Question

The marital status distribution of the U.S. male population, age 15 and older, is as shown below.

Marital Status	Percent
never married	31.3
married	56.1
widowed	2.5
divorced/separated	10.1

Suppose that a random sample of 400 U.S. young adult males, 18 to 24 years old, yielded the following frequency distribution. We are interested in whether this age group of males fits the distribution of the U.S. adult population at the 5% level. Calculate the frequency one would expect when surveying 400 people. Fill in the table below, rounding to two decimal places.

Marital Status	Frequency	Expected Frequency
never married	139
married	237
widowed	3
divorced/separated	21

• Part (a)

  State the null hypothesis.

  The data fit the distribution of marital status for the U.S. adult population.The data do not fit the distribution of marital status for the U.S. adult population.    

• Part (b)

  State the alternative hypothesis.

  The data do not fit the distribution of marital status for the U.S. adult population.The data fit the distribution of marital status for the U.S. adult population.    

• Part (c)

  What are the degrees of freedom? (Enter an exact number as an integer, fraction, or decimal.)

• Part (d)

  State the distribution to use for the test.

  χ²₄

  t₃

      

  t₄

  χ²₃

• Part (e)

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

• Part (f)

  What is the p-value? (Round your answer to four decimal places.)
  
  
  Explain what the p-value means for this problem.If

  H₀

  is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.If

  H₀

  is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value.    If

  H₀

  is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.If

  H₀

  is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value.

• Part (g)

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

• Part (h)

  Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write the appropriate conclusion.(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 do not 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 reject the null hypothesis.

  
  (iv) Conclusion:

  There is sufficient evidence to conclude that the data do not fit the distribution of marital status for the U.S. adult population.There is not sufficient evidence to conclude that the data do not fit the distribution of marital status for the U.S. adult population.   

Answer 1