(Problem re-worded slightly to make the claim more explicit.) Adults aged 18 yea
ID: 2907874 • Letter: #
Question
(Problem re-worded slightly to make the claim more explicit.)
Adults aged 18 years old and older were randomly selected for a survey on obesity. Adults are considered obese if their body mass index (BMI) is at least 30. The researchers wanted to determine if (i.e. wanted to test the claim that) the proportion of women who are obese in the south is less than the proportion of southern men who are obese. The results are shown in the table below. Test at the 1% level of significance.
If you are using subscripts 1 and 2, assume that 1 represents Women and 2 represents Men.
Step 1:
Note: The subscripts do not show up correctly in the choices (e.g. ?d will appear as ?d, etc.)
Step 2:
Significance level: ? = Answer.05.01
Step 3:
Test: Answer2Samp Z-Test2Samp T-Test2-Prop Z-TestT-Test
Type of Input: AnswerDataStatsNA (if using 2-Prop Z-Test)
The following table shows you what values you'll need to enter depending on what test you're using and what order you should enter them.
Values Entered in Calculator
Use the drop-down lists below to fill in the left column using the order given in the table above. Then enter the appropriate values in the right column. (Whenever NA is on the left, put NA on the right also.)
Answer?1List1x-bar1x1?0: Answer
Answer?2List2Sx1n1Listx-bar: Answer
AnswerList1x-bar1Freq1n1x2FreqSx: Answer
AnswerList2n1Freq2x-bar2n2nNA: Answer
AnswerFreq1x-bar2Sx2NA: Answer
AnswerFreq2n2NA: Answer
If using 2-Samp T-Test, answer the following question "Yes" or "No." Otherwise, choose "NA."
Pooled: AnswerYesNoNA
Alternate hypothesis: Answer?1 ? ?2?1 < ?2?1 > ?2p1 ? p2p1 < p2p1 > p2? ? ?0? < ?0? > ?0
p-value (round to five decimals): Answer
Step 4:
Note: Read the choices carefully.
Decision and Reason: AnswerReject H0 because ? > p-valueReject H0 because ? ? p-valueDo not reject H0 because ? > p-valueDo not reject H0 because ? ? p-value
Conclusion: Give a conclusion statement in the context of the problem (in words, not symbols).
Answer
Number who are obese Sample Size Men 42,769 155,525 Women 67,169 248,775 CLaamExplanation / Answer
Solution:
Here, we have to use Z test for difference between two population proportions. The null and alternative hypotheses for this test are given as below:
Null hypothesis: H0: The proportion of obese women in south is same as the proportion of southern obese men.
Alternative hypothesis: Ha: The proportion of obese women in south is less than the proportion of southern obese men.
H0: p1 = p2 vs. Ha: p1 < p2
This is a one/lower/left tailed test.
We are given
Level of significance = ? = 0.01
X1 = 67169, N1 = 248775
X2 = 42769, N2 = 155525
P1 = X1/N1 = 67169/248775 = 0.269998995
P2 = X2/N2 = 42769/155525 = 0.274997589
Z = (P1 – P2) / sqrt[(P1*(1 – P1)/N1) + (P2*(1 – P2)/N2)]
(P1 – P2) = 0.269998995 - 0.274997589 = -0.00499859
Z = -0.00499859 / sqrt[(0.269998995*(1 - 0.269998995)/ 248775)+( 0.274997589*(1 - 0.274997589)/ 155525)]
Z = -0.00499859 /0.0014
Z = -3.570421429
P-value = 0.0003
(by using z-table)
? = 0.01
P-value < ? = 0.01
So, we reject the null hypothesis that the proportion of obese women in south is same as the proportion of southern obese men.
There is sufficient evidence to conclude that the proportion of obese women in south is less than the proportion of southern obese men.
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