stats

A phlebotomist measured the cholesterol levels of a sample of \[25\] people between the ages of \[35\] and \[44\] years old. Here are summary statistics for the samples:

a

A health researcher was curious if women in India lived longer on average than men in India. They obtained data from a random sample of \[216\] records of people in India. Here is a summary of their lifespans (in years):

a

Amelie has balloons from two different brands. She wants to test the durability of each brand by measuring the volume of water that can be pumped into the balloons before they burst. Here is a summary of the results:

a

An exercise scientist wanted to test the effectiveness of a new program designed to increase the flexibility of senior citizens. They recruited participants and rated their flexibility according to a standard scale before starting the program. The participants all went through the program and had their flexibility rated again after a month. The scientist wants to test if the flexibility ratings are significantly higher after a month of the program. Assume that these participants can be considered a representative sample and that all other necessary conditions for inference were met.

a

At basketball tryouts, Jeremiah will shoot a \[1\]-point shot, a \[2\]-point shot, and a \[3\]-point shot one after the other. The table below shows Jeremiah's probability of making each shot:

a

Gordon grows a new variety and an older variety of bananas. He took a random sample of each variety to test if the new variety weighs more, on average, than the older variety. Here are the results (weights shown are in grams):

a

José is designing a game that involves flipping \[3\] fair coins and counting how many land showing "heads". Here is the sample space showing the possible outcomes when flipping \[3\] coins:

a

Katie grows two varieties of pears—Bosc and Anjou. She took a sample of each variety to test if their mean weights were significantly different. Here is a summary of her results (weights are shown in grams):

a

Kayla is designing a video game. When a player defeats a certain enemy, there is a \[30\%\] probability that enemy drops an object for the player to claim, and a \[70\%\] probability they drop nothing. Suppose a player defeats \[2\] of these enemies, and we categorize them as dropping an object (D) or not (N). Here is a sample space showing the possible outcomes:

a

Luc is playing a trivia game with multiple choice questions. He runs out of time and needs to guess on the last \[2\] questions. Each question has \[4\] multiple choice options (\[1\] of which is correct), so Luc has a \[\dfrac{1}4\] probability of correctly guessing the answer to any given question. We categorize each guess as correct (C) or incorrect (I). Here is a sample space showing the possible outcomes:

a

A teacher wonders if students who listen to music while taking an exam will score higher than students who don't listen to music. They have \[10\] students listen to music and \[10\] other students not listen to music on the same exam. The teacher wants to use a two-sample \[t\] test to see if there is a significant difference between the average scores of the groups.

a, b, and c

A board game uses a spinner like one below, where \[0\], \[1\], \[2\], and \[3\] are all equally likely.

b

A zoologist was curious if elephants living in captivity had a different average lifespan than elephants living in the wild. They obtained separate samples of each type of elephant. Here is a summary of the lifespans (in years):

b

Ciara is designing a game that involves flipping \[4\] fair coins and counting how many land showing "heads". Here is the sample space showing the possible outcomes when flipping \[4\] coins:

b

Dan, an office manager, wants to replace the catering company in charge of the office lunch. The new company promises the same quality of food at a smaller cost. Before he makes the switch between companies, Dan sends out a satisfaction survey of the old company to a sample of \[30\] employees. After a month with the new company, he sends out the same satisfaction survey to the same group of employees. Each survey produces a satisfaction rating.

b

Having more cars running on a roller coaster shortens wait times but slows the ride. The owners asked two samples of \[24\] customers to rate how exciting the roller coaster was on a scale from \[1\] to \[7\]. The sample who rode the coaster when there were \[4\] cars gave the coaster an average rating of \[5.7\] points with a standard deviation of \[0.6\] points. The sample who rode when there were \[3\] cars gave an average rating of \[6.1\] points with a standard deviation of \[0.5\] points. The owners wants to estimate the difference in the mean excitement ratings for the different numbers of cars on the roller coaster \[(4\, \text{cars}-3\,\text{cars})\]. Assume that the conditions for inference have been met.

b

A software company creates two versions of a new feature and releases one or the other version to each of their beta testers. A week later, they ask the beta testers to rate the feature on a scale of \[1\] to \[7\]. The ratings are left-skewed. They plan to conduct a two-sample \[t\] test to see whether there is a significant difference between the mean ratings based on which version the tester received.

b and c

A board game has players roll two dice — one \[6\]-sided and one \[4\]-sided — and subtract the numbers showing on the faces. The game only looks at non-negative differences. For example, if a player rolls a \[1\] and a \[4\], the difference is \[3\]. Here is the sample space showing the possible (equally likely) outcomes of a single roll:

c

A sociologist studying fertility in Malaysia and South Korea wanted to compare how many babies, on average, women in each country have. The sociologist obtained a random sample of women from each country. Here is a summary of the number of babies for the women in each sample:

c

Esteban suspects that right-handed participants have an unfair advantage on a memory test because the input device uses the right hand. He selects a random sample of existing test data and summarizes it in the following table.

c

Gabriella collects cards, and she knows there's a \[50\%\] probability that any given pack contains a certain card that she wants. She plans on buying packs of cards until she gets this particular card, but she can afford at most \[3\] packs. Here's a table summarizing the possible outcomes:

c

Jillian plays darts professionally. Suppose that she has a \[20\%\] probability of hitting the bullseye when she aims for it in any given throw. Jillian is going to attempt \[2\] throws at the bullseye. We can categorize each throw as hitting the bullseye (B) or not (N). Here is a sample space showing the possible outcomes:

c

Members of a parenting organization want to use a two-sample \[t\] test to determine whether the average tuition for private schools in their state is significantly different for high school students than for elementary students. They plan to take tuition estimates from random samples of \[10\] schools serving each level.

c

Suppose that there is a \[10\%\] probability that any given person in a population is left-handed, and a \[90\%\] probability they are not left-handed. Say we randomly select \[2\] people and categorize them as left-handed (L) or not (N). Here is a sample space showing the possible outcomes:

c

The managers of a fast food chain want their products to be as similar as possible across locations. They suspect that the burgers at their Albuquerque branch have bigger patties than the burgers at the Santa Fe branch, so they take a sample of \[7\] patties from each restaurant and measure their weights (in grams):

c

Yuna grows two varieties of pears—Bosc and Anjou. She took a sample of each variety to test if their average caloric contents were significantly different. Here is a summary of her results:

c

A media streaming service allows users to watch shows on their smartphones or tablets. An analyst wondered if users watching on tablets spend more time watching shows than users on smartphones. They took a separate random sample of each type of user to see how many hours they watched in total last month. Here is a summary of the results:

d

Linn wanted to determine how much of a difference it makes to use a certain product to treat the water she used to irrigate her corn crops. She used a randomized block design experiment to select parts of her land to irrigate with untreated lake water and others to irrigate with treated water. Then she measured the heights of the plants in those areas. Here are summary statistics for her experiment:

d

Shelby is skeptical of her friend's claim that Gerald's Café has much stronger coffee (in terms of caffeine content) than Sabine's Beans does. So Shelby takes a random sample of large coffees from both shops, and measures the amount of caffeine content in each coffee. Here is a summary of the results:

e