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Chapter 7: Q. 7.2 (page 295)

7.2 Why should you generally expect some error when estimating a parameter (e.g., a population mean) by a statistic (e.g., a sample mean)? What is this kind of error called?

Short Answer

Expert verified

There are some mistakes when estimating the population parameter using the statistic value. This kind of error is called Sampling Error.

Step by step solution

01

Concept introduction

When a critic fails to choose a model that accurately depicts the entire population of data, this is known as a sampling error.

02

Explanation

Calculate the population parameter (a function of population observation, example population means) by a statistic (a function of sample observations example sample means).
Expect some inaccuracies because just a portion of the population is used (i.e. sample).
If the sample contains an outlier (an observation that is very dissimilar to the overall nature of the population observations), the statistic's value will not reflect the true nature of the population, i.e. there will be mistakes, then estimate the population parameter using the statistic's value.
Sampling error is the name for this type of error.
As a result, there are some mistakes when estimating the population parameter using the statistic value. This is known as the Sampling Error.

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Most popular questions from this chapter

Refer to Exercise 7.4 on page 295.

a. Use your answers from Exercise 7.4(b) to determine the mean, μs, of the variable x¯for each of the possible sample sizes.

b. For each of the possible sample sizes, determine the mean, μs, of the variable x¯, using only your answer from Exercise 7.4(a).

Population data: 2,3,5,5,7,8

Part (a): Find the mean, μ, of the variable.

Part (b): For each of the possible sample sizes, construct a table similar to Table 7.2on the page 293and draw a dotplot for the sampling for the sampling distribution of the sample mean similar to Fig 7.1on page 293.

Part (c): Construct a graph similar to Fig 7.3and interpret your results.

Part (d): For each of the possible sample sizes, find the probability that the sample mean will equal the population mean.

Part (e): For each of the possible sample sizes, find the probability that the sampling error made in estimating the population mean by the sample mean will be 0.5or less, that is, that the absolute value of the difference between the sample mean and the population mean is at most0.5.

America's Riches. Each year, Forbes magazine publishes a list of the richest people in the United States. As of September l6, 2013, the six richest Americans and their wealth (to the neatest billion dollars) are as shown in the following table. Consider these six people a population of interest.

(a) For sample size of 5construct a table similar to table 7.2 on page293.(There are 6 possible sample) of size 5

(b) For a random sample of size 5determine the probability that themean wealth of the two people obtained will be within 3(i.e,3billion) of the population mean. interpret your result in terms of percentages.

Consider simple random samples of size n without replacement from a population of size N.

Part (a): Show that if n≤0.05N,then0.97≤N-nN-1≤1,

Part (b): Use part (a) to explain why there is little difference in the values provided by Equations (7.1)and (7.2)when the sample size is small relative to the population size- that is, when the size of the sample does not exceed 5% of the size of the population.

Part (c): Explain why the finite population correction factor can be ignored and the simpler formula, Equation (7.2), can be used when the sample size is small relative to the population size.

Part (d): The term N-n/N-1is known as the finite population correction factor. Can you explain why?

Nurses and Hospital Stays. In the article "A Multifactorial Intervention Program Reduces the Duration of Delirium. Length of Hospitalization, and Mortality in Delirious Patients (Journal of the American Geriatrics Society, Vol. 53. No. 4. pp. 622-628), M. Lundstrom et al. investigated whether education programs for nurses improve the outcomes for their older patients. The standard deviation of the lengths of hospital stay on the intervention ward is 8.3days.

a. For the variable "length of hospital stay," determine the sampling distribution of the sample mean for samples of 80patients on the intervention ward.

b. The distribution of the length of hospital stay is right-skewed. Does this invalidate your result in part (a)? Explain your answer.

c. Obtain the probability that the sampling error made in estimating the population means length of stay on the intervention ward by the mean length of stay of a sample of 80patients will be at most 2days.
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