Business
Engineering
Math
Science
Social ScienceIn 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?
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?
Expert Answer
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,
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.
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.
- ...
Related Statistics Q&A
Q: 30. Let B = {2, 4, 6, 8, 10}and C = {11, 12, 13, 14, 15}.Write CNB using the listing method. (Enter ...
A: 30 B = {2,4,6,8,10} C = {11,12,13,14,15} There is no common elements in B and C, So,
Q: #4
A: Click to see the answer
Q: A large tank of fish from a hatchery is being delivered to a lake. The hatchery claims that the mean...
A: Consider X be a random variable which follows normal distribution indicates the length of fish in th...
Q: The amount of warpage in a type of wafer used in the manufacture of integrated circuits has mean 1.3...
A: The Central Limit Theorem: Mean:
Q: Each of the following hypothetical data sets represents some repeated weighings of a standard weight...
A: Solution: a. The mean weight is µ. State the hypotheses. Null hypothesis: That is, the mean weight ...
Q: Compute the following. (a) P6, 3" (b) C5, 3- (c) P10, 10' (d) C11, 11"
A: Click to see the answer
Q: An ink cartridge for a laser printer is advertised to print an average of 10,000 pages. A random sam...
A: Click to see the answer
Q: Question 75 parts A, B, and C
A: Solution: 75. a. From the given information, the sample size is n=40 and p=0.59. Here, Here, np and...
Q: With Ha : p >> 88%you obtain a test statistic of z=1.255z=1.255. Find the p-value accurate to ...
A: Concept of p-value: The p-value in hypothesis testing is the probability of obtaining a test statist...
