Question

Calculate PART A PART B PART C:

PART A:  

A national poll was conducted to determine the proportion of people that prefer a Congressional candidate by the name of Jeff. After completing the poll, a 99% confidence interval was calculated to show the proportion of the population that preferred Jeff. The confidence interval was:

0.469 < p < 0.577

Can we be reasonably sure that Jeff will have at least 50% of the vote?

• Yes
• No

Why or why not?

PART B:

The Math 122 Midterm Exam is coming up. Suppose the exam scores are normally distributed with a population mean of 77.7% and a standard deviation of 17.8%.

Let's first create a simulation to observe the expected results for a class of Math 122 students. In Excel, create 25 random samples of 22 students each. This means you should have 22 entries in each column, and you should be using columns A - Y. If you need a refresher for creating a random sample that is normally distributed, you can review the Technology Corner from Module 2.

After creating your random samples, copy all the numbers then use the "Paste Values" option in Excel to lock the numbers in place. Save your file, then attach it here:

Now find the mean of each sample.

What is the highest mean?

What is the lowest mean?

Note: While there are no points associated with the attachment or the highest/lowest mean, points will be deducted for not completing this portion or doing it incorrectly. These should be used to help you understand the remainder of the problem.

What is the probability of a student getting a score of 90% or better?  (Round to four decimal places.)

What is the probability of a class of 22 students having a mean of 90% or better?  (Round to six decimal places.)

Explain, in your own words, why the answers to these two questions are drastically different. Your explanation should include:

• references to your simulation
• references to your calculations
• common sense explanation

Answer 1

A national poll was conducted to determine the proportion of people that prefer a Congressional candidate by the name of Jeff. After completing the poll, a 99% confidence interval was calculated to show the proportion of the population that preferred Jeff. The confidence interval was:

0.469 < p < 0.577

Can we be reasonably sure that Jeff will have at least 50% of the vote?
No, based on the national poll we are 99% confident that Jeff will get votes between 46.9% to 57.5%.

Hence, can say that he will at least get 46.9% votes.

What is the probability of a student getting a score of 90% or better?  (Round to four decimal places.)

What is the probability of a class of 22 students having a mean of 90% or better?  (Round to six decimal places.)

Explain, in your own words, why the answers to these two questions are drastically different. Your explanation should include:

In the first case, the probability is determined based on the entire population but in the second case, is determined based on the same. Due to which the sample size, reduces the standard, which inturn increases the zscore, causing a small probability.