Inference for Quantitative Data: Slopes

Explain the concept of inference in the context of sampling distribution of slopes.

• Inference involves calculating the mean of the sample slopes

• Inference is not relevant in sampling distribution of slopes

• Inference in the context of sampling distribution of slopes involves making conclusions about the population slope based on the sample slope.

• Inference is only applicable to large sample sizes

Discuss the importance of standard error in making inferences from the sampling distribution of slopes.

• Standard error does not affect the width of the confidence interval

• Standard error is only relevant for categorical variables, not continuous ones

• Standard error has no impact on the reliability of the slope estimate

• Standard error is important as it quantifies the precision of the slope estimate and influences the confidence interval width, hypothesis testing, and overall reliability of the inference.

How can confidence intervals be used in inference based on the sampling distribution of slopes?

• Confidence intervals provide a range of plausible values for the population slope based on the sample data and its variability.

• Confidence intervals are calculated based on the mean of the sample, not the slope.

• Confidence intervals are used to determine the exact population slope without any margin of error.

• Confidence intervals are only applicable to categorical data, not slopes.

• A plane ride costs $0.136 (13 cents)

• For every 1 mile flown, the cost goes up  $ 0.136 dollars (13 cents)

• For every 1 mile flown, the cost goes up $74

The table represents a used car salesman's monthly salary including commission made on the sale of cars.  What is the slope and what does it represent?

• The slope is $850/car and it represents the commission per car sold.

• The slope is $425/car and it represents the commission per car sold.

• The slope is $1500 and it represents the monthly salary before commission.

• The slope is $850 and it represents the monthly salary before commission.

• For every 160 meters in elevation there's a decrease of 1 Celsius in temperature

• For every meter of elevation there's a decrease of 1 Celsius in temperature 

• For every  160 meters in elevation there's an increase of 1 Celsius in temperature

• For every 22.5 meters there's a decrease of 1/160 Celsius in temperature.

• A plane ride costs $0.136 (13 cents)

• For every 1 mile flown, the cost goes up  $ 0.136 dollars (13 cents)

• For every 1 mile flown, the cost goes up $74

A veterinarian student tracks the weight of a kitten, in ounces, from the age of 0 to 32 weeks. She graphs the data and determines the line of best fit is y hat = 4.03x + 3.27. What does the slope represent in this situation?

• For every week the kitten ages, we predict the kittens weight to increase by 4.03 ounces

• For every week the kitten ages, the kittens weight to increase by 4.03 ounces

• For every ounce the kitten weighs, we predict the kittens age to increase by 4.03 weeks

• The kitten gains 4.03 ounces a week

If the line of best fit shows the relationship between elevation and average annual temperature in celsius, what does the slope represent? Assume the line of best fit is represented by the equation

• For every 160 meters in elevation there's a decrease of 1 Celsius in temperature

• For every meter of elevation there's a decrease of 1 Celsius in temperature 

• For every  160 meters in elevation there's an increase of 1 Celsius in temperature

• For every 22.5 meters there's a decrease of 1/160 Celsius in temperature.

What does the slope mean in the context of the problem?

• The cost will increase by $1.40 per topping

• The cost will decrease by $1.40 per topping

• The cost will increase by $1.90 per topping

• The cost will decrease by $1.90 per topping