Chi Squared Test
What is the appropriate test for this problem?
Chi-Squared Test for Goodness of Fit
How many degrees of freedom are there?
10
Name 2 sampling methods that can be used to sample random overtime games?
SRS, Stratified Random Sample, Cluster Sampling, Systematic
What are the null and alternative hypotheses of the test?
Ho: p1 - p2 = 0
HA: p1 - p2 ≠ 0
What values are on the x-axis and what values are on the y-axis?
x-axis: year
y-axis: average points per year
How many degrees of freedom?
31
What is the alternative hypothesis?
Ho = 22.8
Ha > 22.8
True or false: there are 11 degrees of freedom
False, Z tests do not have degrees of freedom
What effect does increasing the sample size for each sample, given that the two proportions remain the same, have on the P value?
P value decreases
What is the equation of the line of best fit?
(points per game)= 369 - 0.133(year)
What are the three conditions that need to be satisfied?
Counted Data Condition, Randomization Condition, Expected Cell Frequency Condition
List 2 out of the 3 assumptions/conditions for all 1 Sample T Tests?
Normally Distributed, Independent, Randomized
Provide the Null and Alternative Hypothesis?
Po = 0.5
Pa > 0.5
If the null hypothesis were to be one sided instead of two sided, what would happen to the p value?
The P value would be halved
How many degrees of freedom are there?
DF: 7
Find the chi squared statistic.
18.37
Calculate the T score and P value (state a conclusion with a= 0.05)
t=0.702, p=0.249
We fail to reject the null hypothesis that tend indoor teams score more than everyone else.
Provide the Z statistics and P value; draw a conclusion
z = 2.309
p= 0.01; reject the null hypothesis assuming a=0.05
What are the 4 assumptions/conditions?
10% condition, success/failure condition, randomization, independence
What is the slope of the line of best fit? Interpret this value.
Slope: -0.133
Because of the negative slope, the data has a decreasing trend: as x(year) increases, y(points per game) decreases.
Find and interpretate the p value in the context of this problem.
p = 0.965. If the null hypothesis (predictions are accurate), there is a 0.965 chance that the shown results will be repeated. We fail to reject the null hypothesis with an alpha level of 0.05.
Calculate the standard deviation
No calculator!!
4.6
What is the margin of error at a confidence level of 90%?
0.237
Given the p-value, what can be interpreted from the test?
T-value: -0.874
p-value: 0.4111
One can fail to reject the null hypothesis that the average score has changed over the past 40 years, as there is no sufficient evidence to overturn the null.