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Chapter 8: Q 8.61 (page 331)

Formula 8.2on page 327provides a method for computing the sample size required to obtain a confidence interval with a specified confidence level and margin of error. The number resulting from the formula should be rounded up to the nearest whole number.

a. Why do we want a whole number?

b. Why do we round up instead of down?

Short Answer

Expert verified

a. We want a whole number as the sample cannot be in fraction.

b. This is due to the fact that margin of error is obtained from the smallest value of the sample size.

Step by step solution

01

Given Information

It is given that the number obtained from the formula rounded up to nearest whole number.

02

a. Explanation of need of whole number

  • We want a whole number as number of observation cannot be in fraction or part of member of population.
  • Hence, number of observation should be a whole number.
03

b. Why round up instead of down 

  • We round up instead of down because from the smallest value of sample size, required value of margin of error is obtained.
  • Rounded up provide us number that is larger than the actual sample size.

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Most popular questions from this chapter

M\&Ms. In the article "Sweetening Statistics-What M\&M's Can Teach Us" (Minitab Inc., August 2008), M. Paret and E. Martz discussed several statistical analyses that they performed on bags of M\&Ms. The authors took a random sample of 30 small bags of peanut M\&Ms and obtained the following weights, in grams (g).

a. Determine a 95%lower confidence bound for the mean weight of all small bags of peanut M\&Ms. (Note: The sample mean and sample standard deviation of the data are 52.040gand 2.807grespectively.)

b. Interpret your result in pant (a).

c. According to the package, each small bag of peanut M\&Ms should weigh 49.3gComment on this specification in view of your answer to part (b) It provides equal confidence with a greater lower limit.

Part (c) Because the weight of 49.3g is below the 95% lower confidence bound.

Table IV in Appendix A contains degrees of freedom from I to 75 consecutively but then contains only selected degrees of freedom.

a. Why couldn't we provide entries for all possible degrees of freedom?

b. Why did we construct the table so that consecutive entries appear for smaller degrees of freedom but that only selected entries occur for larger degrees of freedom?

c. If you had only Table IV, what value would you use for t0 os with df =87 with df=125? with df=650? with df=3000 ? Explain your answers.

What is a confidence interval estimate of a parameter? Why is such an estimate superior to a point estimate?

A simple randoes sample is taken from a population and yields the following data for a variable of the population:

find a point estimate for the population standard deviation (i.e., the standard deviation of the variable).

Digital Viewing Times. Refer to Exercise 8.130

a. Find and interpret a 90%lower confidence bound for last year's mean time spent per day with digital media by American adults.

b. Compare your one-sided confidence interval in part (a) to the (two-sided) confidence interval found in Exercise 8.130.
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