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Chapter 5: Q39E (page 320)

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

  1. FindEP铃�and蟽p铃�
  2. Describe the shape of the sampling distribution ofp铃�.
  3. Find

Short Answer

Expert verified

Random sampling is a sample strategy in which every sample has an equal probability of being selected. A random sample is intended to provide an impartial reflection of the overall population.

Step by step solution

01

 Step 1: (a) The data is given below

The calculation is given below:

Given,

p=0.85Population Proportion= 1-P=1-0.85=0.15

n=250Sample Size

The sample proportionis p铃�.

Mean =渭p铃�P=0.85

SD蟽p铃�=p1-p/ n=0.85脳0.15250=0.02258317

渭p铃�=0.85蟽p铃�=0.02258317

02

(b) The data is given below

The calculation is given below:

Since bothn脳p and n脳1-pare>=10, so

The p铃�sampling distribution is about normal.

03

(c) The data is given below

The calculation is given below:

pp铃�-渭p铃�/蟽p铃�<0.9-渭p铃�/渭p铃�=PZ<0.9-0.85/0.02258317=PZ<2.21=0.9864...use z table

pp铃�<0.9=0.9864

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Most popular questions from this chapter

Fecal pollution at Huntington Beach. California mandates fecal indicator bacteria monitoring at all public beaches. When the concentration of fecal bacteria in the water exceeds a certain limit (400 colony-forming units of fecal coliform per 100 millilitres), local health officials must post a sign (called surf zone posting) warning beachgoers of potential health risks. For fecal bacteria, the state uses a single-sample standard; if the fecal limit is exceeded in a single sample of water, surf zone posting is mandatory. This single-sample standard policy has led to a recent rash of beach closures in California. A study of the surf water quality at Huntington Beach in California was published in Environmental Science & Technology (September 2004). The researchers found that beach closings were occurring despite low pollution levels in some instances, while in others, signs were not posted when the fecal limit was exceeded. They attributed these "surf zone posting errors" to the variable nature of water quality in the surf zone (for example, fecal bacteria concentration tends to be higher during ebb tide and at night) and the inherent time delay between when a water sample is collected and when a sign is posted or removed. To prevent posting errors, the researchers recommend using an averaging method rather than a single sample to determine unsafe water quality. (For example, one simple averaging method is to take a random sample of multiple water specimens and compare the average fecal bacteria level of the sample with the limit of 400 CFU/100 mL to determine whether the water is safe.) Discuss the pros and cons of using the single sample standard versus the averaging method. Part of your discussion should address the probability of posting a sign when the water is safe and the probability of posting a sign when the water is unsafe. (Assume that the fecal bacteria concentrations of water specimens at Huntington Beach follow an approximately normal distribution.

Salary of a travel management professional. According to the most recent Global Business Travel Association (GBTA) survey, the average base salary of a U.S. travel management professional is \(94,000. Assume that the standard deviation of such salaries is \)30,000. Consider a random sample of 50 travel management professionals and let 蠂炉 represent the mean salary for the sample.

  1. What is渭蠂炉?
  2. What is蟽蠂炉?
  3. Describe the shape of the sampling distribution of蠂炉.
  4. Find the z-score for the value蠂炉=86,660
  5. FindP蠂炉>86,660.

Consider the following probability distribution:

a. Find渭.

b. For a random sample of n = 3 observations from this distribution, find the sampling distribution of the sample mean.

c. Find the sampling distribution of the median of a sample of n = 3 observations from this population.

d. Refer to parts b and c, and show that both the mean and median are unbiased estimators of渭for this population.

e. Find the variances of the sampling distributions of the sample mean and the sample median.

f. Which estimator would you use to estimate渭? Why?

Question:Quality control. Refer to Exercise 5.68. The mean diameter of the bearings produced by the machine is supposed to be .5 inch. The company decides to use the sample mean from Exercise 5.68 to decide whether the process is in control (i.e., whether it is producing bearings with a mean diameter of .5 inch). The machine will be considered out of control if the mean of the sample of n = 25 diameters is less than .4994 inch or larger than .5006 inch. If the true mean diameter of the bearings produced by the machine is .501 inch, what is the approximate probability that the test will imply that the process is out of control?

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

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