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Hypothesis Estimations for Tax Refuns and Car Ownership

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Question 3
You wish to estimate with 95 percent confidence the proportion of families that own two cars.
a)How large a sample do you need if you allow an error of up to 2 percent in each direction?
b)What will be the sample size if your prior estimate for p was 0.7?

Question 4
A sample of 400 people getting a tax refund showed the mean to be $900 and standard deviation to be $200.
a)Design a 99 percent confidence interval.
b)How large a sample do you need if you want the error to be no more than $10?

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Solution Summary

The solution performs two hypothesis tests to determine proportions of families owning cars and tax refund amounts.

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Question 3
You wish to estimate with 95 percent confidence the proportion of families that own two cars.
a)How large a sample do you need if you allow an error of up to 2 percent in each direction?

Solution. As we do not have any information of p, we assume that p=0.50. For the 95 percent confidence level, we know that z=1.96. So, the margin of error is

By the given ...

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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