Hypothesis testing
What are the two hypotheses in hypothesis testing?
Null and Alternative
What is the shape of a normal distribution?
The Bell Curve
You have 9 balls, all identical except one that’s heavier or lighter. You have a balance scale and can use it twice. How do you find the odd ball?
Divide the balls into three groups of three. Weigh two groups; if equal, the odd is in the third. Weigh again two balls within that group to identify it. If equal, the lighter ball is the last one remaining.
Tells you how many standard deviations you are away from the mean.
standarized value(z-score)
What are the two possible outcomes in a binomial experiment called?
Success and failure
If p-value < 0.05, what happens to the null hypothesis?
reject it
What amount of data lies outside of 2 standard deviations of the mean?
5%
You have two ropes and a lighter. Each rope takes exactly one hour to burn but doesn’t burn evenly. How do you measure 45 minutes?
Light both ends of one rope and one end of the other. When the first rope burns out, 30 minutes have passed; then light the second end of the other rope.
The average amount for a Ziyatker sweatshirt at a store is 14 990tg with standard deviation of 500tg. Meirzhan buys a sweatshirt that costs 14 990. Calculate Meirzhan's z-score.
0
If a coin is flipped 5 times, what is the probability of getting exactly 3 heads?
31.25%
BONUS QUESTION
FREE POINTS
The speeds of cars are measured using a radar unit, on a motorway. The speeds are normally distributed with a mean of 90 km/hr and a standard deviation of 10 km/hr. What is the probability that a car selected at chance is moving at more than 100 km/hr?
0.1
A man lives on the 10th floor but only takes the elevator to the 7th and walks up unless it’s raining. Why?
He’s short and can only reach the 7th-floor button unless he uses an umbrella.
84th percentile ranking
percentile ranking if I am 1 stardandard deviation above the mean.
A Kaisar has a 70% chance of being late to the Math AI SL class. What is the probability that he will be late at least 4 times in 2 weeks?
74.43%
In the population, the average IQ is 100 with a standard deviation of 15. A team of scientists want to test a new medication to see if it has either a positive or negative effect on intelligence, or not effect at all. A sample of 30 participants who have taken the medication has a mean of 140. Did the medication affect intelligence? State the null hypothesis and alternative hypothesis
H0: medication affects intelligence
Ha: medication does not affect intellignece
The scores of students in a recent math test are normally distributed with a mean of 25.8 and a standard deviation of 0.5.
(a) Determine the probability that a randomly selected student's score is:
(b) Determine, to two decimal places, the score exceeded by 75% of students. (4 marks)
0.55
0.646
25.47
A fish’s head is 3 centimeters long. Its tail is the same length as the head plus half the body. The body is as long as the head and tail together. How long is the fish?
24 centimeters. The head is 3 cm long, the body is 12 cm long, and the tail is 9 cm long.
The grades on a Math AI SL at SA #5 are roughly symmetric with mean = 33 and standard deviation = 5.0
Aibibi scored 32 on the exam.
Find the z-score for Aibibi's exam grade.
-0.2
What formula calculates binomial probabilities?
(almost impossible)
P(X=k) = (n/k)(p^k)(1-p)^(n-k)
A teacher claims that the average time students spend on homework is exactly 2 hours per day. A student believes that the actual average time is different from 2 hours.
State the null hypothesis and the alternative hypothesis for this situation.
Knowledge. Inquiry. Reflection. Communication.
Long ago, Arda and Nurdaulet attended math classes together in harmony.
Then, everything changed when the mysterious trend began.
Now, if one of them shows up to class, the other mysteriously disappears.
Only mr. Asset, master of all math topics, can uncover the truth.
But when the class needed answers most, the explanation vanished...
Math Task: Normal Distribution
Arda's time spent on homework follows a normal distribution with a mean of 45 minutes and a standard deviation of 10 minutes. Nurdaulet's time also follows a normal distribution but with a mean of 50 minutes and a standard deviation of 8 minutes.
(a) What is the probability that on a randomly selected day, Arda spends less than 40 minutes on homework?
(b) What is the probability that Nurdaulet spends between 45 and 55 minutes on homework?
(c) If Arda and Nurdaulet both do their homework independently, what is the probability that Arda spends more time on homework than Nurdaulet on a given day?
30,85
46,81
34,83
Three friends share a €300 hotel room. They each pay €100, but the hotel manager realizes there was a discount and gives the bellboy €50 to return. The bellboy keeps €20 and gives €10 back to each person, meaning they each paid €270. But 3 x €90 = €270, plus the €20 the bellboy kept, makes €290. Where’s the missing dollar?
There’s no missing dollar. The math mixes amounts in an invalid way. The €270 already includes the bellboy’s €20.
Use the z-scores provided to find two IQ scores taken from a populationwith a mean of 100 and standard deviation of 16:
z = 2.19
z = -0.06
135 and 99
A student in a Math AI SL class has a chance of falling asleep during a lesson, which depends on how long the class lasts. The probability of staying awake during a class of t minutes is given by:
P=(3/200)(90-t)
Each minute is considered independently.The student attends a 60-minute class.
Find, to the nearest integer, the value of t if the student has an 80% chance of staying awake for the entire class.
Finally, the student endures a 60-minute class every day for 100 days.Using a suitable approximation, estimate the probability that the student falls asleep at least 95 times over the 100 days.
t=37
probability almost zero