Question
Asked Feb 22, 2020
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In a study conducted by the U.S. Department of Health and Human Services, a sample of 546 boys aged 6–11 was weighed, and it was determined that 87 of them were overweight. A sample of 508 girls aged 6–11 was also weighed, and 74 of them were overweight. Can you conclude that the proportion of boys who are overweight differs from the proportion of girls who are overweight?

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Expert Answer

Step 1

A sample of 546 boys aged 6–11 was weighed and it was determined that 87 of them were overweight. A sample of 508 girls aged 6–11 was also weighed and 74 of them were overweight.

The sample proportion pX is,

Statistics homework question answer, step 1, image 1

The sample proportion pY is,

Statistics homework question answer, step 1, image 2

Step 2

Assumptions:

  • The samples are independent.
  • There are at least 10 success and 10 failures for each samples.

Here, the samples are independent.

Verify the condition:

For boys,

Statistics homework question answer, step 2, image 1

For girls,

Statistics homework question answer, step 2, image 2

Thus, the conditions are satisfied.

Step 3

State the test hypotheses.

Null hypotheses:

H0:pX−pY=0

Alternative hypothesis:

H1:pX−pY≠0

Test statistic and P-value:

Software Procedure:

Step-by-step procedure to obtain the test statistic and P- value using the MINITAB software:

  • Choose Stat > Basic Statistics > 2 Proportions.
  • Choose Summarized data.
  • In First sample, enter Trials as 546 and Events as 87.
  • In Second sample, enter Trials as 508 and Events as 74.
  • Choose Options.
  • Choose Pooled proportions.
  • In Confidence level, enter 95.
  • In Alternative, select not equal.
  • ...

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