Question

Directions:  Show all work including steps used during computations using formulas and diagrams when appropriate.  Write a DETAILED statement explaining the meaning of your computations (conclusions) for all problems- hypothesis tests and confidence intervals.  Remember that the conclusions for hypothesis tests need both a statement about the null and alternative hypotheses and another sentence or two describing how that applies specifically to the context given in the question.

EXTRA CREDIT:   You intend to poll students in order to determine the proportion of all students who will vote in an upcoming election.  What sample size do you need to choose to ensure that the margin of error is less than 2% assuming a 95% level of confidence?  Hint:  “To ensure” means that, even in the worst case scenario which is when the variation is largest, your confidence interval would still have a 95% chance of containing the true proportion of all students.   

Answer 1

Answer

It is given that margin of error (E) = 2%

= 2/100

= 0.02

and z score for 95% confidence level using z table is 1.96

No prior estimate of proportion is given, so we use the following formula

sample size n = 0.25*(z/E)^2

setting the value of z = 1.96 and E = 0.02

we get

= 0.25*(1.96/0.02)^2

= 0.25*(98)^2

= 0.25*9604

= 2401

therefore, required sample size is n = 2401