Find a 95% confidence interval for population mean

In summary, the conversation discusses a mistake on a math exam paper where the symbol for the sample mean was written incorrectly as "x" instead of "##\bar x##". The other steps to the solution are deemed easy to follow as long as one knows the t-formula and how to interpret a t-distribution table. The mistake in the paper is acknowledged and it is suggested that it may be a typo or a limitation of the author.
  • #1
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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  • #2
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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  • #3
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.
 

FAQ: Find a 95% confidence interval for population mean

1. What is a confidence interval?

A confidence interval is a range of values that is likely to contain the true population parameter with a certain level of confidence. In this case, we are looking for a 95% confidence interval, which means that there is a 95% chance that the true population mean falls within this range.

2. Why do we need to find a 95% confidence interval for population mean?

Finding a confidence interval allows us to estimate the true population mean based on a sample. This is important because it helps us make inferences about the entire population without having to collect data from every single individual.

3. How is a 95% confidence interval calculated?

A 95% confidence interval is calculated using the sample mean, sample standard deviation, sample size, and a critical value from a t-distribution table. The formula is: sample mean ± (critical value * (sample standard deviation / √sample size)).

4. What does a 95% confidence interval tell us about the population mean?

A 95% confidence interval tells us that there is a 95% chance that the true population mean falls within this range. It also gives us an idea of how precise our estimate is, as a wider interval means there is more uncertainty about the true population mean.

5. How do we interpret a 95% confidence interval?

We can interpret a 95% confidence interval as follows: "We are 95% confident that the true population mean falls between the lower and upper bounds of this interval." This means that if we were to repeat the study multiple times, 95% of the time the true population mean would fall within this range.

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