What is the test statistic?

Question

The table below contains information from a survey among 499 participants classified according to their age groups. The second column shows the percentage of obese people per age class among the study participants. The last column comes from a different study at the national level that shows the corresponding percentages of obese people in the same age classes in the USA. Perform a hypothesis test at the 5% significance level to determine whether the survey participants are a representative sample of the USA obese population.

 

Age Class (Years) Obese (Percentage) Expected USA average (Percentage)
20–30                 76.0                       32.6
31–40                 26.5                       32.6
41–50                 12.6                       36.6
51–60                 20.9                       36.6
61–70                 21.0                       39.7

 

 

What is the test statistic?

Age Class (Years)	Obese (Percentage)	Expected USA average (Percentage)
20–30	76.0	32.6
31–40	26.5	32.6
41–50	12.6	36.6
51–60	20.9	36.6
61–70	21.0	39.7

•  

Answer 1

Not even close...

 

Sample Proportion         Population Proportion           Difference             Denominator         Test Stat
       0.76                                0.326                           0.434                  0.046874727     9.258720655
      0.265                                0.326                         -0.061                  0.046874727    -1.301340922
      0.126                                0.366                          -0.24                   0.048170946    -4.982256358
      0.209                                0.366                           -0.157                0.048170946    -3.259226034
      0.21                                  0.397                            -0.187               0.0489276        -3.821973725

 

With the exception of the second row, all of those test stats exceed the thresh hold

for any confidence interval.

 

There is a small problem regarding the population sizes. These calculations were done

under the ASSUMPTION that there are 100 people in each age class. Otherwise, there

is no way to compute the test statistic, for which the formula is:

 

   (sample proportion - expected proportion)

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                              D

 

where denominator D is hte SQUARE ROOT OF [  (expected proprotion * ( 1 - expected proportion) / N ]