Question

About 130000 high school students took the AP exam in 2010 .the free response section of the exam consisted of five open ended problems and an investigative task each free

Answer 1

Complete question is;

About 130,000 high school students took the AP Statistics exam in 2010. The free-response section of the exam consisted of five open-ended problems and an investigative task. Each free-response question is scored on a 0 to 4 scale (with 4 being the best). For one of the problems, a random sample of 30 student papers yielded the scores that are graphed in the dot plot attached. The mean score for this sample is x¯ = 1.267 and the standard deviation is s = 1.230.

(a) Find and interpret the standard error of the mean.

(b) Construct and interpret a 99% confidence interval to estimate the mean score on this question. Use the four-step process.

Answer:

A) SOE = 0.225

The interpretation of this is that: if a sample size of 30 was taken, the difference between a sample mean score and a population mean score will be an average of 0.225

B) CI = (0.648, 1.886)

The interpretation of this is that;

We are 99% confident that that interval (0.648, 1.886) captures the true mean score of the AP Statistics exam in 2010

Step-by-step explanation:

A) We are given;

sample mean; x¯ = 1.267

Sample standard deviation; s = 1.230

Sample size; n = 30

Formula for standard error of the mean is;

SOE = s/√n

SOE = 1.23/√30

SOE = 0.225

The interpretation of this is that: if a sample size of 30 was taken, the difference between a sample mean score and a population mean score will be an average of 0.225.

B) we have a sample size of n = 30.

Thus;

DF = 30 - 1 = 29

We want to do a 99% Confidence interval.

From the attached t-table, we can see that critical t-value for DF = 29 and CL of 99%, we have t = 2.756

Formula for CI is;

CI = x¯ ± t(s/√n)

CI = 1.267 ± 2.756(1.23/√30)

CI = 1.267 ± 0.619

CI = (0.648,1.886)

The interpretation of this is that;

We are 99% confident that that interval (0.648, 1.886) captures the true mean score of the AP Statistics exam in 2010.