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.

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

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.

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.

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.