M.A18.38
Interpret the parameters in a linear or exponential function in terms of a context.
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):
They want to use these results to carry out a test of independence. Assume that all conditions for inference were met.
What is the value of the test statistic for their test?
| 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 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):
They want to use these results to carry out a test of independence. Assume that all conditions for inference were met.
What is the value of the test statistic for their test?
| 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 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):
They want to use these results to carry out a test of independence. Assume that all conditions for inference were met.
What is the value of the test statistic for their test?
| 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 test of independence. Assume that all conditions for inference were met.
What is the value of the test statistic for their test?
Khan Academy ResourcesIntro to slopeSlope formulaSlope reviewSlope-intercept form reviewSlope-intercept introSlope from two pointsSlope-intercept from two pointsSlope from graphSlope-intercept equation from graphSlope from equationWorked example: slope from graphConverting to slope-intercept formSlope of a line: negative slopeWorked example: slope from two pointsSlope of a horizontal lineSlope & direction of a linePositive & negative slopeSlope from equationWorked examples: slope-intercept introIntro to slope
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