- #1
PrudensOptimus
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An SRS of 16 Orange County Schools' juniors had a mean SAT MATH of x = 500; and a Standard Deviation of s=100. We know that the population of SAT Math scores for juniors in the district is approximately normaly distributed. We wish to determine a 90% confidence interval for the mean SAT math score mu for the population of all juniors in the district.
Question: 1. For the SAT MATH Data above, find the power of the test against the alternative mu=500 at the 5percent significance level. Assume that Sigma=100.
2. You regard your calculated power to be too low. How could you change the problem to increase the power? Verify your answer.
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Nitrites are often added to meat products as preservatives. In a study of the effect of these chemicals on bacteria, the rate of uptake of a radio-labeled amino acide was measured for a number of cultures of bacteria, some growing in a medium to which nitrites had been added. Here are the summary statistics from this study.
Group n x s
--------------------------------
Nitrite 30 7880 1115
Control 30 8112 1250
Q: 1. Carry out a test of the research hypothesis that nitrites decrease amino acid uptake and report your results.
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The Table below gives the pretest and posttest scores on the MLA listening test in Spanish for 20 high school Spanish teachers who attended an intensive summer course in Spanish.
Subject PreTest Posttest
-------------------------------------
1 30 29
2 28 30
3 31 32
4 26 30
5 20 16
6 30 25
7 34 31
8 15 18
9 28 33
10 20 25
11 30 32
12 29 28
13 31 34
14 29 32
15 34 32
16 20 27
17 26 28
18 25 29
19 31 32
20 29 32
Q. 1. We hope to show that attending the institute improves listening skills. State an appropriate H(naught) and H(Alternative). Be sure to identify the parameters appearing in the hypothesis.
2. Make a graphical check for outliers or strong skewness in the data that you will use in your statistical test, and report your conclusions on the validity of the test. You can use the space to the right.
3. Carry out a test. Can you reject H(naught) at the 5% significance level? At 1%?
4. Give a 90% conf. interval for the mean increase in listening score due to attending the summer institute.
Question: 1. For the SAT MATH Data above, find the power of the test against the alternative mu=500 at the 5percent significance level. Assume that Sigma=100.
2. You regard your calculated power to be too low. How could you change the problem to increase the power? Verify your answer.
-------------------
Nitrites are often added to meat products as preservatives. In a study of the effect of these chemicals on bacteria, the rate of uptake of a radio-labeled amino acide was measured for a number of cultures of bacteria, some growing in a medium to which nitrites had been added. Here are the summary statistics from this study.
Group n x s
--------------------------------
Nitrite 30 7880 1115
Control 30 8112 1250
Q: 1. Carry out a test of the research hypothesis that nitrites decrease amino acid uptake and report your results.
-------------------
The Table below gives the pretest and posttest scores on the MLA listening test in Spanish for 20 high school Spanish teachers who attended an intensive summer course in Spanish.
Subject PreTest Posttest
-------------------------------------
1 30 29
2 28 30
3 31 32
4 26 30
5 20 16
6 30 25
7 34 31
8 15 18
9 28 33
10 20 25
11 30 32
12 29 28
13 31 34
14 29 32
15 34 32
16 20 27
17 26 28
18 25 29
19 31 32
20 29 32
Q. 1. We hope to show that attending the institute improves listening skills. State an appropriate H(naught) and H(Alternative). Be sure to identify the parameters appearing in the hypothesis.
2. Make a graphical check for outliers or strong skewness in the data that you will use in your statistical test, and report your conclusions on the validity of the test. You can use the space to the right.
3. Carry out a test. Can you reject H(naught) at the 5% significance level? At 1%?
4. Give a 90% conf. interval for the mean increase in listening score due to attending the summer institute.
