Question

Are the variances for incomes on the East Coast and the West Coast the same? Suppose that the table below shows the results of a study. Income is shown in thousands of dollars. Assume that both distributions are normal. Use a level of significance of 0.05.

East	West
37	70
46	125
29	43
81	52
74	44
52	89
116	87
66

• Part (a)

  State the null hypothesis.

  H₀: σ_east² > σ_west²H₀: σ_east² = σ_west²    H₀: σ_east² < σ_west²H₀: σ_east² ≠ σ_west²

• Part (b)

  State the alternative hypothesis.

  H_a: σ_east² < σ_west²H_a: σ_east² = σ_west²    H_a: σ_east² > σ_west²H_a: σ_east² ≠ σ_west²

• Part (c)

  Enter an exact number as an integer, fraction, or decimal.
  df(num) =

• Part (d)

  Enter an exact number as an integer, fraction, or decimal.
  df(denom) =

• Part (e)

  State the distribution to use for the test.

  F_{13, 13}F_{7, 13}    F_{7, 6}F_{13, 6}F_{6, 7}

• Part (f)

  What is the test statistic? (Round your answer to two decimal places.)

• Part (g)

  What is the p-value? (Round your answer to four decimal places.)

• Part (h)

  Sketch a picture of this situation. Label and scale the horizontal axis, and shade the region(s) corresponding to the p-value.

• Part (i)

  Indicate the correct decision ("reject" or "do not reject" the null hypothesis) and write appropriate conclusions.(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)
  α =
  
  (ii) Decision:

  reject the null hypothesisdo not reject the null hypothesis    

  
  (iii) Reason for decision:

  Since α < p-value, we reject the null hypothesis.Since α > p-value, we do not reject the null hypothesis.    Since α > p-value, we reject the null hypothesis.Since α < p-value, we do not reject the null hypothesis.

  
  (iv) Conclusion:

  There is sufficient evidence to conclude that the variances are different.There is not sufficient evidence to conclude that the variances are different.

Answer 1

conclusion: there is not sufficient evidence to conclude that variances are different.