Statistics 10B Free Response Flashcards

Questions and Answers

What is the procedure to construct and interpret a 90% confidence interval for the difference in the proportion of cockroaches that die on each surface?

Use a 2-proportion z-interval with x1 = 25, x2 = 18, and both n1 and n2 = 36.

Based only on the interval (0.00807, 0.38082), is there a significant difference in the proportion of cockroaches that die on each surface?

Yes, because zero is not in the interval, indicating evidence of a difference.

What additional information is needed to confirm that the conditions for the test have been met?

We need to know if the sample is Normal and information about symmetry and outliers since the sample size is less than 30.

What is the formula to calculate the test statistic for the given test?

<p>t = (µ₂ - µ₁) / (√((σ₂)²/n₂) + (σ₁²/n₁))</p> Signup and view all the answers

How do you find the degrees of freedom (df) when calculating the test statistic?

<p>Subtract 1 from the smaller n-value.</p> Signup and view all the answers

Study Notes

Confidence Interval for Proportions

Objective is to estimate the difference in proportions of cockroaches dying on plasterboard (pp) versus glass (pg) with 90% confidence.
A two-proportion z-interval is used for calculation.
Random assignment is crucial for validity.
Experiment design ensures independent groups of cockroaches.
Sample size (n) is 36 for both groups.
Success counts are x1 = 25 (glass) and x2 = 18 (plasterboard).
Calculations indicate n(x/n) and n(1-(x/n)) should be greater than 10.
Statistical software can compute the interval, requiring inputs for successes and sample sizes.

Significance of Proportion Difference

The calculated 90% confidence interval is (0.00807, 0.38082).
Since the interval does not include zero, it suggests a significant difference in cockroach mortality rates based on surface type.
This implies evidence of a treatment effect between glass and plasterboard surfaces.

Checking Normality Conditions

Verification needed regarding the normality of the sample; sample sizes of 10 do not meet n ≥ 30 criteria.
Lack of information on the population's normality requires assessment of data symmetry and outliers.
Understanding distribution shape is crucial for the validity of results.

Test Statistic and P-Value Calculation

Test statistic is calculated using the formula: t = (µ₂ - µ₁) / (√(σ₂²/n₂ + σ₁²/n₁)).
Degrees of freedom (df) calculated by subtracting 1 from the smaller sample size.
A t-table is referenced using the calculated t-value and df to determine the corresponding probabilities.
Final probability must fall between two calculated outcomes, providing context for significance testing.

Description

This quiz features flashcards that help learners construct and interpret confidence intervals, specifically focusing on the difference in proportions related to a cockroach study. It encompasses key concepts like random assignment, independent groups, and the use of a 2-proportion z-interval. Perfect for students preparing for advanced statistics assessments.