Find a 95% confidence interval for population mean

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SUMMARY

The discussion centers on calculating a 95% confidence interval for the population mean using the t-distribution. Participants identify a typographical error in the notation for the sample mean, where 'x' should be represented as '𝑥̄'. The correct degrees of freedom for the t-distribution are noted as dof1 = 9 and a significance level of dof2 = 0.025, yielding a critical value of 2.262. Overall, the calculation process is confirmed to be accurate aside from the notation issue.

PREREQUISITES
  • Understanding of the t-distribution and its applications
  • Familiarity with confidence intervals and their significance
  • Knowledge of degrees of freedom in statistical analysis
  • Ability to interpret t-distribution tables
NEXT STEPS
  • Study the derivation of the t-distribution and its properties
  • Learn how to calculate confidence intervals using the t-formula
  • Explore advanced topics in statistical inference
  • Review common notation in statistics to avoid typographical errors
USEFUL FOR

Students preparing for statistics examinations, educators teaching statistical concepts, and anyone involved in data analysis requiring confidence interval calculations.

chwala
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Homework Statement
see attached
Relevant Equations
t distribution
I am refreshing on this...

1662157094596.png


I think there is a mistake on the circled part in red...right? not correct symbol for sample mean...This is the part that i need clarity on.

1662157179394.png


The other steps to solution are pretty easy to follow...as long as one knows the t-formula and also the knowledge to interpret the t-distribution table with dof_{1} = ##9## and significance level i.e dof_{2}= ##0.025## that gives us the desired ##2.262##.

cheers
 
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The calculation is fine. The only thing I see wrong is that they wrote x for the sample mean instead of ##\bar x##. Possibly a typo or maybe the author is unable to write this symbol.
 
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Mark44 said:
The calculation is fine. The only thing I see wrong is that they wrote x for the sample mean instead of ##\bar x##. Possibly a typo or maybe the author is unable to write this symbol.
@Mark44 This is from a Further Maths Examination Paper Mark scheme.
 

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