Chapter 12: Further Statistics 2: Confidence Intervals and Tests Using the t-Distribution

A-level Further MathsFurther Statistics 1 & 25 topicsHigher

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Further Statistics 2: Confidence Intervals and Tests Using the t-Distribution: Edexcel Further Maths Optional Long-Answer Questions

Examiner-style long-answer practice with automatic marking, improvement advice and ProofCoach tracking.

4 questions32 marks64 min

standard / hard / synoptic

8 marksfindstandardEdexcel

FS12-1 Find the required result for Further Statistics 2: Confidence Intervals and Tests Using the t-Distribution. Given Two independent samples have n1 = 9, mean 18.4, s1 = 2.1 and n2 = 11, mean 16.9, s2 = 1.8. Use use pooled variance and a two-sample t confidence interval. (8 marks)

Define the variables, diagram labels, distribution parameters or algorithm table columns needed.
Substitute the concrete values from the question before simplifying.
Show the intermediate line that earns the main method mark.
Complete the calculation, table trace or proof and state the final result.

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8 marksshow thathardEdexcel

FS12-2 Show that pooled variance uses

8s1^{2}

10s2^{2}

over 18 for Further Statistics 2: Confidence Intervals and Tests Using the t-Distribution. Start from Two independent samples have n1 = 9, mean 18.4, s1 = 2.1 and n2 = 11, mean 16.9, s2 = 1.8. (8 marks)

Define the variables, diagram labels, distribution parameters or algorithm table columns needed.
Substitute the concrete values from the question before simplifying.
Show the intermediate line that earns the main method mark.
Complete the calculation, table trace or proof and state the final result.

0 characters

Write your answer first, then mark it.

8 marksdeterminehardEdexcel

FS12-3 Determine the requested value in this structured Further Statistics 2: Confidence Intervals and Tests Using the t-Distribution problem: construct a 95% interval for the difference in means. Use the same data: Two independent samples have n1 = 9, mean 18.4, s1 = 2.1 and n2 = 11, mean 16.9, s2 = 1.8. (8 marks)

Define the variables, diagram labels, distribution parameters or algorithm table columns needed.
Substitute the concrete values from the question before simplifying.
Show the intermediate line that earns the main method mark.
Complete the calculation, table trace or proof and state the final result.

0 characters

Write your answer first, then mark it.

8 markshencesynopticEdexcel

FS12-4 Hence use the result pooled variance uses

8s1^{2}

10s2^{2}

over 18 to complete the extension for Further Statistics 2: Confidence Intervals and Tests Using the t-Distribution: construct a 95% interval for the difference in means. (8 marks)

Define the variables, diagram labels, distribution parameters or algorithm table columns needed.
Substitute the concrete values from the question before simplifying.
Show the intermediate line that earns the main method mark.
Complete the calculation, table trace or proof and state the final result.

0 characters

Write your answer first, then mark it.

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11. Further Statistics 2: Further Hypothesis Tests

End of Further Statistics 1 & 2

Key learning objectives

Understand the key principles behind Further Statistics 2: Confidence Intervals and Tests Using the t-Distribution.
Apply these ideas to exam-style questions.
Recall the essential definitions and key terms.