Question

Losing weight Refer to Exercise 6.

a. Explain what would happen to the length of the interval if the confidence level was decreased to $90\%$.

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

c. As Gallup indicates, the $3$percentage point margin of error for this poll includes only sampling variability (what they call “sampling error”). What other potential sources of error (Gallup calls these “non sampling errors”) could affect the accuracy of the 95% confidence interval?

Short answer

a. Length of interval decreases.

b. Tripling the sample size will result in narrower confidence interval than original confidence interval.

c. Under coverage bias, Selection, Non response bias.

Step-by-step solution

Given Information

Confidence interval$90\%,95\%$are given.

a. Effect on Length

If confidence level decreases from $95\%\text{to}90\%$, there would be less assurance that confidence interval would have true population parameter. Confidence interval will have less values for true population parameters.

b. Comparison of confidence interval on tripling the sample size and original confidence interval.

Tripling sample size implies increase in sample size. It will give more details regarding population resulting in more accurate estimates. Hence, the estimate will be close to correct value and confidence interval will be narrower.

c. Potential Sources of Error

The errors can be:

• Under Coverage Bias/ Selection: It exclude portion of population.
• Response bias: It results in value different from correct value.
• Non Response Bias: It is result of not containing data for everybody in sample.