A simple random sample of 40 colleges and universities in the United States has a mean...

A simple random sample of 40 colleges and universities in the United States has a mean tuition of 17800 with a standard deviation of 11000. Construct a 95% confidence interval for the mean tuition for all colleges and universities in the United States. Round the answers to the nearest whole number.

Solutions

Expert Solution

Solution :

Given that,

Point estimate = sample mean = =17800

sample standard deviation = s =11000

sample size = n =40

Degrees of freedom = df = n -1= 40-1= 39

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,39 = 2.023

Margin of error = E = t/2,df * (s / $\sqrt$ n)

= 2.023*(11000/ $\sqrt$ 40)

Margin of error = E = 3519

The 95% confidence interval estimate of the population mean is,

- E < < + E

17800 - 3519 < < 17800 + 3519

14281 < < 21319

(14281,21319)

orchestra answered 1 year ago

Next > < Previous

Related Solutions

A simple random sample of 40 colleges and universities in the United States has a mean...

A simple random sample of 40 colleges and universities in the United States has a mean tuition of 18,800 with a standard deviation of 10,100. Construct a 98% confidence interval for the mean tuition for all colleges and universities in the United States. Round the answers to the nearest whole number.

A simple random sample of 35 colleges and universities in the United States has a mean...

A simple random sample of 35 colleges and universities in the United States has a mean tuition of 18700 with a standard deviation of 10800. Construct a 99% confidence interval for the mean tuition for all colleges and universities in the United States. Round the answers to the nearest whole number.

A simple random sample of 300 colleges and universities was selected and for each it was...

A simple random sample of 300 colleges and universities was selected and for each it was determined whether they planned to move summer 2020 classes online or not. Of the 300 colleges and universities in the sample, 90 responded that they will move summer 2020 classes online , and 210 responded that they will not move summer 2020 classes online. . If appropriate, use this information to calculate and interpret a 99% confidence interval for the proportion of all colleges...

A simple random sample of birth weights in the United States has a mean of...

A simple random sample of birth weights in the United States has a mean of 3433g. The standard deviation of all birth weights (for the population) is 495g. If this data came from a sample size of 75, construct a 95% confidence interval estimate of the mean birth weight in the United States. If this data came from a sample size of 7,500, construct a 95% confidence interval estimate of the mean birth weight in the United States. Which...

A simple random sample of 80 colleges and universities is selected, and 16 indicated will move...

A simple random sample of 80 colleges and universities is selected, and 16 indicated will move their summer 2020 classes online while the other 64 indicated they did not plan to move their summer 2020 classes online . If appropriate, use this information to test the hypotheses stated in question 10 at the a = .10 level of significance. Please type your answer in the box below. Hypothesis: H0: π = 0.14 versus HA: π > 0.14

What percent of undergraduate enrollment in coed colleges and universities in the United States is male?...

What percent of undergraduate enrollment in coed colleges and universities in the United States is male? A random sample of 50 such institutions give the following data (Source: USA Today College Guide). Percent Males Enrolled in Coed Universities and Colleges 42 36 53 72 53 37 39 34 36 53 35 69 39 36 59 36 35 51 47 32 49 57 33 39 45 47 52 21 41 46 24 37 42 32 39 49 62 52 45 72...

Your company produces mass spectrometers for sale to colleges and universities throughout the United States. On...

Your company produces mass spectrometers for sale to colleges and universities throughout the United States. On February 12, the University of Washtaw contacts your company to purchase 12 mass spectrometers at $1,000,000 per unit. You enter into a contract with the university on March 1 under those terms, along with a delivery date of December 1. On April 10, you receive a letter from the university stating that, due to ambiguities in the contract language, they believe you are only...

A simple random sample of 101 cities and counties in the United States was selected and...

A simple random sample of 101 cities and counties in the United States was selected and the number of positive COVID-19 cases per 1000 citizens was recorded for each. The mean number of positive cases for this sample of 101 counties and cities was 253, with a standard deviation of 11.4. Due to a couple of cities with extremely high numbers of cases the distribution is skewed heavily to the right. If appropriate, use this information to calculate and interpret...

A simple random sample of 40 items resulted in a sample mean of 80. The population...

A simple random sample of 40 items resulted in a sample mean of 80. The population standard deviation is s=20. a. Compute the 95% confidence interval for the population mean. Round your answers to one decimal place. b. Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean. Round your answers to two decimal places. c. What is the effect of a larger sample size on the...

A simple random sample of size n=40 is drawn from a population. The sample mean is...

A simple random sample of size n=40 is drawn from a population. The sample mean is found to be x=121.7 and the sample standard deviation is found to be s=13.3. Construct a 99% confidence interval for the population mean. The lower bound is (Round to two decimal places as needed.)

Subjects