Equations
What is the equation for p hat
r/n
What is the null hypothesis based on?
historical value, claim or a production specification
A random sample of size 20 from a normal distribution with sigma = 4 and a sample mean of 8. Alpha = 0.05.
Null - u=7 and Alternate - u not equal to 7.
Determine if we reject or fail to reject the null
z = 1.12 and p(value) = 0.2628
Fail to reject
The z chart of the back always gets us the area for what type of test?
left
What is the equation to find the test statistic when SIGMA IS KNOWN?
x bar - mu divided by sigma/sqrt(n)
What are the three possibilities for the alternative hypothesis?
greater than , less than, or different than (not equal to)
Sample of 25. The sample mean is 10 and sample standard deviation is 2. Level of sig = 0.05.
Conduct a two-tailed test with the population mean = 9.5
d.f = 24, t=1.250 Fail to reject
If we have a right tailed test, what do we need to do with the number from the z chart?
1 - that
What is the equation for the test statistic when SIGMA IS NOT KNOWN?
t = xbar - mu divided by s/sqrt(n)
Let's say you have a p value of 0.04 and alpha is 0.01, what would you do with the null hypothesis?
Fail to reject
Let z = 1.54
You are doing a right-tailed test with alpha = 0.01
Use the critical region method to determine what you would do with H not
Fail to reject
When do you need to multiply your p(value) by 2? How do we know if we do 1 - p(value) first?
What is the equation for the test statistic when you are testing a proportion?
z = phat - p divided by sqrt(pq/n)
Sample is 60 and it resulted in 18 successes. Test the claim that the population proportion of successes exceeds 18%. Use level of significance of 0.01
p - 0.18
p hat = 0.30
z = 2.42
p value = 0.0078
Reject the null
What does it mean if we reject h not?
we accept h1
If using the critical region method and you are looking for z not, which chart do you use?
small back of the book
A candidate for state representative of a certain state claims to be favored by 12 of the voters. You think that is much to high. If a hypothesis test is performed, what would your null and alternate hypothesis be?
Null - mu=12
Alternate - mu < 12
A local juice manufacturer distributes juice in bottles labeled 32 ounces. A government agency thinks that the company is cheating its customers. The agency selects 50 of these bottles, measures their contents, and obtains a sample mean of 31.6 ounces with a sample standard deviation of 0.90 ounce. At a 0.01 significance level, run a 5 step hypothesis test to test the agency's claim that the company is cheating its customers.
null hyp: m = 32 alt hyp: m < 32 z-score: -3.14 p-value: .0008 reject null hypothesis Yes, the company is cheating it's customers.