Question

Prayer in school Refer to Exercise 5.

a. Explain what would happen to the length of the interval if the confidence level were increased to $99\%$.

b. How would a $95\%$confidence interval based on double the sample size compare to the original $95\%$interval?

c. The news article goes on to say: “The theoretical errors do not take into account

additional errors resulting from the various practical difficulties in taking any survey of public opinion.” List some of the “practical difficulties” that may cause errors which are not included in the $\pm 3$ percentage point margin of error.

Short answer

a. The length of interval increases.

b. On basis of double the sample size, confidence interval is narrower than original confidence interval.

c. It is not accountable for errors made during date of sample collection.

Step-by-step solution

Given Information

Confidence levels of$95\%,99\%$are given.

a. To explain effect on length of interval

If confidence level increases from $95\%\text{to}99\%$, confidence that interval is having true parameter of population increases.

It has more possible values of true population parameter.

Hence, length of interval increases.

b. To explain how would a 95%confidence interval based on double the sample size compare to the original 95% interval.

Sample size increases when sample size is doubled. Hence, it will have more data about population and more correct estimates would be obtained.

Estimates would be more close to true value.

Hence., confidence interval needs to be narrower.

c. To determine that not included in ±3 percent point margin of error.

Margin of error contains possible variations only. It is not responsible for the errors made while collecting sample date.

Possible bias are:

• Selection will exclude portion of population.
• Response bias will use procedure showing values different from correct value.
• Not containing data for everybody will cause no response bias.