1. A sample of 25 adults living in Kentucky had an average IQ of 102. The margin
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Question
1. A sample of 25 adults living in Kentucky had an average IQ of 102. The margin of error for a 95% confidence interval is 18. We are interested in a 99% confidence interval for the average IQ of all adults in Kentucky.
2. Ecologist will sometimes use tags placed on birds to track and learn about the birds. The tags are typically small metal bands that go around the bird’s leg. Recently ecologist have started to use electronic tags and are interested in learning if there is a difference in the survival rate between the two types of tags. A study looked at the 10-year survival rate of swallows tagged either with a metal tag or an electronic tag. 20% of the 167 metal tagged swallows survived, compared to 36% of the 189 electronic tagged swallows. The margin of error for a 90% confidence interval was found to be 5%. We are interested in a 90% confidence interval for the difference in proportions.
3. 80 first-year students at EKU were randomly assigned roommates. There were 30 students assigned to roommates who brought a video game to college: average GPA after the first semester was 2.84. There were 50 students assigned to roommates who did not bring a video game to college, average GPA after the first semester was 3.105. The margin of error for a 90% confidence interval was found to be .43%. We are interested in a 90% confidence interval for the difference in means.
Explanation / Answer
Solution
1) sample size, n = 25, t value df = 24, 95% = 2.064
average IQ = 102
Margin of error = 18 = 2.064*(s/5) ,s = 43.60
99% confidence interval = ( 102 +- 2.797(43.6/5)) = (77.61,126.39)
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