Question

In: Statistics and Probability

The head of a computer science department is interested in estimating the proportion of students entering...

The head of a computer science department is interested in estimating the proportion of students entering the department who will choose the new computer engineering option. A preliminary sample indicates that the proportion will be around 0.208.

What size sample should the department head take if she wants to be 95% confident that the estimate is within 0.02 of the true proportion?

Expert Solution

Solution :

Given that,

= 0.208

1 - = 1 - 0.208 = 0.792

margin of error = E = 0.02

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table )

Sample size = n = (Z/2 / E)2 * * (1 - )

= (1.96 / 0.02)2 * 0.208 * 0.792

= 1582.12

Sample size =1582

orchestra answered 2 years ago

You are the head of a computer science department at a university. Your boss (a “dean”)...

You are the head of a computer science department at a university. Your boss (a “dean”) wants you to find a way to tweak your curriculum so undergrads are more likely to choose your department for their major. How would you respond in a way that islegal, moral, and ethical?

1. We are interested in estimating the proportion of students at a university who smoke. Out...

1. We are interested in estimating the proportion of students at a university who smoke. Out of a random sample of 200 students from this university, 40 students smoke. (1) Calculate a 95% confidence interval for the proportion of students at this university who smoke and interpret this interval in context. (2) If we wanted the margin of error to be no larger than 2% at a 95% confidence level for the proportion of students who smoke, how big of...

Caraline is interested in estimating the proportion of students at a certain college who have at least two written final exams.

Caraline is interested in estimating the proportion of students at a certain college who have at least two written final exams. She takes a random sample and finds that 60 of the 75 students she surveyed did indeed have at least 2 written finals. Compute a 99% confindence interval for her and interpret it.

Overview A cyber-security company called UltraHackz is interested in finding talented computer science students. To do...

Overview A cyber-security company called UltraHackz is interested in finding talented computer science students. To do so, they post a challenge you find very interesting. They upload a txt file that contains 100 records containing information about 100 system accounts. Each record has a username, a salt value, and a hashed password. Each record is stored as follows: <username>,<salt value>,<hashed password> That is, there is one line per record in the file, where the three values are separated by commas....

A regional hardware chain is interested in estimating the proportion of their customers who own their...

A regional hardware chain is interested in estimating the proportion of their customers who own their own homes. There is some evidence to suggest that the proportion might be around 0.70. Given this, what sample size is required if they wish a 90 percent confidence level with a margin of error of ± .025? About 355 Almost 1,300 Approximately 910 100

1. The produce manager for a local grocery store is interested in estimating the proportion of...

1. The produce manager for a local grocery store is interested in estimating the proportion of apples that arrive on a shipment with major bruises. The supplier claims the rate will be about 10%. a) The produce manager wants to estimate the true proportion of bruised apples to within ±2%, with 90% confidence. How many apples should he sample? b) A random sample of 150 apples showed 12 with major bruises. Conduct a full hypothesis test to see if this...

1. A researcher in a small town is interested in estimating the true proportion of adults...

1. A researcher in a small town is interested in estimating the true proportion of adults in the town who smoke. 215 adults were randomly selected from the town, and it was found that 36 of them smoke. We would like to construct a 90% confidence interval estimate for the true proportion of adults in the town that smoke. a. What are the values of ??/2, ?, ?̂, and ?̂? (Round ?̂and ?̂ to three decimal places if needed.) ??/2...

A quality control engineer is interested in estimating the proportion of defective items coming off a...

A quality control engineer is interested in estimating the proportion of defective items coming off a production line. In a sample of 255 items, 45 are defective. Calculate a 95.0% confidence interval estimate for the proportion of defectives from this production line. (Use 3 decimal places in calculations and in reporting your answers.) Lower Limit: Upper Limit:

We are interested in estimating the proportion of graduates at a mid-sized university who found a...

We are interested in estimating the proportion of graduates at a mid-sized university who found a job within one year of completing their undergraduate degree. We can do so by creating a 95% confidence interval for the true proportion p. Suppose we conduct a survey and find out that 340 of the 430 randomly sampled graduates found jobs within one year. Assume that the size of the population of graduates at this university is large enough so that all our...

Exhibit 3 The management of a department store is interested in estimating the difference between the...

Exhibit 3 The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those customers using a national major credit card. You are given the following information. Store's Card Major Credit Card Sample size 164 89 Sample mean $140 $135 Population standard deviation $10 $8 Refer to Exhibit 3. A 95% confidence level the interval estimate for the difference between the average purchases of the customers...