mean___proportion_worksheet
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San Francisco State University *
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Mathematics
Date
Apr 3, 2024
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Uploaded by BrigadierGull326
Two Proportion Inference Worksheet 1.
An association of Christmas tree growers in Indiana sponsored a sample survey of 500 randomly selected Indiana households to help improve the marketing of Christmas trees. One question the researchers asked was, “Did you have a Christmas tree this year?” Respondents who had a tree during the holiday season were asked if they lived in an urban area or in a rural area. The tree growers want to know if there is a difference in preference for natural trees versus artificial trees between urban and rural households. Among the 160 who lived in rural areas, 64 had a natural tree. Among the 261 who lived in an urban area, 89 had a natural tree. (a)
Construct and interpret a 95% confidence interval for the difference in proportion of rural and urban Indiana residents who had a natural Christmas tree this year. (b)
Does the interval in part (a) provide evidence of a difference in the proportion of rural and urban residents Indiana residents who had a natural Christmas tree this year? (c)
Interpret the 95 percent confidence level in context. 2.
A study of “adverse symptoms” in users of over
-the-counter pain relief medications assigned subjects at random to one of two common pain relievers: acetaminophen and ibuprofen. In all, 650 subjects took acetaminophen and 44 experienced some adverse symptom. Of the 347 subjects who took ibuprofen, 49 had an adverse symptom. (a)
Is this an experiment or observational study? Justify your answer. (b)
Does the data provide convincing evidence that the two pain relievers differ in the proportion of people who experience adverse symptoms? Support your conclusion with a test of significance. Use α = 0.05.
(c)
Interpret the p-value in context. 3.
A state policeman has a pet theory that people who drive red cars are more likely to drive too fast. On hi
s day off, he borrows one of the department’s radar guns, parks his car in a rest area, and measures the proportion of red cars that are driving too fast. (He decides ahead of time to define “driving too fast” as exceeding the speed limit by more than 5 miles per hour.) To produce a random sample, he rolls a die and only includes a car in his sample if he rolls a 5 or a 6. He finds that 18 of 28 red cars are driving too fast, and 75 of 205 other cars are driving too fast. (a)
Is this an experiment or observational study? Justify your answer. (b)
Is this convincing evidence that people who drive red cars are more likely to drive too fast, as the policeman has defined it? Support your conclusion with a test of significance, using α = 0.05.
(c)
Construct and interpret a 95% confidence interval for the difference in proportion of red cars that drive too fast and other cars that drive too fast. (d)
What is the difference in the standard deviation formula used in part (b) and the standard error formula used in part (c)?
Mean Inference Worksheet 4.
As non-native English speaker, Sanda is convinced that people find more grammar and spelling mistakes in essays when they think the writer is a non-native English speaker. To test this, she randomly sorts a group of 40 volunteers into two groups of 20. Both groups are given the same paragraph to read. One group is told that the author of the paragraph is someone whose native language is not English. The other group is told nothing about the author. The subjects were asked to count the number of spelling and grammar mistakes in the paragraph. While the two groups found about the same number of real
mistakes in the passage, the number of things that were incorrectly identified as mistakes was more interesting. Here are the results: (a)
Is this an experiment or observational study? Justify your answer. (b)
Do these data provide convincing evidence that readers are more likely to incorrectly identify errors in writing if they think the author’s native language is not English? Support your conclusion with an appropriate statistical test. 5.
In many parts of the northern United States, two color variants of the Eastern Gray Squirrel
—
gray and black
—
are found in the same habitats. A scientist studying squirrels in a large forest wonders if there is a difference in the sizes of the two color variants. He collects random samples of 40 squirrels of each color from a large forest and weighs them. The 40 black squirrels have a mean weight of 20.3 ounces and a standard deviation of 2.1 ounces. The 40 gray squirrels have a mean weight of 19.2 ounces and a standard deviation of 1.9 ounces. There are no outliers in either sample. (a)
Construct and interpret a 90% confidence interval for the difference in mean weight of black and grey squirrels in this forest. (b)
Does this interval in part (a) provide evidence of a difference in mean weight of black and gray squirrels in this forest? 6.
Police trainees were seated in a darkened room facing a projector screen. Ten different license planes were projected on the screen, one at a time, for 5 seconds each, separated by 15-second intervals. After the last 15-second interval, the lights were turned on and the police trainees were asked to write down as many of the 10 license plate numbers as possible, in any order at all. A random sample of 15 trainees who took this test were then given a week-long memory training course and were then retested. The results are shown in the table below. # of plates correctly identified after training 6 8 6 7 9 8 9 6 7 5 9 8 6 8 6 # of plates correctly identified before training 6 5 6 5 7 5 4 6 7 8 4 5 4 6 7 (a)
Is this one sample or two? How do you know? (b)
Test, at the 5% level of significance, that the memory course improved the ability of the trainees to correctly identify license plates. “Native English Speaker”
0 1 3 0 0 1 0 0 0 2 1 2 0 0 3 2 0 0 2 0 “Non
-native English Speaker”
2 1 4 0 1 4 8 7 6 0 1 0 1 4 7 4 2 1 4 5
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