Question

One of the more popular statistics reported in the media is the​ president's job approval rating. The approval rating is reported as the proportion of the population who approve of the job that the sitting president is doing and is typically based on a random sample of registered voters. Complete parts​ (a) and​ (b) below. ​a) This proportion tends to fluctuate from week to week. Name some reasons for the fluctuation in the statistic. Select all valid reasons below. A. The proportion could be changing because the sampling size of the poll is changing. B. The proportion could be changing due to a large change in the composition of the population. C. The proportion could be changing due to sampling​ error; different people are in the sample. D. The proportion could be changing because​ people's attitudes are changing.

Answer 1

Concepts and reason

Proportion:

The ratio of the number of favorable outcomes and total number of possible outcomes is in the sample called as the proportion. A fraction of the total that represents a particular feature is termed as proportion. In other words, the number of occurrences of certain characteristic divided by the total number of all characteristic is termed as proportion.

Sampling error:

The sample that is taken from the population does not provide appropriate or accurate information, about the population even though the sample is a representative of the population. There would be a difference in the results obtained from the sample and its corresponding population because the sample does not involve all the units taken in the population. The error that occurs while estimating the population by using the sample is called as the sampling error.

Fundamentals

Population proportion:

If the proportion is computed for population it is termed as population proportion and is denoted by p.

Any statistical measure based on all units in the population or measurable characteristic of the population is called as population parameter. The proportion of the whole population with a certain characteristic is called population proportion.

Sample proportion:

If the proportion is computed for sample it is termed as sample proportion and is denoted by $\hat p$ .

The incorrect options are explained below:

From the information, the statistics have reported that president's job approval rating. A random sample of the registered voters is taken and the proportion of the voterswho approve of the job is considered. Also, the proportion is fluctuating every week.

The reason for fluctuation would not be proportion because of the sample size because the sample size would not change. Also, the sample portion is not based on the population it is calculated from the sample and a change in the composition of the population would not change the proportion.

The correct option is explained below:

From the information, the statistics have reported that president's job approval rating. A random sample of the registered voters is taken and the proportion of the voterswho approve of the job is considered. Also, the proportion is fluctuating every week.

When the sample of registered voters is taken, there might be difference between each of the individual in the sample because each person would be different. This indicates that the sampling error might occur, due to this reason the proportion might be fluctuating from week to week.

The option, ‘the proportion could be changing due to sampling​ error; different people are in the sample’ is correct.

The correct option is explained below:

From the information, the statistics have reported that president's job approval rating. A random sample of the registered voters is taken and the proportion of the voterswho approve of the job is considered. Also, the proportion is fluctuating every week.

When the sample of registered voters is taken, there might be difference in the attitudes or opinions of the individual in the sample based on the Presidents job, this indicates that the sample proportion might be changing from week to week.

The option ‘The proportion could be changing because people's attitudes are changing’ is correct.

Ans:

The proportion could be changing due to sampling error; different people are in the sample.

The proportion could be changing because people's attitudes are changing.