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Chapter 5: Q13E (page 314)

Will the sampling distribution ofχ¯ always be approximately normally distributed? Explain

Short Answer

Expert verified

A sampling distribution is statistics derived by continuous sampling from a greater populace.

Step by step solution

01

Sampling distribution

A sampling distributionis a probabilistic distribution of a statistic resulting from the selection of randomized samples from a particular population. It reflects the distribution of frequency on how far apart certain events will be for a specific demographic.

02

Explanation

No, since the central limit theorem asserts that if the sample size increases sufficient, the sampling distributions of x overbar are nearly distributed normally.

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Most popular questions from this chapter

A random sample of n = 250 measurements is drawn from a binomial population with a probability of success of .85.

  1. FindEP⏞andσp⏞
  2. Describe the shape of the sampling distribution ofp⏜.
  3. Find

Question:A random sample of n = 500 observations is selected from a binomial population with p = .35.

a. Give the mean and standard deviation of the (repeated) sampling distribution ofp^the sample proportion of successes for the 500 observations.

b. Describe the shape of the sampling distribution of p^. Does your answer depend on the sample size?

Purchasing decision. A building contractor has decided to purchase a load of the factory-reject aluminum siding as long as the average number of flaws per piece of siding in a sample of size 35 from the factory's reject pile is 2.1 or less. If it is known that the number of flaws per piece of siding in the factory's reject pile has a Poisson probability distribution with a mean of 2.5, find the approximate probability that the contractor will not purchase a load of siding

A random sample of n = 80 measurements is drawn from a binomial population with a probability of success .3.

  1. Give the mean and standard deviation of the sampling distribution of the sample proportion,P^
  2. Describe the shape of the sampling distribution ofP⏜
  3. Calculate the standard normal z-score corresponding to a value ofP⏜=.35.
  4. FindP(P⏜=.35.)

Downloading “apps” to your cell phone. Refer toExercise 4.173 (p. 282) and the August 2011 survey by thePew Internet & American Life Project. The study foundthat 40% of adult cell phone owners have downloadedan application (“app”) to their cell phone. Assume thispercentage applies to the population of all adult cell phoneowners.

  1. In a random sample of 50 adult cell phone owners, howlikely is it to find that more than 60% have downloadedan “app” to their cell phone?
  2. Refer to part a. Suppose you observe a sample proportionof .62. What inference can you make about the trueproportion of adult cell phone owners who have downloadedan “app”?
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