Question

Confidence intervals seek to estimate a population parameter with an interval of values calculated from an observed sample statistic. Demonstrate that you understand this concept by describing a situation in which one could use a sample mean or sample proportion to produce a confidence interval as an estimate of a population mean or population proportion. I am asking you to make up a situation where a confidence interval might be computed. Clearly identify the population, sample, parameter, and statistic involved in your example. Choose an appropriate confidence level and compute the interval. Do not use any example that appeared in your book or in class. The population is (describe what the population is, in words) The sample is (describe what the sample is, in words) In my example, I am computing a confidence interval for a The parameter is (describe in words) The statistic is (describe in words, and assign a value to the statistic) The % confidence interval is from to . Finally, explain what this confidence interval means in the context of your example.

Answer 1

(a) Situation:

The mean score of a random sample of 60 students is 145 with SD of 40. To find the 95% confidence limits for the population mean.

(b) Population:

All the students of the College

(c) Sample:

sample of 65 students

(d)

Parameter:

mean score of all students of the College

(e) Statistic:

mean score of 60 students

(f) Confidence level:

= 0.05

(g)

n = 60

= 145

s = 40

95% Confidence interval:

= (134.88,155.12)

Summary:

(i) Population is: score of all students of the college

(ii) Sample is : score of 60 students

(iii) In my example, I am computing a confidence interval for average score of students of the college

(iv) The % confidence interval is from : 1.34 % to 1.55 %

(v) EXPLANATION: If repeated samples are taken and the 95% confidence interval is computed for each sample, 95% of the intervals will contain the population mean.