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Chapter 8: Q 20. (page 508)

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 3percentage point margin of error for this poll includes only sampling variability (what they call 鈥渟ampling error鈥�). What other potential sources of error (Gallup calls these 鈥渘on sampling errors鈥�) could affect the accuracy of the 95% confidence interval?

Short Answer

Expert verified

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

01

Given Information

Confidence interval90%,95%are given.

02

a. Effect on Length

If confidence level decreases from 95%to90%, there would be less assurance that confidence interval would have true population parameter. Confidence interval will have less values for true population parameters.

03

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.

04

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.

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Most popular questions from this chapter

Going to the prom Tonya wants to estimate the proportion of seniors in her school who plan to attend the prom. She interviews an SRS of 20of the 750seniors in her school and finds that 36plan to go to the prom.

How confident? The figure shows the result of taking 25SRSs from a Normal population and constructing a confidence interval for the population mean using each sample. Which confidence level鈥攔ole="math" localid="1654197644211" 80%,90%,95%,or99%鈥攄o you think was used? Explain your reasoning.

Do you go to church? The Gallup Poll plans to ask a random sample of adults

whether they attended a religious service in the last 7 days. How large a sample would be required to obtain a margin of error of at most 0.01 in a 99% confidence interval for the population proportion who would say that they attended a religious service?

More online sales Refer to Exercise 35. Calculate and interpret the standard error ofp^=xn for these data.

After deciding on a 95% confidence level, the researcher is deciding between a sample of size n=500 and a sample of size n=1000. Compared with using a sample size of n=500, a confidence interval based on a sample size of n=1000 will be

a. narrower and would involve a larger risk of being incorrect.

b. wider and would involve a smaller risk of being incorrect.

c. narrower and would involve a smaller risk of being incorrect.

d. wider and would involve a larger risk of being incorrect.

e. narrower and would have the same risk of being incorrect.
See all solutions

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