MHB Confidence intervals and point estimate problems

Click For Summary
To determine the sample size used in a study with a 99% confidence interval of 152 to 158 and a standard deviation of 10, the calculation involves using the formula for the margin of error, which leads to a sample size of approximately 36. For the second problem, the point estimate of the proportion of students responding "no opinion" can be calculated by dividing the number of "no opinion" responses by the total number of responses, resulting in a proportion of 0.05. The discussions highlight the need for clarity in applying statistical formulas to solve confidence interval and point estimate problems. Participants express a desire for guidance on these calculations, emphasizing a common struggle with understanding statistical concepts. Overall, the thread seeks assistance in navigating these statistical challenges.
colle
Messages
1
Reaction score
0
I am lost on how to do these two problems and can't find info on how to solve them anywhere. If anyone can get me on the right track as to how to start, that would be amazing!

1. A 99% confidence interval for a population mean was reported to be 152 to 158. If the standard deviation is 10, what sample size was used in this study?

2. A survey for a sample of 300 students resulted in 175 yes responses, 110 no responses, and 15 no opinions. What is the point estimate of the proportion in the population who respond "no opinion"?
 
Mathematics news on Phys.org
colle said:
I am lost on how to do these two problems and can't find info on how to solve them anywhere. If anyone can get me on the right track as to how to start, that would be amazing!

1. A 99% confidence interval for a population mean was reported to be 152 to 158. If the standard deviation is 10, what sample size was used in this study?

As reported in...

http://mathhelpboards.com/questions-other-sites-52/unsolved-statistics-questions-other-sites-part-ii-1566-post12072.html#post12072

... is [approximately] $ \text{erfc}\ (x) = .01$ for $x \sim 1.8$ so that is $\displaystyle \frac{10}{\sqrt{n}} = \frac{5}{3} \implies n=36$... Kind regards $\chi$ $\sigma$
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
View full post »

Similar threads

MHB Construct the 99% confidence interval estimate
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Convergence of 2 sample means with 95% confidence
  • · Replies 7 ·
Replies
7
Views
2K
MHB Confidence interval of difference
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Correct understanding of confidence intervals....
  • · Replies 22 ·
Replies
22
Views
3K
Undergrad Is Unbiasedness in Estimation Truly Reflective of Population Parameters?
  • · Replies 9 ·
Replies
9
Views
2K
MHB 95% Confidence Interval for Staying Awake at UMUC
  • · Replies 2 ·
Replies
2
Views
4K
MHB Point Estimate, Margin of Error and Confidence Level
  • · Replies 1 ·
Replies
1
Views
2K
MHB What is the formula for determining the length of a confidence interval?
  • · Replies 4 ·
Replies
4
Views
2K
MHB Estimate the cost for tyres using the mean
  • · Replies 9 ·
Replies
9
Views
2K
MHB Is my calculation of the confidence interval for $\mu$ correct? (Wondering)
  • · Replies 4 ·
Replies
4
Views
2K