomatoes from each shipment. If the sample shows convincing evidence that more than 8%8%8, percent of the tomatoes in the entire shipment are bruised, then the company will request a new shipment of tomatoes. So the company tests H0:p=0.08H0​:p=0.08H, start subscript, 0, end subscript, colon, p, equals, 0, point, 08 versus Ha:p>0.08Ha​:p>0.08H, start subscript, start text, a, end text, end subscript, colon, p, is greater than, 0, point, 08, where ppp is the proportion of tomatoes in the entire shipment that are bruised.

p=0.2266

Quintin read a report claiming that 4%4%4, percent of police officers in the US have had a formal complaint filed against them. Quintin suspects that this figure is higher in his state. He obtains a random sample of records for 500500500officers from the approximately 20,00020,00020, comma, 000 officers in his state. He wants to use these data to test H0:p=0.04H0​:p=0.04H, start subscript, 0, end subscript, colon, p, equals, 0, point, 04versus Ha:p>0.04Ha​:p>0.04H, start subscript, start text, a, end text, end subscript, colon, p, is greater than, 0, point, 04, where ppp is the proportion of officers in Quintin's state who have had a formal complaint filed against them.

a,b,c

Asha owns a car-wash and is trying to decide whether or not to purchase a vending machine so customers can buy coffee while they wait. She'll get the machine if she's convinced that more than 30%30%30, percent of her customers would buy coffee. She plans on taking a random sample of nnn customers and asking them whether or not they would buy coffee from the machine, and she'll then do a significance test using α=0.05α=0.05alpha, equals, 0, point, 05 to see if the sample proportion who say "yes" is significantly greater than 30%30%30, percent.

b

Elliot read a report from a previous year saying that 6%6%6, percent of adults in his city biked to work. He wants to test whether this has changed, so he is going to take a random sample of adults in his city and see what percent of them bike to work.

b

Jasper was testing H0:μ=36H0​:μ=36H, start subscript, 0, end subscript, colon, mu, equals, 36 versus Ha:μ≠36Ha​:μ​=36H, start subscript, start text, a, end text, end subscript, colon, mu, does not equal, 36 with a sample of 161616 observations. His test statistic was t=2.4t=2.4t, equals, 2, point, 4. Assume that the conditions for inference were met.

b

Donated blood is tested for infectious diseases and other contaminants. Since most donated blood is safe, it saves time and money to test batches of donated blood rather than test individual samples. A certain test is performed to see if a certain toxin is present, and the entire batch is discarded if the toxin is detected. This is similar to using a null and an alternative hypothesis to determine whether to discard or keep the batch. The hypotheses being tested could be stated as:

b-The batch is discarded when it actually doesn't contain the toxin. type ii error-D

A significance test is going to be performed using a significance level of α=0.05α=0.05alpha, equals, 0, point, 05. Suppose that the null hypothesis is actually true.

b-The probability of a Type I error would decrease.

West High School requires that teachers assign students an average of 3.53.53, point, 5 hours of homework each night. The school board believes that teachers are assigning students less than this, so they take a random sample of West High School students to determine if there is convincing evidence to support their suspicion.

b-​H0​:μ=3.5 hoursHa​:μ<3.5 hours​ t=1.5

A business knows that 30%30%30, percent of its customers are less than 252525 years old. The business wants to increase this percentage, so they create a marketing campaign that targets this age group. After the campaign, they take a random sample of 505050 customers to test H0:p=0.30H0​:p=0.30H, start subscript, 0, end subscript, colon, p, equals, 0, point, 30 versus Ha:p>0.30Ha​:p>0.30H, start subscript, start text, a, end text, end subscript, colon, p, is greater than, 0, point, 30, where ppp is the proportion of this business's customers who are less than 252525 years old after the marketing campaign.

c

A campaign manager for a political candidate released a series of advertisements criticizing their opponent in an upcoming election. Their opponent previously had the support of 45%45%45, percent of voters, and the campaign manager wants to sample voters to test if support for their opponent has decreased.

c

Evelynn was testing H0:μ=52H0​:μ=52H, start subscript, 0, end subscript, colon, mu, equals, 52 versus Ha:μ<52Ha​:μ<52H, start subscript, start text, a, end text, end subscript, colon, mu, is less than, 52 with a sample of 999 observations. Her test statistic was t=−2.83t=−2.83t, equals, minus, 2, point, 83. Assume that the conditions for inference were met.

c

The mayor of a town sees an article that claims the national unemployment rate is 8%8%8, percent. They suspect that the unemployment rate is lower in their town, so they plan to take a sample of 200200200 residents to test if the proportion of residents that are unemployed in the sample is significantly lower than the national rate.

c

The ages of workers in a certain industry are approximately normally distributed with a mean of 303030 years and a standard deviation of 3.53.53, point, 5 years. A recruiter wondered if that held true for workers in a certain state. The recruiter took a random sample of n=3n=3n, equals, 3 of these workers from the state, and the mean age of the workers in the sample was xˉ=26xˉ=26x, with, \bar, on top, equals, 26 years.

c p-value≈0.07

A large poll showed that 42%42%42, percent of adults approved of their nation's prime minister. Margot wants to test if it is now lower, so she takes a random sample of 1,0001,0001, comma, 000 adults in that nation and finds that 390390390—or 39%39%39, percent of those sampled—approved of the prime minister.

d

According to a very large poll in 2015, about 90%90%90, percent of homes in California had access to the internet. Market researchers want to test if that proportion is now higher, so they take a random sample of 1,0001,0001, comma, 000 homes in California and find that 920920920—or 92%92%92, percent of homes sampled—have access to the internet.

d

Abdullah is a quality control expert at a factory that paints car parts. He knew that the factory was painting 20%20%20, percentof the parts with an error, so he made a change in the painting process. After the change, he wanted to test H0:p=0.2H0​:p=0.2H, start subscript, 0, end subscript, colon, p, equals, 0, point, 2 versus Ha:p<0.2Ha​:p<0.2H, start subscript, start text, a, end text, end subscript, colon, p, is less than, 0, point, 2, where ppp is the proportion of parts that the factory was painting with an error.

p=0.1056

A fast-food company advertises that the pre-cooked weight for its half-pound burgers is, on average, 0.5 lbs0.5 lbs0, point, 5, start text, space, l, b, s, end text. Jayda is in charge of a quality control test that involves weighing a sample of burgers to see if if the sample mean weight is significantly different than 0.5 lbs0.5 lbs0, point, 5, start text, space, l, b, s, end text. She takes a random sample of 303030 burgers and finds a mean weight of 0.54 lbs0.54 lbs0, point, 54, start text, space, l, b, s, end text and a sample standard deviation of 0.02 lbs0.02 lbs0, point, 02, start text, space, l, b, s, end text.

t=30​0.02​0.54−0.5​

Jules works on a small team of 404040 employees. Each employee receives an annual rating, the best of which is "exceeds expectations." Management claimed that 10%10%10, percent of employees earn this rating, but Jules suspected it was actually less common. She obtained an anonymous random sample of 101010 ratings for employees on her team. She wants to use the sample data to test H0:p=0.1H0​:p=0.1H, start subscript, 0, end subscript, colon, p, equals, 0, point, 1 versus Ha:p<0.1Ha​:p<0.1H, start subscript, start text, a, end text, end subscript, colon, p, is less than, 0, point, 1, where ppp is the proportion of all employees on her team who earned "exceeds expectations."

A

A quality control expert at a pretzel factory took a random sample of 101010 bags from a batch of over 500500500 bags and measured the amount of pretzels in each bag in the sample. The target amount is 440 g440 g440, start text, space, g, end text, and they want to test if the mean amount is on target or not.

D-​H0​:μ=440 g Ha​:μ​=440 g​

A restaurant advertises that its burritos weigh 250 g250 g250, start text, space, g, end text. A consumer advocacy group doubts this claim, and they obtain a random sample of these burritos to test if the mean weight is significantly lower than 250 g250 g250, start text, space, g, end text.

c-H0​:μ=250 gHa​:μ<250 g​ c-242-250/12

A city had an unemployment rate of 7%7%7, percent. The mayor pledged to lower this figure and supported programs to decrease unemployment. A group of citizens wanted to test if the unemployment rate had actually decreased, so they obtained a random sample of citizens to see what proportion of the sample was unemployed.

d

A factory fills bottles with a beverage, and each bottle is supposed to contain 500 mL500 mL500, start text, space, m, L, end text. Norah is in charge of a quality control test that involves measuring the amounts in a sample of bottles to see if the sample mean amount is significantly different than 500 mL500 mL500, start text, space, m, L, end text. She takes a random sample of 161616 bottles and finds a mean amount of 497 mL497 mL497, start text, space, m, L, end text and a sample standard deviation of 6 mL6 mL6, start text, space, m, L, end text.

-2

Francisco was testing H0:μ=10H0​:μ=10H, start subscript, 0, end subscript, colon, mu, equals, 10 versus Ha:μ>10Ha​:μ>10H, start subscript, start text, a, end text, end subscript, colon, mu, is greater than, 10 with a sample of 666 observations. His test statistic was t=1.952t=1.952t, equals, 1, point, 952. Assume that the conditions for inference were met.

B

Amelie was testing H0:μ=15H0​:μ=15H, start subscript, 0, end subscript, colon, mu, equals, 15 versus Ha:μ<15Ha​:μ<15H, start subscript, start text, a, end text, end subscript, colon, mu, is less than, 15 with a sample of 101010 observations. Her test statistic was t=−2.77t=−2.77t, equals, minus, 2, point, 77. Assume that the conditions for inference were met.

B-0.0109

Caterina was testing H0:μ=0H0​:μ=0H, start subscript, 0, end subscript, colon, mu, equals, 0 versus Ha:μ≠0Ha​:μ​=0H, start subscript, start text, a, end text, end subscript, colon, mu, does not equal, 0 with a sample of 666 observations. Her test statistic was t=2.75t=2.75t, equals, 2, point, 75. Assume that the conditions for inference were met.

C .04

Jamarion was testing H0:μ=45H0​:μ=45H, start subscript, 0, end subscript, colon, mu, equals, 45 versus Ha:μ<45Ha​:μ<45H, start subscript, start text, a, end text, end subscript, colon, mu, is less than, 45 with a sample of 555 observations. His sample mean was 404040 and his sample standard deviation was 333. Assume that the conditions for inference were met.

C p(t)

Daisy was testing H0:μ=33H0​:μ=33H, start subscript, 0, end subscript, colon, mu, equals, 33 versus Ha:μ>33Ha​:μ>33H, start subscript, start text, a, end text, end subscript, colon, mu, is greater than, 33 with a sample of 111111 observations. Her test statistic was t=1.368t=1.368t, equals, 1, point, 368. Assume that the conditions for inference were met.

D

Nicolas was testing H0:μ=24H0​:μ=24H, start subscript, 0, end subscript, colon, mu, equals, 24 versus Ha:μ≠24Ha​:μ​=24H, start subscript, start text, a, end text, end subscript, colon, mu, does not equal, 24 with a sample of 121212 observations. His test statistic was t=−1.79t=−1.79t, equals, minus, 1, point, 79. Assume that the conditions for inference were met.

d

A company advertises that its cans of caviar each contain 100 g100 g100, start text, space, g, end text of their product. A consumer advocacy group doubts this claim, and they obtain a random sample of 888 cans to test if the mean weight is significantly lower than 100 g100 g100, start text, space, g, end text. They calculate a sample mean weight of 99 g99 g99, start text, space, g, end text and a sample standard deviation of 0.9 g0.9 g0, point, 9, start text, space, g, end text.

d-t=99-100

The mayor of a town read an article that claimed the national unemployment rate was 8%8%8, percent. They suspected that the unemployment rate was lower in their town, so they took a sample of 128128128 residents to test H0:p=0.08H0​:p=0.08H, start subscript, 0, end subscript, colon, p, equals, 0, point, 08versus Ha:p<0.08Ha​:p<0.08H, start subscript, start text, a, end text, end subscript, colon, p, is less than, 0, point, 08, where ppp is the proportion of residents that are unemployed.

D-Fail to reject H0H0​H, start subscript, 0, end subscript. This isn't enough evidence to conclude that the town's unemployment rate is lower than 8%8%8, percent.

A business knows that 3%3%3, percent of its orders that are shipped to customers arrive late. The business changes its system for processing orders, and they want to test if the proportion of orders that arrive late has changed. They take a sample of 500500500 orders and find that 202020—or 4%4%4, percent of orders sampled—arrived late. Let

a

A local pizza store knows the mean amount of time it takes them to deliver an order is 454545 minutes after the order is placed. The manager has a new system for processing delivery orders, and they want to test if it changes the mean delivery time. They take a sample of delivery orders and find their mean delivery time is 484848 minutes.

a

Elliot read a report from a previous year saying that 6%6%6, percent of adults in his city biked to work. He wanted to test whether this had changed, so he took a random sample of 240240240 adults in his city to test H0:p=0.06H0​:p=0.06H, start subscript, 0, end subscript, colon, p, equals, 0, point, 06 versus Ha:p≠0.06Ha​:p​=0.06H, start subscript, start text, a, end text, end subscript, colon, p, does not equal, 0, point, 06, where ppp is the proportion of adults in Elliot's city that bike to work.

p=0.0734

Jumbo eggs in Australia, on average, are supposed to weigh 68 g68 g68, start text, space, g, end text. Margot is in charge of a quality control test that involves weighing a sample of eggs to see if if the sample mean weight is significantly different than 68 g68 g68, start text, space, g, end text. She takes a random sample of 100100100 eggs and finds a mean weight of 67 g67 g67, start text, space, g, end text and a sample standard deviation of 1 g1 g1, start text, space, g, end text.

-10

Fernanda runs a large bowling league. She suspects that the league average score is greater than 150150150 per game. She takes a random sample of 363636 game scores from the league data. The scores in the sample have a mean of 156156156 and a standard deviation of 303030.

1.2 cNo, because 0.13>0.050.13>0.050, point, 13, is greater than, 0, point, 05.

A ketchup company regularly receives large shipments of tomatoes. For each shipment that is received, a supervisor takes a random sample of 500500500 tomatoes to see what percent of the sample is bruised and performs a significance test. If the sample shows convincing evidence that more than 10%10%10, percent of the entire shipment of tomatoes is bruised, then they will request a new shipment of tomatoes.

H0​:p=0.1 Ha​:p>0.1​

A restaurant owner installed a new automated drink machine. The machine is designed to dispense 530 mL530 mL530, start text, space, m, L, end text of liquid on the medium size setting.

H0​:μ=530 mL Ha​:μ>530 mL​

A class did an experiment to see if students could taste water and identify bottled water versus tap water. Each student was presented with three cups of water—one of which contained bottled water—and they were directed to identify which cup they thought contained bottled water. The class wants to test if they correctly identified the bottled water significantly better than they would have done by simply guessing.

a

Abdullah is a quality control expert at a factory that paints car parts. He knows that the factory paints 20%20%20, percent of parts with an error. He recommended a change in the painting process, and he wants to see if this error rate has changed. He takes a random sample of 303030 of the 100100100 total parts painted one day to test H0:p=0.2H0​:p=0.2H, start subscript, 0, end subscript, colon, p, equals, 0, point, 2 versus Ha:p≠0.2Ha​:p​=0.2H, start subscript, start text, a, end text, end subscript, colon, p, does not equal, 0, point, 2, where ppp is the proportion of all parts that the factory painted with the error that day.

a

Leanne manages an apartment building that houses 100100100 residents. She read an article claiming that 15%15%15, percent of people in their state were senior citizens, and she thought that it may be higher for residents in her building. She took a random sample of 202020 residents, and she wants to test H0:p=0.15H0​:p=0.15H, start subscript, 0, end subscript, colon, p, equals, 0, point, 15 versus Ha:p>0.15Ha​:p>0.15H, start subscript, start text, a, end text, end subscript, colon, p, is greater than, 0, point, 15, where ppp is the proportion of residents that are senior citizens.

a

read a report saying that 49%49%49, percent of teachers in the United States were members of a labor union. She wants to test whether this holds true for teachers in her state, so she is going to take a random sample of these teachers and see what percent of them are members of a union.

a

A large poll showed that 24%24%24, percent of US voters identified as Republicans. Mabel is a political analyst who suspects that this figure is lower in her state. She plans on taking a random sample of 250250250 voters in her state to test H0:p=0.24H0​:p=0.24H, start subscript, 0, end subscript, colon, p, equals, 0, point, 24 versus Ha:p<0.24Ha​:p<0.24H, start subscript, start text, a, end text, end subscript, colon, p, is less than, 0, point, 24, where ppp is the proportion of voters in Mabel's state who identify as Republican.

a,b,c

Alden claims he is psychic. His friend designs a game to test his psychic abilities. The friend will present Alden with four different cards and ask him to identify which card has a certain picture on it. Only one card has the correct picture, and the friend will randomly assign the position of the correct picture on each trial. So they're willing to assume that Alden has a 25%25%25, percent chance of guessing correctly on any given trial.

a,b,c

According to a report from the United States Environmental Protection Agency, burning one gallon of gasoline typically emits about 8.9 kg8.9 kg8, point, 9, start text, space, k, g, end text of CO2CO2​start text, C, O, end text, start subscript, 2, end subscript. A fuel company wants to test a new type of gasoline designed to have lower CO2CO2​start text, C, O, end text, start subscript, 2, end subscript emissions. Here are their hypotheses:

b

Catalina read a report saying that the average daily high temperature in Buenos Aires a few years ago was 18.2∘C18.2∘C18, point, 2, degrees, start text, C, end text. She believes that last year was warmer than this. To test her belief, she takes a simple random sample of 202020 days from last year and records the daily high temperature on each chosen day. In Buenos Aires, the average daily high temperature temperature in a year is reported to be 18.2∘C18.2∘C18, point, 2, degrees, start text, C, end text. Catalina believes that last year was warmer than usual. In order to test her belief, she takes a simple random sample of 202020days from last year, and records the daily high temperature on each chosen day. She finds that the sample mean temperature is 19.1∘C19.1∘C19, point, 1, degrees, start text, C, end text and the sample standard deviation is 7.9∘C7.9∘C7, point, 9, degrees, start text, C, end text.

c b. t=

A campaign manager for a political candidate released a series of advertisements criticizing the opposing candidate in an upcoming election. The opposing candidate previously had the support of 45%45%45, percent of voters, so the manager wants to test H0:p=0.45H0​:p=0.45H, start subscript, 0, end subscript, colon, p, equals, 0, point, 45 versus Ha:p<0.45Ha​:p<0.45H, start subscript, start text, a, end text, end subscript, colon, p, is less than, 0, point, 45, where ppp is the proportion of voters that support the opposing candidate.

c. p(z)

Amanda read a report saying that 49%49%49, percent of teachers in the United States were members of a labor union. She wanted to test whether this was true in her state, so she took a random sample of 300300300 teachers from her state to test H0:p=0.49H0​:p=0.49H, start subscript, 0, end subscript, colon, p, equals, 0, point, 49 versus Ha:p≠0.49Ha​:p​=0.49H, start subscript, start text, a, end text, end subscript, colon, p, does not equal, 0, point, 49, where ppp is the proportion of teachers in her state who are members of a labor union. The sample results showed 180180180 teachers were members of a labor union. Assuming that the conditions for inference have been met, identify the correct test statistic for Amanda's significance test. Choose 1 answer:

d

Fay read an article that said 26%26%26, percent of Americans can speak more than one language. She wants to test if this figure is higher in the city she lives, so she plans on taking a sample of people to see what proportion of them speak more than one language.

d

Ricky is testing soil for a contaminant at a building site. He'll take action to stop construction if there's strong evidence that the soil has more than 400400400 parts per million (ppm) of the contaminant. He plans on using soil from n=30n=30n, equals, 30 randomly selected locations at the building site. His hypotheses are H0:μ≤400 ppmH0​:μ≤400 ppmH, start subscript, 0, end subscript, colon, mu, is less than or equal to, 400, start text, space, p, p, m, end text and Ha:μ>400 ppmHa​:μ>400 ppmH, start subscript, start text, a, end text, end subscript, colon, mu, is greater than, 400, start text, space, p, p, m, end text, where μμmu is the mean amount of the contaminant in the soil at this site.

d type ii-bnat

A public opinion survey investigated whether a majority of adults supported a tax increase to help fund the local school system. A random sample of 200200200 adults showed that 120120120 of those sampled supported the tax increase. Researchers want to use these results to test H0:p=0.5H0​:p=0.5H, start subscript, 0, end subscript, colon, p, equals, 0, point, 5 versus Ha:p>0.5Ha​:p>0.5H, start subscript, start text, a, end text, end subscript, colon, p, is greater than, 0, point, 5, where ppp is the true proportion of adults that support the tax increase.

d p(z)

Nala wrote an app that has both a desktop and a mobile version. She wonders which platform is more common, so she takes an SRS of 888 users from over 100010001000 active users. She wants to use the sample data to test H0:p=0.5H0​:p=0.5H, start subscript, 0, end subscript, colon, p, equals, 0, point, 5 versus Ha:p≠0.5Ha​:p​=0.5H, start subscript, start text, a, end text, end subscript, colon, p, does not equal, 0, point, 5, where ppp is the proportion of all users who are using the mobile version.

a,c

Mr. Jensen told his class that he plays basketball frequently, and he claimed that he could make 80%80%80, percent of his free-throw attempts. The class suspected that Mr. Jensen was actually less than an 80%80%80, percent free-throw shooter. To test their theory, they had Mr. Jensen shoot a series of 404040 free-throws. He made p^=60%p^​=60%p, with, hat, on top, equals, 60, percent of them.

A

A professor gives a multiple choice exam where each question has five choices. The professor decides not to count a question against students if the class as a whole does significantly worse on the question than they would have done simply by guessing. In other words, the teacher tests H0:p=0.20H0​:p=0.20H, start subscript, 0, end subscript, colon, p, equals, 0, point, 20 versus Ha:p<0.20Ha​:p<0.20H, start subscript, start text, a, end text, end subscript, colon, p, is less than, 0, point, 20for each question, where ppp is the proportion of students who would correctly answer the question.

-1.5

Abdullah is a quality control expert at a factory that paints car parts. He knows that 20%20%20, percent of parts have an error in their painting. He recommended a change in the painting process, and he wanted to see if this error rate had changed. He took a random sample of 400400400 parts painted in a month and found that 606060 had an error.

-2.5

Rory suspects that teachers in his school district have less than 555 years of experience on average. He decided to test H0:μ=5H0​:μ=5start text, H, end text, start subscript, 0, end subscript, colon, mu, equals, 5 versus Ha:μ<5Ha​:μ<5start text, H, end text, start subscript, start text, a, end text, end subscript, colon, mu, is less than, 5 using a sample of 252525 teachers. His sample mean was 444 years and his sample standard deviation was 222 years.

-2.5

Reports say that the mean birth weight of babies of European heritage is 3.5 kg3.5 kg3, point, 5, start text, space, k, g, end text. Marta wants to perform a significance test to see if this holds true in her nation.

...equal to 3.5 kg3.5 kg3, point, 5, start text, space, k, g, end text.

Lena is a college basketball player who has made 75%75%75, percent of the free-throws she has attempted in her career. She decided to practice a new technique for shooting her free-throws.

...not equal to 75%75%

In 2011, 51%51%51, percent of cell phone owners in a country reported that their cell phone was a smartphone. The following year, the researchers wanted to test H0:p=0.51H0​:p=0.51H, start subscript, 0, end subscript, colon, p, equals, 0, point, 51 versus Ha:p>0.51Ha​:p>0.51H, start subscript, start text, a, end text, end subscript, colon, p, is greater than, 0, point, 51, where ppp is the proportion of cell phone owners in that country who have a smartphone.

.0537 p

The mayor of a town read an article that claimed the national unemployment rate was 8%8%8, percent. They suspected that the unemployment rate was lower in their town, so they took a sample of 128128128 residents to test H0:p=0.08H0​:p=0.08H, start subscript, 0, end subscript, colon, p, equals, 0, point, 08versus Ha:p<0.08Ha​:p<0.08H, start subscript, start text, a, end text, end subscript, colon, p, is less than, 0, point, 08, where ppp is the proportion of residents that are unemployed.

0.0838 p

Carlos is designing a video game, and he's concerned that one of the levels is too difficult. He will redesign the level if he has convincing evidence that it takes the average player longer than 454545 minutes to complete the level. He plans on recruiting players to play the level until they complete it, and he'll use their completion times to perform a significance test.

C-​H0​:μ=45 minutesHa​:μ>45 minutes​

An employee at an aquarium monitors how much their sea otters eat. The amount of food a particular otter eats daily is approximately normally distributed with a mean of 171717 pounds and a standard deviation of 111 pound. They suspected this otter was not eating enough, so they took a random sample n=10n=10n, equals, 10 days and observed a sample mean of xˉ=16.5xˉ=16.5x, with, \bar, on top, equals, 16, point, 5 pounds of food per day.

D

Ellie read an article claiming that 10%10%10, percent of people in her county were senior citizens, and she thought that it may be higher for residents in her city. She took a random sample of 225225225 people from her city and found that 363636 of them were senior citizens.

3 p=0.0588

A quality control expert at a drink bottling factory took a random sample of bottles from a batch and measured the amount of liquid in each bottle in the sample. The amounts in the sample had a mean of 503 mL503 mL503, start text, space, m, L, end text and a standard deviation of 5 mL5 mL5, start text, space, m, L, end text. They want to test if this is convincing evidence that the mean amount for bottles in this batch is different than the target value of 500 mL500 mL500, start text, space, m, L, end text.

A

A large nationwide poll recently showed an unemployment rate of 9%9%9, percent in the US. The mayor of a local town wonders if this national result holds true for her town, so she plans on taking a sample of her residents to see if the unemployment rate is significantly different than 9%9%9, percent in her town.

A-She concludes the town's unemployment rate is not 9%9%9, percent when it actually is.

Evie read an article that said 6%6%6, percent of teenagers were vegetarians, but she thinks it's higher for students at her large school. To test her theory, Evie took a random sample of 252525 students at her school, and 20%20%20, percent of them were vegetarians.

D

A healthcare provider saw that 48%48%48, percent of their members received their flu shot in a recent year. The healthcare provider tried a new advertising strategy in the following year, and they took a sample of members to test if the proportion who received their flu shot had changed. What are appropriate hypotheses for their significance test? Choose 1 answer:

B

A nutritionist suspected that her company's clients had below average cholesterol. They obtained a random sample of 888 clients of the same age and gender. These clients had a mean cholesterol level of xˉ=4.28 mmol/Lxˉ=4.28 mmol/Lx, with, \bar, on top, equals, 4, point, 28, start text, space, m, m, o, l, slash, L, end text (millimoles per liter).

B .05

According to a large poll in a previous year, about 80%80%80, percent of homes in a certain county had access to high-speed internet. The following year, researchers wanted to test H0:p=0.8H0​:p=0.8H, start subscript, 0, end subscript, colon, p, equals, 0, point, 8 versus Ha:p<0.8Ha​:p<0.8H, start subscript, start text, a, end text, end subscript, colon, p, is less than, 0, point, 8, where ppp is the proportion of homes in this county with high-speed internet access.

B-At the α=0.10α=0.10alpha, equals, 0, point, 10 significance level, they should conclude that less than 80%80%80, percent of homes in the county had access to high-speed internet.

A company sells cans of caviar that say they each contain 100 g100 g100, start text, space, g, end text of product. A consumer advocacy group suspects that the company is under-filling these cans. The group obtains a sample of cans and measures how much product is in each can. They calculate a sample mean of 99 g99 g99, start text, space, g, end text and a sample standard deviation of 1 g1 g1, start text, space, g, end text. They will take further action if this is significantly lower than the advertised amount.

B-H0​Ha​​:μ=100 g:μ<100 g​

A class in New Zealand found a report suggesting that teenagers' heights in New Zealand are approximately normally distributed with a mean of 160 cm160 cm160, start text, space, c, m, end text and a standard deviation of 15 cm15 cm15, start text, space, c, m, end text. They thought the mean height at their school was probably larger, so they took a random sample of n=24n=24n, equals, 24students. The mean height of students in their sample was xˉ=166.5 cmxˉ=166.5 cmx, with, \bar, on top, equals, 166, point, 5, start text, space, c, m, end text.

C

Elian heard that spinning a coin on a flat surface—rather than flipping it—made the probability of the coin landing showing "heads" something other than 50%50%50, percent. To test this theory, he spun a nickel a series of 808080 times and observed that p^=60%p^​=60%p, with, hat, on top, equals, 60, percent of the spins landed showing "heads."

C

A pharmaceutical company produces caffeine pills that are each supposed to contain 200 mg200mg200, start text, m, g, end text of caffeine. A quality control expert took a random sample of pills from a batch and measured the amount of caffeine in each pill in the sample. They want to test if the mean amount is significantly different than 200 mg200 mg200, start text, space, m, g, end text.

C-H0:μ=200 mgHa:μ≠200 mg​H0​:μ=200 mgHa​:μ​=200 mg​

Ava read an article claiming that 10%10%10, percent of people in her county were senior citizens, and she wondered if this held true for residents in her city. She took a random sample of 225225225 people from her city to test H0:p=0.10H0​:p=0.10H, start subscript, 0, end subscript, colon, p, equals, 0, point, 10versus Ha:p≠0.10Ha​:p​=0.10H, start subscript, start text, a, end text, end subscript, colon, p, does not equal, 0, point, 10, where ppp is the proportion of people in her city that are senior citizens.

C-No, because 0.06>0.050.06>0.05

A factory produces ball bearings whose diameters are meant to have a mean of 3 mm3 mm3, start text, space, m, m, end text. Suppose that the actual sizes are normally distributed with a mean of 3 mm3 mm3, start text, space, m, m, end text and a standard deviation of 0.2 mm0.2 mm0, point, 2, start text, space, m, m, end text. The overseers took a random sample of n=100n=100n, equals, 100 ball bearings to see if their mean diameter was significantly different than the target. The mean diameter of the ball bearings in the sample was xˉ=2.96 mmxˉ=2.96 mmx, with, \bar, on top, equals, 2, point, 96, start text, space, m, m, end text.

D

An economist read a report that claimed that 60%60%60, percent of residents in her large city owned their homes. She wondered if that figure was still accurate, so she took a random sample of n=50n=50n, equals, 50 residents in the city and observed that p^=70%p^​=70%p, with, hat, on top, equals, 70, percent of those sampled owned their homes.

D

A class found a report suggesting that teenagers' foot lengths are approximately normally distributed with a mean of 23 cm23 cm23, start text, space, c, m, end text and a standard deviation of 2.6 cm2.6 cm2, point, 6, start text, space, c, m, end text. They wondered if this held true at their school, so they took a random sample of n=9n=9n, equals, 9 students. The mean foot length of students in their sample was xˉ=24.6ˉ cmxˉ=24.6ˉ cmx, with, \bar, on top, equals, 24, point, 6, with, \bar, on top, start text, space, c, m, end text.

D .08

A business knows that 30%30%30, percent of its customers are less than 252525 years old. The business wants to increase this percentage, so they create a marketing campaign that targets this age group. They plan on taking a sample of customers after the marketing campaign is complete to test if the proportion of customers in that age group has significantly increased.

D No, because 0.177>0.100.177>0.100, point, 177, is greater than, 0, point, 10.

An economist is curious about the average cost of rent per month in their large city. They take a random sample of 505050 rental properties and find that those properties have a mean cost of $1,710$1,710dollar sign, 1, comma, 710 per month with a standard deviation of about $290$290dollar sign, 290. They plan to use this data to test the hypothesis that the average rent is now higher than the previous year's average of $1,650$1,650dollar sign, 1, comma, 650.

D-H0​Ha​​:μ=$1,650:μ>$1,650​

A business knows that 30%30%30, percent of its customers are less than 252525 years old. The business wants to increase this percentage, so they create a marketing campaign that targets this age group. They want to test H0:p=0.3H0​:p=0.3H, start subscript, 0, end subscript, colon, p, equals, 0, point, 3versus Ha:p>0.3Ha​:p>0.3H, start subscript, start text, a, end text, end subscript, colon, p, is greater than, 0, point, 3, where ppp is the proportion of this business's customers who are less than 252525 years old after the marketing campaign.

E- p(z)

A website streams movies and television shows to its subscribers. Employees know that the average time a user spends per session on the website is 222 hours. The website updated its design, and they take a random sample of users to test if the average session length is now longer than 222 hours. Let μμmu be the average session length with the updated design and xˉxˉx, with, \bar, on top be the average session length from the sample.

H0​:μ=2 hours Ha​:μ>2 hours​

A fast-food company advertises that the pre-cooked weight for its burgers is, on average, 0.2 kg0.2 kg0, point, 2, start text, space, k, g, end text. The company runs a regular quality control test that involves weighing a sample of burgers to see if the burgers are too light or too heavy. If the sample mean weight is significantly different than 0.2 kg0.2 kg0, point, 2, start text, space, k, g, end text, then they recycle the entire batch.

H0​Ha​​:μ=0.2 kg:μ​=0.2 kg​ d