Question

 

Question 4

What are some of the assumption to use to determine a confidence interval for the population mean with an unknown standard deviation? Provide examples.

Question 5

Define the confidence interval for a population proportion and indicate how it is estimated with an example.

Question 6

What are the factors that determine the sample size? How is sample size calculated for estimating the population mean? Provide examples.

Answer 1

Sol 4:

The assumptions for constructing a confidence interval for the population mean when the population standard deviation is unknown are:

1)We have a simple random sample.

2)Either the sample size is large (>30) or the population is approximately normal.

Sol 5:

The population parameter which is estimated by using sample statistic is termed as point estimate. But, how far the sample statistic can estimate the given population is specified by the confidence interval. A range of values such that the population parameter can likely to contain for the given confidence level is termed as the confidence interval. In other words, it can be defined as an interval estimate of the population parameter which is calculated for the given data based on a point estimate and for the given confidence level.

Moreover, the confidence level indicates the possibility that the confidence interval can contain the population parameter. Usually, the confidence level is denoted by a . The value is chosen by the researcher. Some of the most common confidence levels are 90%, 95%, and 99%.

Interpretation :

It is 95% confident that the population parameter (mean, proportion, standard deviation) lies within the confidence interval. Also, there may be one-sided or two-sided confidence interval.

Diagrammatic representation of one-sided confidence interval:

Thus, there may either an lower bound or upper bound for one-sided confidence interval.

Diagrammatic representation of two-sided confidence interval:

Thus, there is an upper bound and lower bound for a two-sided confidence interval.

Example :

For population mean, the 95% confidence interval is calculated by using the formula is given below:

Sample size (n) less than 30:

Sample size (n) greater than or equal to 30: