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Null Hypothesis Testing statistics problems

Null Hypothesis Test for MEAN example question

A literary critic wants to establish that the mean number of words per sentence, appearing in newly discovered short story is different from 9.1 words. A sample of 36 sentences provided a data with mean of 8.6 words and standard deviation of 1.2 words. Test at a level of significance α = 0.10.

 

Solution to this Hypothesis Testing Statistics practice problem is given in the video below!


 


Null Hypothesis Test for PROPORTION example problem

Out of a sample of n = 625 students interviewed, 139 missed at least one class last week. Let p = proportion of students that missed at least one class last week. Conduct a test with the intent of establishing that the proportion of students that missed at least one class last week is greater than 0.20. Test at a level of significance ╬▒ = 0.05.

 

Solution to this Hypothesis Testing Statistics practice problem is given in the video below!


 

Confidence Interval statistics problems

Confidence Interval for MEAN Normal Distribution example question

A manager at a power company monitored the employee time required to process high-efficiency lamp bulb rebates. A random sample of 40 applications gave a sample mean time of 3.8 minutes and a standard deviation of 1.2 minutes. Construct a 90% confidence interval for the mean time to process ╬╝.

 

Solution to this Confidence Interval Statistics practice problem is given in the video below!


 


T-Distribution Confidence Interval for MEAN example

From a random sample of size 16, one has calculated the 95% confidence interval for μ (population mean) and obtained the result (39.51, 42.49). What are the x̄ (sample mean) and s (sample standard deviation) for the sample? Assume the population is normal.

 

Solution to this Confidence Interval Statistics practice problem is given in the video below!


 


Confidence Interval for PROPORTION Normal Distribution example problem

A telephone survey of 1,000 was taken after movie X came out in the national theater.

a) If 832 liked the movie, with what confidence can it be asserted that 83.2% ┬▒ 3% of the adult population liked this movie?

b) If the adult population in the nation is 150 million, what is the interval estimating the total number of people in the nation who liked the movie?

 

Solution to this Confidence Interval Statistics practice problem is given in the video below!


 

Continuous Distributions probability problems – SOA Exam P CAS Exam 1

Continuous Probability Density Function example question

The number of days that elapse between the beginning of a calendar year and the moment a high-risk driver is involved in an accident is considered to be a random variable with pdf   . An insurance company expects that 30% of high-risk drivers will be involved in an accident during the first 50 days of a calendar year. What portion of high-risk drivers are expected to be involved in an accident during the first 80 days of a calendar year?

 

Solution to this Society of Actuaries Exam P practice problem is given in the video below!



Expected Value problems

Expected Value example question

A box contains 8 green and 4 blue marbles. Two marbles are selected at once without replacement. What is the expected number of green marbles among the selected ones?

a)  1

b) 

c) 

d) 

e) 

f)  none of the above

 

Solution to this Expected Value practice problem is given in the video below!



Expected Value example problem #2

You have 5 pairs of shoes. Four of them are worth $30 each, while the fifth is worth $2,000. You select a pair at random. What is the expected value of the pair you have selected?

a)  $424

b)  $30

c)  $50.20

d)  $432

e)  $1,030

f)  none of the above

 

Solution to this Expected Value practice problem is given in the video below!



Binomial Distribution Expectation example

A sample of 3 items is selected at random from a box containing 20 items of which 4 are defective. Find the expected number of defective items in the sample.

 

Solution to this Binomial Random Variable Expected Value practice problem is given in the video below!



Hypergeometric Distribution Expectation example question

A ball is chosen at random from each of 5 urns. Each urn contains balls as follows:

urn 1: 1 white, 5 black

urn 2: 3 white, 3 black

urn 3: 6 white, 4 black

urn 4: 2 white, 6 black

urn 5: 3 white, 7 black

Compute the expected number of white balls selected.

 

Solution to this Hypergeometric Random Variable Expected Value practice problem is given in the video below!



Continuous Distribution Expected Value example problem

The density function of X is given by

f(x) = {

0 otherwise

If E[X] = , find the values of constants and  .

 

Solution to this Continuous Random Variable Expected Value practice problem is given in the video below!



Independent & Identically Distributed UNIFORM Random Variables Expected Value example

If X1, X2, …, Xn are independent and identically distributed random variables having uniform distributions over (0,1),

find

E [max(X1, …, Xn)]

and

E [min(X1, …,Xn)]

 

Solution to this Uniform Random Variable Expected Value practice problem is given in the video below!



Exponential Distribution Continuous Random Variable problems

Exponential Distribution Probability example question

The time (in hours) required to repair a machine is an exponentially distributed random variable with parameter =  . What is the probability that a repair time exceeds 2 hours? What is the conditional probability that a repair takes at least 10 hours, given that its duration exceeds 9 hours?

 

Solution to this Exponential Continuous Random Variable Distribution Probability practice problem is given in the video below!



Normal Distribution Continuous Random Variable problems

Normal Distribution Probability example question

The annual rainfall (in inches) in a certain region is normally distributed with = 40,  = 4. What is the probability that starting with this year, it will take over 10 years before a year occurs having a rainfall of over 50 inches?

 

Solution to this Normal Continuous Random Variable Distribution Probability practice problem is given in the video below!



Normal Distribution PERCENTILE Probability example problem

The measure of intelligence of a group of people is assumed to be approximately normally distributed with mean 102 and standard deviation 14. If we are told that Tom’s IQ denoted by xT is at the 98th percentile of the IQ distribution of the group of people, find xT.

 

Solution to this Normal Continuous Random Variable Distribution Probability practice problem is given in the video below!



Uniform Distribution Continuous Random Variable problems

Uniform Distribution Probability example question

You arrive at a bus stop at 10 o’clock, knowing that the bus will arrive at some time uniformly distributed between 10 and 10:30. What is the probability that you will have to wait longer than 10 minutes? If at 10:15┬áthe bus has not yet arrived, what is the probability that you will have to wait at least an additional 10 minutes?

 

Solution to this Uniform Continuous Random Variable Distribution Probability practice problem is given in the video below!



 

Independent & Identically Distributed UNIFORM Random Variables Expected Value example

If X1, X2, …, Xn are independent and identically distributed random variables having uniform distributions over (0,1),

find

E [max(X1, …, Xn)]

and

E [min(X1, …,Xn)]

 

Solution to this Uniform Random Variable Expected Value practice problem is given in the video below!



Continuous Distribution Random Variable problems

Continuous Distribution Probability example question

X is a continuous random variable with probability density function given by

f(x) = {

0 otherwise

a. Find the value of C

b. What is the probability that X > 1?

 

Solution to this Continuous Random Variable Distribution Probability practice problem is given in the video below!






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