# Statistics

The National Assessment of Educational Progress tested a simple random sample of 1000 thirteen year old students in both 2004 and 2008 and recorded each student's score. The average and standard deviation in 2004 were 257 and 39, respectively. In 2008, the average and standard deviation were 260 and 38, respectively.

Your goal as a statistician is to assess whether or not there were statistically significant changes in the average test scores of students from 2004 to 2008. To do so, you make the following modeling assumptions regarding the test scores:

X1,…,X1000 represent the scores in 2004.

X1,…,X1000 are iid Gaussians with standard deviation 39 .

E[X1]=μ1 , which is an unknown parameter.

Y1,…,Y1000 represent the scores in 2008.

Y1,…,Y1000 are iid Gaussians with standard deviation 38 .

E[Y1]=μ2 , which is an unknown parameter.

X1,…,Xn are independent of Y1,…,Yn .

You define your hypothesis test in terms of the null H0:μ1=μ2 (signifying that there were not significant changes in test scores) and H1:μ1≠μ2 . You design the test

ψ=1(√n | (Xn−Yn)/ √ ( 38^2+39^2) ∣≥qη/2).

where qη represents the 1−η quantile of a standard Gaussian.

Hint: Under H0:μ1=μ2 , the test statistic is distributed as a standard Gaussian:

√n *( (Xn−Yn)/ √ ( 38^2+39^2) )∼N(0,1)

You are encouraged to check this.(Compute the mean and variance and recall that the sum of iid Gaussians is again Gaussian.)

What is the largest possible value of η so that ψ has level 10% ?

η= ?

What is the p-value for this data set?

1. 👍
2. 👎
3. 👁

## Similar Questions

1. ### statistics

A travel company is investigating whether the average cost of a hotel stay in a certain city has increased over the past year. The company recorded the cost of a one-night stay for a Friday night in January of the current year and

2. ### statistics

Based on data collected by the National Center for Health Statistics and made available to the public in the Sample Adult database, an estimate of the percentage of adults who have at some point in their life been told they have

3. ### stat

The heights of young American women, in inches, are normally distributed with mean mu and standard deviation 2.4 (sigma). I select a simple random sample of four young American women and measure their heights. The four heights, in

4. ### STAT

A college faculty consists of 400 men and 250 women. The college administration wants to draw a sample of 65 faculty members to ask their opinion about a new parking fee. They draw a simple random sample of 40 men and another

1. ### Grammar

Identify the simple subject and simple predicate in each sentence. 1. The neurologice exam tested her Babinski reflex. Answer: simple subject: exam simple predicate: tested 2. There are children waiting in the lobby. Answer:

2. ### computer science

When \$1000 is deposit at 5% simple interest, the amount grows by \$50 each year. When money is invested at 5% compound interest, then the amount at the end of each year is 1.05 times the amount at the beginning of the year. Write a

3. ### statistics

A simple random sample of 60 items resulted in a sample mean of 80. The population standard deviation is 15. a) Compute the 95 % confidence interval for the population mean. b) Assume that the same sample mean was obtained from a

4. ### algebra

A simple random sample is drawn from a normally distributed population. The value of which of the following will not be known for certain but can be inferred?

1. ### math URGENT!

28. You are surveying students to find out their opinion of the quality of food served in the school cafeteria. You decide to poll only those students who buy hot lunch on a particular day. Is your sample random? Explain. 29. Ira

2. ### Algebra

Eloise is investing and retirement account. She plans on adding an additional \$50 at the end of every year and the expected monthly rate of return is 3% of the amount invested, calculated at the end of the month. If she starts

3. ### statistics

The scores of students on the ACT college entrance examination in a recent year had a normal distribution with a mean of 18.6 and a standard deviation of 5.9. A simple random sample of 50 students who took the exam is selected for

4. ### statistics

A simple random sample of 50 items from a population with σ  6 resulted in a sample mean of 32. a. Provide a 90% confidence interval for the population mean