Question

A manufacturing company produces electric insulators. You define the variable of interest as the strength of the insulators. If the insulators break when in use, a short circuit is likely. To test the strength of the insulators, you carry out destructive testing to determine how much force is required to break the insulators. You measure force by observing how many pounds are applied to the insulator before it breaks. You collect the force data for 30 insulators selected for the experiment and find out that the mean force is 1670. Based on that, you construct an interval from 1570 to 1770 and claim that this interval can be one of the 95% intervals around the sample means that contain the population mean force. This interval is

Check all that apply.

1. a statistic

2. a confidence interval

3. an interval estimate

4. a parameter

5. a point estimate

  
The reason that we want to develop a confidence interval for the population mean is because

(Only two correct answers)
Answers:  
1. the value of the sample mean varies from sample to sample.
2. the sampling distribution of the sample mean is normally distributed.
3. the sample mean is an efficient estimate of the population mean.
4. the sample mean is an unbiased estimate of the population mean.
5. the standard error of the sample mean is an efficient estimate of the population error.

Answer 1

​​​​​​This interval is: (options 1, 2 and 3 are correct).

"1. a statistic (because it is based on the sample, i.e., a sample measure).

2. a confidence interval (because the interval is for a given confidence level of 95%)

3. an interval estimate (because it gives the range of of values instead of a single point estimate)".

It's not a parameter because parameter is a population measure, i.e., measured by taking all the values of the population.

It's not a point estimate because it doesn't give a single value but gives a range of values.

The reason that we want to develop a confidence interval for the population mean is because: (option 5 is correct).

"5. the standard error of the sample mean is an efficient estimate of the population error (i.e, population standard deviation)".

And the standard error is used in computing the confidence interval estimate.

For a given sample size of n, the standard error of the mean is, SE =

The Standard Error, SE is the actual or estimated standard deviation of the sampling distribution of the sample statistic(here, sample mean) in case of normal probability distribution. Sample size of 30 is a large sample and for large samples, Central Limit Theorem (CLT) says that the sampling distribution of the sample mean can be approximated by a normal probability distribution.