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Biomedical researchers are testing a cancer treatment to see if it is safe for human use. This can be thought of as a hypothesis test with the following hypotheses.
The following is an example of what type of error?
The sample suggests that the medicine is safe, but it actually is not safe.
type IIGood job! The statement describes a situation where we fail to reject a false null hypothesis. This is a type II error....
Read MoreThe Wechsler Adult Intelligence Scale (IQ test) is constructed so that Full Scale IQ scores follow a normal distribution, with a mean of 100, and a standard deviation of 15. Dr.Smartyskirt is a University professor and believes that university professors are smarter than the national average but she is worried that too many people see doctors and lawyers as being the smartest professionals. She wants to test to see if doctors and lawyers are smarter than the national average for marketing purposes (she wants to recruit more young people to the PhD track).
A researcher is hired to conduct a study to determine whether doctors and lawyers, on average, have higher Full Scale IQs than the population. A random sample of 100 doctors and lawyers from various practices were given the IQ test and were found to have an average Full Scale IQ of 130.
Which hypothesis test should be used to determine whether the mean Full Scale IQ score of the professors is higher than the national average?
Correct! Since the population mean is being assessed and the population standard deviation is known, the appropriate hypothesis test would be the z-test for the population mean.
What are the null and alternative hypotheses?
What is the value of the test statistic used to determine whether the mean Full Scale IQ score of the doctors and lawyers is higher than the national average?
z-test for the population meanCorrect! Since the population mean is being assessed and the population standard deviation is known, the appropriate hypothesis test would be the z-test for the population mean.H0: μ = 100Ha: μ > 100Correct! The researcher wants to test whether the mean Full Scale IQ...
Read Morez-test for the population proportionCorrect! Since the population proportion is being assessed and the population standard deviation is known, the appropriate hypothesis test would be the z-test for population proportion....
Read MoreFrom her survey data, the statistics student calculates that the mean number of Facebook friends for her sample is 459.2 with a standard deviation of 79.3. She analyzed her data using a t-test and obtained a P-value of p < .00001
What conclusion can she draw from her data?
Even though 459.2 is significantly different from 520, the relationship goes in the wrong direction. In other words, the data do not provide enough evidence to conclude that the mean number of Facebook friends of all SJSU college students is higher than 520....
Read MoreAccording to recent statistics, the people with the most friends on Facebook (the top 15%) has an average of 520 Facebook friends. For a statistics project a student at San Jose State College tests the hypothesis that SJSU students will average more than 520 Facebook friends.
She randomly selects 3 classes from the schedule of classes and distributes a survey in these classes. Her sample contains 45 students.
Here are the null and alternative hypotheses for her study: H0: µ = 520, Ha: µ > 520.
What does µ represent in these hypotheses?
mean number of Facebook friends for SJSU studentsThe population of interest is SJSU students, so µ is the mean number of Facebook friends for this population....
Read MoreAccording to a Pew Research Center, in May 2011, 35% of all American adults had a smartphone (one which the user can use to read email and surf the Internet). A communications professor at a university believes this percentage is higher among community college students.
She selects 300 community college students at random and finds that 126 of them have a smartphone. In testing the hypotheses: H0: p = 0.35 versus HA: p > 0.35, she calculates the test statistic as Z = 2.54.
Use the Normal Table to help answer the p-value part of this question.
Click here to access the normal table.
There is enough evidence to show that more than 35% of community college students own a smartphone (P-value = 0.0055).Good job! The area to the right of Z = 2.54 on the standard normal curve is about 0.0055. This is smaller than α = 0.10 so we reject the null hypothesis and accept the alternative hy...
Read MoreA quality control engineer at a potato chip company tests the bag filling machine by weighing bags of potato chips. Not every bag contains exactly the same weight. But if more than 15% of bags are over-filled then they stop production to fix the machine.
They define over-filled to be more than 1 ounce above the weight on the package. The engineer weighs 100 bags and finds that 31 of them are over-filled.
He plans to test the hypotheses: H0: p = 0.15 versus HA: p > 0.15 (where p is the true proportion of overfilled bags).
What is the test statistic?
4.48Good job! The sample proportion is about 4.48 standard errors above the p = 0.15....
Read MoreAre unnecessary c-sections putting moms and babies health at risk? The procedure is a major surgery which increases risks for the baby (breathing problems and surgical injuries) and for the mother (infection, hemorrhaging, and risks to future pregnancies). According to the Center for disease control and prevention, about 32.2% of all babies born in the U.S. are born via c-section. The World Health Organization recommends that the US reduce this rate by 10%.
Some states have already been working towards this. Suspecting that certain states have lower rates than 32.2%, researchers randomly select 1200 babies from Wisconsin and find that 20.8% of the sampled babies were born via c-section.
Let p be the proportion of all babies in the U.S. that are born via c-section. Give the null and alternative hypotheses for this research question.
H0: p = .322Ha: p < .322Good job! The researchers want know if the proportion of c-section births for women who give birth in Wisconsin is less than 0.322....
Read MoreWhich of the following is a step in hypothesis testing?
Choosing a sample and collecting dataCorrect! This is the 2nd step of hypothesis testing. Great job!...
Read MoreA magazine editor uses a data informed approach to determine which freelance writers should be offered a more permanent position. They take a pool of recommended freelance writers and determine that at least 80% of their work has been accepted for publication over a 2 year period.
The editor considers 50 candidates for hire. Of the 50 candidates, 3 of them have not been accepted for publication at an acceptable rate. With this data we test the following hypotheses at a 5% significance level:
H0: The proportion of accepted publications of writers being recommended for hire is equal to .8
Ha: The proportion of accepted publications of writers being recommended for hire is less than .8
The p-value is .43. What should the editor conclude?
Fail to reject H0.Good job! The P-value is greater than the significance level. (0.43 > 0.05) So we “fail to reject” H0....
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