Question

1. Explain the difference between the point estimate and interval estimate (confidence interval).

2. What is margin of error?

3. Why must we use the point estimate pˆ (sample proportion) in the calculation of the standard error when producing a confidence interval for p (population proportion)?

4. Assamplesizeincreases,whatistheeffectonthemarginoferror? Why?

5. Asconfidencelevelincreases,whatistheeffectonthemarginof error? Why?

6. Whatdetermineswhethertouseat-distributionoranormaldistribution for finding a confidence interval for μ ?

7. What is the condition to use Chi-squared distribution when estimating the population standard deviation?

8. Describe the shape of a chi-squared distribution. How does the shape change as the number of degrees of freedom increases? When degree of freedom is larger than 30, what does the shape look like?

Answer 1

1)

Point estimation gives us a particular value as an estimate of the population parameter

Interval estimation gives us a range of values which is likely to contain the population parameter. This interval is called a confidence interval.

2)

Margin of error = Critical value x Standard deviation of the statistic

The margin of error measures accuracy

3)

When the true population proportion P is not known, the standard deviation of the sampling distribution cannot be calculated. Under these circumstances, use the standard error. The standard error (SE) can be calculated from the equation below.

SE_p = sqrt[ p * ( 1 - p ) / n ] * sqrt[ ( N - n ) / ( N - 1 ) ]

where p is the sample proportion, n is the sample size, and N is the population size. When the population size at least 20 times larger than the sample size, the standard error can be approximated by:

SE_p = sqrt[ p * ( 1 - p ) / n ]

4)

sample size increase, margin of error decreases

because standard deviation of statistic decreases

5)

as confidence level increases, margin of error increases

because critical value increase as we increase confidence level