Question

1. A random sample of 49 children with working mothers showed that they were absent from school an average of 6 days per term with a standard deviation of 1.8 days.

1. Write down the equation you should use to construct the confidence interval for the average number of days absent per term for all the children.
2. Determine a 98% confidence interval estimate for the average number of days absent per term for all the children.
3. Determine a 95% confidence interval estimate for the average number of days absent per term for all the children.
4. Discuss why 98% and 95% confidence intervals are different.

Answer 1

Given Information

• Since the population standard deviation is not known, the % Confidence Interval is given by
  
  
  
• 
  The 98% Confidence Interval is given by
  
  
  
  
• 
  The 95% Confidence Interval is given by
  
  
  
  
• As we increase the confidence of claiming the interval, the interval increases. This is quite obvious, as to be more confident of something, we have to relax the boundaries, to accept more values. Hence, with increase of confidence level, the confidence interval relaxes it's boundaries.
  
  

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