chapter 5
5 principles of probability
1. all probabilities are a number between 0-1
2. the sum of all probabilities is 1
3. complement rule
4. addition rule
5. multiplication rule
probability of making a type I error
significance level
interpret a t interval
we are___ % confident the interval from __ to __ captures the true mean of __
conditions
random, independent, normal
In a class of 30 students, 18 students play basketball, 12 students play soccer, and 6 students play both basketball and soccer. If a student is selected at random from the class, what is the probability that the student plays either basketball or soccer?
T(n) = 30.
alpha relationship to hypothesis
less than - reject
more than -failure to reject
two sample vs paired data:
two sample data compares the results vof the two categories
paired data
FITS
fixed number of trials
independent
two outcomes
success stays the same
In MAO there are 50 students, 25 are freshmen, 15 are sophomores, and the rest are juniors. If a student is randomly selected from the group, what is the probability that the student is a junior?
p(junior)=10/50=0.2
Bens books’ supplier claims that the proportion of defective products produced by their new assembly line is less than 5%. To test this claim, a random sample of 200 products from the assembly line is selected, and 8 of them are found to be defective. Conduct a hypothesis test at the 0.05 level of significance to determine if there is enough evidence to support the company's claim.
p-0.04
power is
likelihood of rejecting null hypothesis when hypothesis is false
trials until success
indepents
success stays the same
In a survey of 150 students, 90 students own a smartphone, 60 students own a tablet, and 30 students own both a smartphone and a tablet. If a student is selected at random from the survey, what is the probability that the student owns either a smartphone or a tablet?
0.4
A researcher wants to determine if there is a difference in the proportions of male and female students who passed a math exam. In a random sample of 200 male students, 140 passed the exam, and in a random sample of 250 female students, 160 passed the exam. Conduct a hypothesis test at the 0.05 level of significance to determine if there is a significant difference in the proportions of male and female students who passed the exam.
p=0.67
Mr. Ferris wants to estimate the average amount of time per week that high school students spend on homework. A random sample of 50 ben franklin students is selected, and their weekly homework times are recorded. The sample mean homework time is found to be 8.5 hours, with a sample standard deviation of 2.3 hours.
Calculate a 95% confidence interval for the average amount of time high school students spend on homework per week.
(7.863,9.137)
The ap government class is conducting a study of how the snack box affected them, from a random sample of 100 students . 40% show damage. is the normal condition met?
yes
In a survey of franklin 200 students, it was found that 120 students own a bicycle, 80 students own a skateboard, and 40 students own both a bicycle and a skateboard. If a student is selected at random from the survey, what is the probability that the student owns either a bicycle or a skateboard?
0.8
Ms Foley wants to determine if there is a difference in the proportions of students who prefer online learning between two universities, University A and University B. In a random sample of 300 students from University A, 180 prefer online learning. In a random sample of 250 students from University B, 120 prefer online learning. Conduct a hypothesis test at the 0.05 level of significance to determine if there is a significant difference in the proportions of students who prefer online learning between the two universities.
0.5
researcher wants to determine if a new teaching method improves students' math test scores. A random sample of 25 students is selected, and they are taught using the new method. After completing the course, their math test scores are recorded. The sample mean test score is 85, with a sample standard deviation of 6.
Perform a hypothesis test at the 0.05 level of significance to determine if there is sufficient evidence to support the claim that the new teaching method improves students' math test scores. Assume the population standard deviation is unknown.
t=4.17 pvalue=0.0002
A study is conducted to investigate the average amount of time spent daily on social media by high school students. A random sample of 100 high school students is selected, and their daily social media usage times (in minutes) are recorded. The sample mean is found to be 90 minutes, with a standard deviation of 15 minutes. Assume that the population follows a normal distribution.
Construct a 95% confidence interval for the population mean time spent daily on social media by high school students.
(87.06,92.94)
So, we can be 95% confident that the population mean time spent daily on social media by high school students is between 87.06 and 92.94 minutes.