Is Goblins free for teachers?

Yes. Goblins offers a generous free tier that includes 1 live feedback assignment per week, insights on student mastery and replays, and the ability to upload your own content. The Max plan adds unlimited assignments, superadaptive mode, grade exports, standards growth reports, and SSO/LMS integration, with per-student pricing for schools and districts.

How does Goblins work?

Three simple steps: (1) Share an assignment from thousands of standards-aligned topics using a share code. (2) Students speak and draw their thinking naturally, and Goblins responds with Socratic questioning that sounds just like their teacher. (3) Teachers get real-time formative insights showing what students struggle with and suggestions to inform instruction.

Does Goblins prevent cheating?

Yes. Goblins uses a purpose-trained AI model that evaluates cheating signals in real time. It can detect when students are copying answers, using external tools inappropriately, or not genuinely working through problems. Copy-pasting answers is also blocked.

Can I use my own voice with Goblins?

Yes. Teachers can record their voice and take a selfie to create a custom 3D avatar in about 30 seconds. Students then hear help in their own teacher's voice and see a familiar face, making the experience more personal and effective.

What math levels does Goblins cover?

Goblins covers math from Grade 5 through AP Calculus, including thousands of standards-aligned topics. Teachers can also upload their own content for custom assignments at any level.

Is Goblins FERPA compliant?

Yes. Goblins is FERPA and state compliant. Student data privacy and security are a top priority.

Does Goblins support English Language Learners?

Yes. Goblins supports 30+ languages so teachers don't have to translate every worksheet. It is especially helpful for ELL students who need accessible math instruction in their native language.

A1.36.a

Aggregate data from several groups to find an overall association between two categorical variables.

Example Problems

A retailer wondered whether preferred payment method depended on age group. They surveyed a random sample of 270 customers. Here are the outcomes and partial results of a chi-square test (expected counts appear below observed counts):

Age Group	Cash	Card	Mobile	Total
Under 30	20	40	30	90
(Expected)	25	45	20
Age 30–54	25	70	20	115
(Expected)	31.9	57.5	25.6
Age 55+	30	25	10	65
(Expected)	18.1	32.5	14.4
Total	75	135	60	270

They want to use these results to carry out a

\chi^2

test of independence. Assume that all conditions for inference were met.

What is the value of the test statistic for their test?

A nutrition researcher wondered whether preference for spicy food was related to diet type. They surveyed a random sample of 210 adults. Here are the outcomes and partial results of a chi-square test (expected counts appear below observed counts):

Diet Type	Likes spicy	Does not like spicy	Not sure	Total
Vegetarian	20
(29.1), 30
(22.3), 10
(8.6), 60
Omnivore	70
(58.3), 35
(44.6), 15
(17.1), 120
Vegan	12
(14.6), 13
(11.1), 5
(4.3), 30
Total	102	78	30	210

They want to use these results to carry out a

\chi^2

test of independence. Assume that all conditions for inference were met.

What is the value of the test statistic for their test?

A city council wondered whether residents' recycling habits differed by housing type. They surveyed a random sample of 180 residents. Here are the outcomes and partial results of a chi-square test (expected counts appear below observed counts):

Category	Apartment	Single-family	Condo	Total
Recycles regularly (observed)	50	60	20	130
Recycles regularly (expected)	54.2	54.2	21.7
Does not recycle regularly (observed)	25	15	10	50
Does not recycle regularly (expected)	20.8	20.8	8.3
Total	75	75	30	180

They want to use these results to carry out a

\chi^2

test of independence. Assume that all conditions for inference were met.

What is the value of the test statistic for their test?

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