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StatisticsQ&A LibraryIn 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?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?

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,

The sample proportion pY is,

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*,*

For girls,

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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