Statistics 12 problems

Question

For the following problems, choose and perform the appropriate statistical test. For your answer, you should provide a null and alternative hypothesis, the statistic you calculated, your comparison and what number you compared it to, the decision this comparison prompted, and give a 1-2 sentence conclusion. (You may provide more but these things are required.)

  1. 1. The following data on the calcium content of wheat is consistent with summary quantities that appeared in the article “Mineral Contents of Cereal Grains as Affected by Storage and Insect Infestation” (Journal of Stored Products Research [1992]). Four different storage times were considered. Is there sufficient evidence to conclude that the mean calcium content is not the same for the four different storage times? Test the appropriate hypotheses at the 0.05 level.

Storage Time Observations

0 months 58.75 57.94 58.91 56.85 55.21 57.30
1 month 58.87 56.43 56.51 57.67 59.75 58.48
2 months 59.13 60.38 58.01 59.95 59.51 60.34
3 months 62.32 58.76 60.03 59.36 59.61 61.95

2. In an elementary school, it was claimed that Mrs. Smith’s students did substantially better than the rest of the school on a particular exam. The school had an average exam score of 79.23 while Mrs. Smith’s 23 students had an average score of 82.6 with a sample standard deviation of 3. Was the higher average due to chance?

3. You would like to determine if the size of a car in 2016 had any effect on its fuel economy. You had the following observation:

Compact Midsize Full Size
A 26 21 19
B 28 26 26
C 24 24 22
D 33 27 24

For the following questions, provide a null and alternative hypothesis and state which statistical test you would perform.

4. You recorded what similar groups from Kansas City, Oklahoma City, and Tulsa spent on Movie Theaters during the summer. You would like to observe whether or not the location was a factor in the differences of amounts that were spent.

5. You are given a model for determining the lifespan of a cricket. You would like to see if this model is acceptable for the grasshopper life spans you have recorded.

6. You are given a substance that resembles water-saline solution that is used in a lab. The solution used in the lab should have a 70ppm concentration. You take 20 samples from the substance you were given and measure their concentrations. You would like to determine with some degree of certainty if the substance you were given is, in fact, the lab solution.

For the following questions, give a 1-2 sentence conclusion:

7. You perform a chi-square test of independence on whether the colour of a goat’s fur had an effect on its choice of grass to eat. Your chi-square statistic was 21.23 with 19 degrees of freedom.

8. You perform a t-test to determine if a scientific instrument is calibrated corrected. Your t-test statistic 2.895 will 17 degrees of freedom.

9. You perform an ANOVA test to see if noise pollution differences in a classroom seem to have an effect on student performance for a particular exam. Students are randomly assigned a Noisy Classroom, a Quiet Classroom, or a White Noise Classroom and their exam results are recorded. Your F statistic is 3.15 with 7,12 degrees of freedom.

Answer the following questions:

10. The regression equation y=2x + 8 represents how many minutes a sound will last after applying x pounds of pressure to the system. If 4 pounds are applied, how long should we expect the sound to last?

11. Give a short explanation of what the graph of correlated data would look like in a scatter plot.

12. Give a short description of how the correlation factor may tell us something about the relationship between two sets of data.

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