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coldgirl [10]
3 years ago
12

About 130000 high school students took the AP exam in 2010 .the free response section of the exam consisted of five open ended p

roblems and an investigative task each free
Mathematics
1 answer:
Bogdan [553]3 years ago
5 0

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.

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