Statistics: Confidence Intervals & Hypothesis Testing

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Questions and Answers

What would be your conclusion if a 95% confidence interval for the difference (underclassmen - upperclassmen) is (-209.800, -17.700)?

There is statistically significant evidence that the population mean rent for upperclassmen is higher than for underclassmen.

Is there statistically significant evidence that the population proportion of Americans who believe we are spending too little on improving the education system was lower in 1988 than in 2008 if the 95% confidence interval for p1 - p2 is (-0.11, -0.03)?

Yes, there is statistically significant evidence.

What is it called when comparing means from dependent samples?

Comparing means from dependent samples.

What does a 95% confidence interval of (-21, -6) for the difference in mean blood pressure between treatment and control groups suggest?

We are 95% confident that the average blood pressure of those who follow the diet is 6 to 21 points lower than those who do not follow the diet. Signup and view all the answers

What is the correct decision if the test statistic for weight loss is 3.45?

We have strong statistically significant evidence to show the population mean weight loss was greater than zero. Signup and view all the answers

What conclusion can we draw if a 95% confidence interval for the difference in mean shelf life of doughnuts is (-0.7, 0.1)?

We are unable to conclude if there is a difference in the average shelf life of the two brands. Signup and view all the answers

What type of analysis is used when comparing two means from independent samples?

Two means from independent samples. Signup and view all the answers

What type of analysis is performed to determine whether there is a correlation between two categorical variables such as sex and blood type?

Chi-squared test of independence. Signup and view all the answers

The closer r is to 0, the weaker is the linear association between the variables.

True Signup and view all the answers

The value of the correlation is always between 0 and 1.

False Signup and view all the answers

What is the null hypothesis for a chi-squared test of independence between sex and blood type?

Ho: there is no association between sex and blood type. Signup and view all the answers

What does a negative value for correlation describe?

A negative linear line. Signup and view all the answers

What is the definition of confidence interval?

Used to estimate the value of a parameter from sample data. Signup and view all the answers

What is sampling distribution?

The distribution of values taken from all random samples. Signup and view all the answers

What is hypothesis testing?

Evaluate a statement about a parameter/prove it. Signup and view all the answers

What is the common interpretation of a 90% confidence interval of (38.4, 41.6)?

We are 90% confident that the mean time of delay for all flights is between 38.4 and 41.6 minutes. Signup and view all the answers

What is the margin of error of a confidence interval of the population mean dependent on?

The sample size increases. Signup and view all the answers

Which variable has the strongest linear association with the number of wins?

Runs allowed. Signup and view all the answers

What can be concluded if the correlation between the total box office receipts and total number of nominations won is 0.49?

Weak linear association in a positive direction. Signup and view all the answers

For the variables time spent on homework and exam grade, which is the response variable and which is the explanatory variable?

Time spent on homework: explanatory, Exam grade: response. Signup and view all the answers

What are the variables and units in the regression analysis predicting electricity usage based on size?

Amount of electricity used is y and size is x. Signup and view all the answers

In a chi-squared test of independence, what is the response variable when investigating car color and accident history?

Whether the car has been in an accident. Signup and view all the answers

Study Notes

Confidence Intervals & Hypothesis Testing

A 95% confidence interval of (-209.800, -17.700) indicates upperclassmen pay significantly more in rent than underclassmen.
A confidence interval of (-0.11, -0.03) shows a significant decrease in the proportion of Americans believing education spending is too low from 1988 to 2008.
Dependent samples are used when comparing means of paired observations, such as leg strength.
A 95% confidence interval for blood pressure difference (-21, -6) indicates a significant reduction when following a diet.
A test statistic of 3.45 suggests strong evidence that the average weight loss in a diet program is greater than zero.
In a shelf life study, a confidence interval of (-0.7, 0.1) signals insufficient evidence of a difference between two brands of doughnuts.

Samples & Data Types

To compare resting heart rates of runners and bikers, use independent samples of two means.
For heart disease prevalence in caffeinated drinkers, the analysis involves two independent proportions.
To assess walking distance between Europeans and Americans, comparing means from independent samples is appropriate.

Regression & Correlation

In a regression analysis predicting electricity usage, larger homes are expected to consume more electricity, indicating a positive slope.
A correlation of 0.49 suggests a weak positive linear association between box office receipts and nominations for best picture.
Time spent exercising and height shows no association in younger individuals aged 18-32.
Correlation strengths indicate weaker relationships as values approach zero, not confined between 0 and 1.

Chi-Square Tests

For associations between categorical variables (e.g., sex and blood type), a chi-squared test of independence is conducted, with a null hypothesis asserting no association.
The chi-squared statistic equals zero when all observed counts match expected counts.
As sample size increases, the margin of error in confidence intervals decreases.

General Concepts

Confidence intervals estimate parameter values from sample data.
Hypothesis testing evaluates claims about population parameters, like the mean significantly differing from a set value.
A t-distribution is often utilized when working with small sample sizes.

Miscellaneous Associations

A positive association between two quantitative variables indicates an increasing trend, while a negative correlation reflects a decreasing trend.
A positive correlation exists when sales of ice cream correlate with temperature, highlighting environmental factors in consumer behavior.

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Description

This quiz covers the concepts of confidence intervals and hypothesis testing in statistics. It includes examples of confidence intervals, comparisons of means, and interpretations of test statistics. Suitable for students learning about statistical methods and data analysis.