Question

Please use ONLY one Excel file to complete the case study and upload the Excel file to the submission link. Please clearly mark your answers (either highlight or font colors). No credit will be granted for problems that are not completed using Excel. In 2011, when the Gallup organization polled investors, 34% rated gold the best long-term investment. In A Gallup surveyed a random sample of U.S. adults. Respondents were asked to select the best long-term investment from a list of possibilities. Only 241 of the 1005 respondents chose gold as the best long-term investment. By contrast, only 91 chose bonds. a. Compute the standard error for each sample proportion. Compute and describe a 95% confidence interval in the context of the question. b. Do you think opinions about the value of gold as a long-term investment have really changed from the old 34% favorability rate, or do you think this is just sample variability? Explain. c. Suppose we want to increase the margin of error to 3%, what is the necessary sample size? d. Based on the sample size obtained in part c, suppose 120 respondents chose gold as the best long-term investment. Compute the standard error for choosing gold as the best long-term investment. Compute and describe a 95% confidence interval in the context of the question. e. Based on the results of part d, do you think opinions about the value of gold as a long- term investment have really changed from the old 34% favorability rate, or do you think this is just sample variability? Explain.

Answer 1

• TRADITIONAL METHOD
  given that,
  possibile chances (x)=241
  sample size(n)=1005
  success rate ( p )= x/n = 0.24
  I.
  sample proportion = 0.24
  standard error = Sqrt ( (0.24*0.76) /1005) )
  = 0.013

  II.
  margin of error = Z a/2 * (stanadard error)
  where,
  Za/2 = Z-table value
  level of significance, α = 0.05
  from standard normal table, two tailed z α/2 =1.96
  margin of error = 1.96 * 0.013
  = 0.026
  III.
  CI = [ p ± margin of error ]
  confidence interval = [0.24 ± 0.026]
  = [ 0.213 , 0.266]
  -----------------------------------------------------------------------------------------------
  DIRECT METHOD

• given that,
  possibile chances (x)=241
  sample size(n)=1005
  success rate ( p )= x/n = 0.24
  CI = confidence interval
  confidence interval = [ 0.24 ± 1.96 * Sqrt ( (0.24*0.76) /1005) ) ]
  = [0.24 - 1.96 * Sqrt ( (0.24*0.76) /1005) , 0.24 + 1.96 * Sqrt ( (0.24*0.76) /1005) ]
  = [0.213 , 0.266]
  -----------------------------------------------------------------------------------------------
  interpretations:
  1. We are 95% sure that the interval [ 0.213 , 0.266] contains the true population proportion
  2. If a large number of samples are collected, and a confidence interval is created
  for each sample, 95% of these intervals will contains the true population proportion

  [ANSWERS]
  a. standard error = 0.013
  b. [0.213 , 0.266]
  c. long term investment value is changed from old 34% since it does n;t lies in the
  interval achived