Interval for the proportion of all Americans

 

A newsgroup is interested in constructing a 95% confidence interval for the proportion of all Americans who are in favor of a new Green initiative. Of the 592 randomly selected Americans surveyed, 370 were in favor of the initiative. Round answers to 4 decimal places where possible.
a. With 95% confidence the proportion of all Americans who favor the new Green initiative is between and .

b. If many groups of 592 randomly selected Americans were surveyed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population proportion of Americans who favor the Green initiative and about percent will not contain the true population proportion.

7. A political candidate has asked you to conduct a poll to determine what percentage of people support her. If the candidate only wants a 0.5% margin of error at a 99.5% confidence level, what size of sample is needed? When finding the z-value, round it to four decimal places.

8.

A fitness center is interested in finding a 98% confidence interval for the mean number of days per week that Americans who are members of a fitness club go to their fitness center. Records of 269 members were looked at and their mean number of visits per week was 2.5 and the standard deviation was 2.9. Round answers to 3 decimal places where possible.
a. To compute the confidence interval use a ? t z distribution.

b. With 98% confidence the population mean number of visits per week is between and visits.

c. If many groups of 269 randomly selected members are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean number of visits per week and about percent will not contain the true population mean number of visits per week.

Sample Solution

We see items in the newspaper during election years that show confidence intervals in proportions or percentages. A survey for a presidential candidate, for example, would suggest that the candidate has 40 percent of the vote within three percentage points of the chevalier (if the sample is large enough). Election polls are frequently calculated using a 95% confidence level, which means that the pollsters are 95% confident that the true proportion of voters who supported the candidate is between 0.37 and 0.43: (0.40 – 0.03,0.40 + 0.03). The genuine proportion of equities that go up and down each week is of interest to stock market investors.

Pinker is a cognitive psychologist. Therefore, it is only fair to say he believes in cognitive science and that cognitive science is proving to be very successful in all fields. Pinker view is that cognitive science can thoroughly understand acesss-conciousness. Basically, he thinks of it as a system; one that can successfully process information while limiting the access of information given for each specific task. Each task will perform its own job and carry out its duties, while serving as a helping hand to other tasks. This means a little bit of information will be shared with others in order to run efficiently. But, the information that is being shared must be relevant to the task at hand. Nonetheless, when intelligence comes to the table, all parts and tasks of the brain need to be grouped as a whole. This whole will serve as one huge taskforce in order to create a game plan and establish the action that will be taken. These tasks that consist of tiny breadcrumbs of information, which is relevant and that will serve as this force make up what is called our individual conscious life. Pinker establishes four functions that make up this operating system which are restriction of sensory information, the spotlight of attention, emotions, and the will. All the information is processed through these senses. For example, we hear words, but not phonemes when people are talking. Additionally, the system is capable of directing attention from one thing to the next in regards to our senses. Furthermore, emotions serve as a huge role in when creating a game plan or strategy. Our emotions stir the direction in which our attention flows. For example, you are in an car crash and you hear your baby sister cry for help. The cry for help from a loved one is the focus of one’s attention. And lastly, our will is what displays our manpower to go through with the action. It is what unleashes the handcuffs before we act.

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