1. One population proportion test: Which of the following situations involves te
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Question
1. One population proportion test: Which of the following situations involves testing a claim about a single population proportion?
A. The Centers for Disease Control estimates that 22.8% of Americans (ages 18 to 24) get 6 or less hours of sleep per night. A researcher believes that the figure for college students is higher than this.
B. The mean SAT math score for Florida is 514. An educational researcher is concerned that this average may be lower in rural counties.
C. A Statistics student wants to determine whether there is a difference in the average number of credit hours male and female students are taking.
D. A growing practice among some parents is called “redshirting,” Redshirting means holding a child back a year from starting kindergarten even though he or she is eligible by age. Many states use August 31 as the cutoff for the 5th birthday in order for a child to start kindergarten. A researcher is curious if the proportion of boys with August birthdays who are redshirted is different than the proportion of girls with August birthdays who are redshirted.
2. In a study of a new treatment for cold sores, researchers randomly assigned 2209 patients to use of the new topical medication or a placebo in a double-blind experiment. Cold sores healed more quickly with the new medication and the improvement was statistically significant at the 0.01 level. Results were published the Journal of the American Medical Association in 1997. (http://jama.jamanetwork.com/article.aspx?articleid=415844)
Which of the following is an appropriate conclusion?
A. With a large sample, statistically significant results suggest a large improvement over the placebo.
B. With a large sample, statistically significant results may come from a small improvement over the placebo.
C. Regardless of the sample size, a statistically significant result means there is a meaningful difference in cold sore relief.
3. Privacy issues: In a Fall 2014 Pew Research survey, 25% of American adults say they are “not at all confident” that the records of their activity maintained by credit card companies will remain private and secure. With numerous data breaches since then, a consumer group is interested in determining whether the proportion has increased this year. They select a random sample of 300 adults and find that 30% state they are not at all confident.
After conducting the hypothesis test for p = 0.25 compared to p > 0.25, we obtain a P?value of 0.023. Which of the following interpretations of the P?value is correct?
A. There is a 2.3% chance that 25% of American adults say they are not at all confident that the records of their activity maintained by credit card companies will remain private and secure.
B. There is a 2.3% chance that 30% of American adults say they are not at all confident that the records of their activity maintained by credit card companies will remain private and secure.
C. There is a 2.3% chance that 30% or more of American adults say they are not at all confident that the records of their activity maintained by credit card companies will remain private and secure if we assume 25% of American adults are not at all confident in 2014.
D. There is a 2.3% chance that 30% or more of a sample of 300 American adults say they are not at all confident that the records of their activity maintained by credit card companies will remain private and secure if 25% of Americans are not at all confident this year.
4.In a survey conducted by the Pew Research Center in 2010 41% of Americans support the legalization of marijuana in the U.S. The researchers note that the margin of error is ± 3% using 95% confidence.
What does this margin of error tell you about the results of the survey?
A. We are 95% confident that the results are off by 3%.
B. 3% of the respondents gave a fake answer.
C. We can be 95% confident that the proportion of all Americans who support legalization of marijuana is within 3% of 41%.
D. We are certain that the proportion of all Americans who support legalization of marijuana is between 38% and 44%.
Explanation / Answer
Solution (1) :
we have to determine which of the following situations involves testing a claim about a single population proportion.
A) We are given that : The Centers for Disease Control estimates that 22.8% of Americans (ages 18 to 24) get 6 or less hours of sleep per night.
That is proportion of Americans (ages 18 to 24) who get 6 or less hours of sleep per night is 22.8%.
A researcher believes that the figure for college students is higher than 22.8%
That is : researcher wishes to test if population proportion of college students is higher than 22.8% or not.
Thus situation A involves testing a claim about a single population proportion.
B) The mean SAT math score for Florida is 514. An educational researcher is concerned that this average may be lower in rural counties.
Since this situation is related to Mean , so this does not involve testing a claim about a single population proportion.
C) A Statistics student wants to determine whether there is a difference in the average number of credit hours male and female students are taking.
In this situation , we are testing difference Average number of credit hours male and female students are taking. So this is related to testing difference in two population mean.
Thus this situation does not involve testing a claim about a single population proportion.
D) A researcher is curious if the proportion of boys with August birthdays who are redshirted is different than the proportion of girls with August birthdays who are redshirted.
In this situation , researcher is testing difference in two population proportions. That is it involves two population proportions.
So this situation does not involve testing a claim about a single population proportion.
Thus correct option is A)
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