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Point Estimate, Margin of Error and Confidence Interval

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1) In an attempt to compare the starting salaries of college graduates majoring in education and social sciences, random samples of 50 recent college graduates in each major were selected and the attached information was obtained.
(see attachment for data table)

a) Find a point estimate for the difference in the average starting salaries of college students majoring in education and the social sciences. What is the margin of error for your estimate?
b) Based on the results of part a, do you think that there is a significant difference in the means for the two groups in the general population? Explain.

2) Do you think that we should let Radio Shack film a commercial in outer space? The commercialism of our space program is a topic of great interest since Dennis Tito paid $20 million dollars to ride along with the Russians on the space shuttle. In a survey of 500 men and 500 women, 20% of the men and 26% of the women responded that space should remain commercial-free.

a) Construct a 98% confidence interval for the difference in the proportions of men and women who think that space should remain commercial-free.
b) What does it mean to say that you are "98% confident"?
c) Based on the confidence interval in part a, can you conclude that there is a difference in the proportions of men and women who think space should remain commercial-free?

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Solution Summary

The solution provides the answers in the question document provided, taking it step by step to explain fully about confidence intervals etc.

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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