Hypotheses
The null hypothesis can only include one of these three mathematical symbols.
=, le, ge
A manufacturer claims that their energy drink contains an average of 80 mg of caffeine per can. A health inspector suspects the actual mean is higher. The population standard deviation is known to be 8 mg.
Should I use a ztest or a ttest for this problem?
ztest because I know the population standard deviation
A marketing team claims that more than 60% of customers are satisfied with their new loyalty program. A consumer watchdog group surveys 150 randomly selected customers and finds that 99 of them report being satisfied.
Write the hypotheses and test the claim.
H0: mu <= 0.6, HA: mu > 0.6
P value = 0.0668
We fail to reject the null hypothesis. There is not enough evidence to support that more than 60% are satisfied.
For our problems, the P value is calculated using critical values and either a _________________ distribution or a _______________ distribution.
normal, Student T
A researcher wants to study the effect of a new teaching method on student performance. Two different approaches are considered matched pairs and independent samples. Explain the difference.
With matched pairs take the same students and grade tests before and after the teaching method. Then compute the difference in the grades and do a T Test. For independent samples choose two separate groups of students and use the original method for one and the new teaching method for the other and then compare the means with a 2 SAMP T Test.
An alternative hypothesis can only use one of these three mathematical symbols.
ne, > or <
A tutoring center claims that students who attend their sessions score an average of 75 or higher on the final exam. A skeptical professor (he thinks they are wrong) collects a random sample of 9 students who attended tutoring and records their scores:
72, 78, 69, 74, 71, 77, 73, 70, 76
Test the professor's suspicion as the 10% level.
P value = 0.074
Since 0.074 < 0.1 Reject the null. There is sufficient evidence (at the 10% significance level) to support the the mean score is actually less than 75.
A university claims that 60% of its students participate in extracurricular activities. A lecturer believes this proportion is lower. She surveys 150 students and finds that 78 participate in extracurricular activities. At a 5% significance level, test the lecturer’s claim.
P value = 0.0228
There is enough evidence to reject the null hypothesis so we can say the proportion is lower than 60%
My P value will come from a Student T distribution if I am hypothesizing about a ____________ and I don't know the __________________ ________________ ____________________.
mean, population standard deviation
sigma
A psychologist wants to test whether a stress-reduction program lowers anxiety scores. She measures anxiety before and after the program for 20 participants. The differences (Before – After) have:
bard = 4.2, s_d = 3.1, n = 20
Test at α = 0.05 if the program reduces anxiety.
P value = 0.0001
There is enough evidence to reject the null hypothesis and state that the stress reduction program lowers anxiety scores.
The symbol for the significance level is called ________ and represents the probability of making a _____________________.
alpha, Type I error
alpha
A tech company wants to know if the average number of hours employees spend on their internal training platform differs from the industry benchmark of 12 hours per month. A random sample of 24 employees shows a sample mean of 11.3 hours with a sample standard deviation of 2.4 hours.
P value = 0.166
Fail to reject the null hypothesis. There is not enough evidence to conclude that the average usage differs from 12 hours.
A survey claims that 50% of adults prefer online shopping to in-store shopping. A researcher believes the proportion is different (could be higher or lower). She surveys 220 adults and finds that 128 prefer online shopping. Test at a 5% significance level.
P value - 0.015
There is enough evidence to support the claim that the proportion is not 50%.
The P value represents the probability that my sample results would occur if _________________________________________
_____________________.
The null hypothesis is really true.
A researcher wants to compare the average exam scores of students taught using two different teaching methods.
n_1=35, barx_1=78.4, s_1=6.2
n_2=40, barx_1=74.1, s_1=5.8
Assume the populations are approximately normal and variances are not equal. Test at α = 0.05 whether there is a significant difference in mean scores.
P value 0.003
There is enough evidence to reject the null and state that the mean exam scores differ with the two different methods.
I will only reject the null hypothesis if there is __________________ evidence to do so.
sufficient
My friend claims the average age of pickle ball players is 60 and I don't think that is true. Would this be a right tail, left tail or two tail test? If the P value for the test is 0.002, I will _______________ the null hypothesis which means __________________________.
Reject, there is sufficient evidence to support my belief that the mean age is not 60.
Why do we compare our P value to alpha when doing a hypothesis test?
Because the P value represents the probability that our sample results would have been what they were if the null hypothesis is true and alpha is the significance level that separates probabilities that are unlikely from those that are likely.
I make a Type I error when I _____________ the ____________________ when it was ____________________________.
reject, the null hypothesis, actually true
A health researcher wants to compare the proportion of smokers in two cities.
At α = 0.05, test whether the proportion of smokers is different between the two cities.
P value 0.0052
There is sufficient evidence to reject the null and believe that there is a difference in the proportion of smokers in the two cities.
The type of test (left tail, two tail or right tail) is determined by the mathematical sign in the ____________ ___________________.
alternative hypothesis
The Student T distribution is dependent on the value of n which is the _____________________________. It's degree of freedom will be = _____________.
sample size, n - 1
What are the requirements for using a 1PropZtest?
npge10 and n(1-p)ge10
I make a Type II error when I __________________ the ____________________ when ____________________________.
Fail to reject, the null hypothesis, it was actually not true
What would a P value of 1.0 mean in the context of this hypothesis test:
I believe that the proportion of red marbles in one bag is more than the proportion of red marbles in another bag.
That P value means that it is practically certain that my data could have come from bags with the same proportion of red marbles.