Prerequisites to this exercise are Exercises . Why do your graphs in parts (c) of those exercises illustrate the impact of increasing sample size on sampling error? Explain your answer.

Short Answer

Expert verified

It can be seen from the findings of Exercises 11.9-11.13that as the sample size grows, the sample percentage approaches the population proportion.

This is in line with the inverse relationship between sample size and margin of error, which states that as the sample size grows, the margin of error/sampling error shrinks.

Step by step solution

01

Concept introduction

The sample is a set of records used to estimate statistical information for a target community. The census was used to select a sample size. The method of evaluating a subset of units from the population in order to assess the demographics of the overall nation is termed as sampling.

02

Explanation

Three males make up the population. Jose, Peter, Carlo, and Gail and Frances, two women. "Female" is the specified attribute.

According to the information provided, the group consists of three men and two women. Being a woman is a specified trait.

It can be seen from the findings of Exercises 11.9-11.13that as the sample size grows, the sample percentage approaches the population proportion.

This is in line with the inverse relationship between sample size and margin of error, which states that as the sample size grows, the margin of error/sampling error shrinks.

Sample size 1

Sample size 2:

Sample size 3:

Sample size 4:

Sample size 5:

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Most popular questions from this chapter

Buckling Up. The National Highway Traffic Safety Administration collects data on seat-belt use and publishes results in the document Occupant Restraint Use. Of 1000 drivers 16-24 years old, 79% said that they buckle up, whereas 924 of 1100 drivers 25-69 years old said that they did. At the 1%significance level, do the data provide sufficient evidence to conclude that there is a difference in seat-belt use between the two age groups?

In this Exercise, we have given the number of successes and the sample size for a simple random sample from a population. In each case,

a. use the one-proportion plus-four z-interval procedure to find the required confidence interval.

b. compare your result with the corresponding confidence interval found in Exercises 11.25-11.30, if finding such a confidence interval was appropriate.

x=40,n=50,95%level

The Organization for Economic Cooperation and Development (OECD) conducts studies on unemployment rates by country and publishes its findings in the document Main Economic Indicators. Independent random samples of 100and75 people in the civilian labor forces of Finland and Denmark, respectively, revealed 7and 3 unemployed, respectively. Find a 95% confidence interval for the difference between the unemployment rates in Finland and Denmark.

Suppose that you can make reasonably good educated guesses, p^1gand p^2g, for the observed values of p^1and p^2.

a. Use your result from Exercise 11.132to show that a (1-α)-level confidence interval for the difference between two population proportions that has an approximate margin of error of Ecan be obtained by choosing

n1=n2=p^1g1-p^1g+p^2g1-p^2gza/2E2

rounded up to the nearest whole number. Note: If you know likely ranges instead of exact educated guesses for the observed values of the two sample proportions, use the values in the ranges closest to 0.5as the educated guesses.

b. Explain why the formula in part (a) yields smaller (or at worst the same) sample sizes than the formula in Exercise 11.133.

c. When reasonably good educated guesses for the observed values of p^1and p^2can be made, explain why choosing the sample sizes by using the formula in part (a) is preferable to choosing them by using the formula in Exercise 11.133.

11.95 Explain the basic idea for performing a hypothesis test, based on independent samples, to compare two population proportions.

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