Z scores/table
What is the Z-score formula?
z=x-μ/σ
What is the T-score formula?
T= x−μ/(Sx/√n)
What is the confidence interval equation for z-score?
x̄ ± z · Sx/√n
What does x-bar represent?
The average for a sample
Scores on an Honors Statistics test have average of 80 with a standard deviation of 6. What is the z-score for a student who earned a 75 on the test?
Z=-0.83
What does df mean and how is it found?
df means degrees of freedom and is found by the formula: (n-1)
What is the confidence interval formula for t-score?
x̄ ± t · Sx/√n
What does n represent in hypothesis testing
Number of data points
A particular leg bone for dinosaur fossils has a mean length of 5 feet with a standard deviation of 3 inches. What is the z-score that corresponds to a length of 62 inches?
Z=0.67
When do you accept vs. reject Ho?
if P<.05 reject Ho, if P> .05 don't reject Ho
What is the proportion confidence interval formula?
P̂ ± z · √[P̂(1-P̂)/n]
Rejecting a true null hypothesis is called a ______ error. (Type I or Type II)
Type I
A normal distribution of scores has a mean of 120 and a standard deviation of 20. What score separates the top 40% of the scores from the rest?
X=125
Why and how is Confidence Interval used in T-scores and T-test?
it is used to determine the accuracy of the data x+or- t. (Sx/√n)
What is the confidence interval for 90% confidence of a sample average of 210, standard deviation of 24, and with the n being 55. Round to the nearest tenth.
(204.7, 215.3)
When should a t-test vs z-test be used
Z-test should be used when the population standard deviation is known, while the t-test should be used when the sample standard deviation is known
Drinks at Spillane’s Beanshop have a mean sugar content of 20g with a standard deviation of 6g. The sugar content in a Grande Cappuccino at Spillane’s Beanshop has a z-score of -0.75 compared to the rest of the drinks at the shop. How much sugar is in a Grande Cappuccino at Spillane’s Beanshop?
X= 15.5g
Conduct a T-test for the following claim:
Claim: Find the 90% confidence interval for the following problem:
x̄=250.7, t=2.069, sx=646.044,n=24
(523.55,-22.15)
The mean monthly rent for a random sample of 60 apartments is $1000. The population standard deviation is $200. Construct a 95% confidence interval
1000 ± 1.96 * 200 /√60
($949.39, $1050.61)
Conduct a hypothesis test: Claim: The average length of a movie is 118 minutes
x̄= 100 minutes, SX= 18, n=30
Z-score: -0.1825 --> -0.183
P-value: 0.42858
0.42858 > 0.05, accept HO
There is evidence to say that the average movie length is greater than 100 minutes