BIOM301 Exam 2 Quiz Questions

You are invited to play a lottery in which one person will win $300, one person will win $50. 100 tickets will be sold and they cost $10 each. What is the average or expected value of a lottery ticket? Be sure to include a negative sign if the average ticket is a losing ticket.

-6.5 discrete random mean = sum of (x * P(x)) = sum of each possible outcome times it probability keeping track of positive and negative values. Here 1 ticket out of 100 wins $290 (= 300 - 10 to buy a ticket), 1 out 100 ticket wins $40 (50-10 buy in) and all the other tickets(98 out of 100) lose $10 (-$10) So population mean (mu) = (1/100 * $290) + (1/100 * $40) + (98/100 * -$10) = -$7.50 The average ticket lose $6.50 since a negative value.

Which statistical test would be used to analyze the following question? You sample 100 apple trees and find that the mean height of trees is 250 cm with a sample standard deviation of 22. If this significantly shorter than the US average of 300cm? - 1 population t test for mu - 1 population z test for mu - 1 population z test for percent

1 population t test for mu it is a question about a mean and a sample std deviation is given, so 1 pop t test for mu

Which statistical test would be used to analyze the following question? You sample 50 people and ask them how many apples they have eaten in the last week. Your sample results show that 25% of people have eaten apples. Is this significantly different than the US average of 20% per week? - 1 population z test for mu - 1 population t test for mu - 1 population z test for percent

1 population z test for percent questions about means are always z tests for percent

For the previous question would the test be: - left tail - right tail - both tails

left tail it is left tail since you want to know if the mean is significantly less than some value. The equation is always set up as sample mean minus some value, so you will only reject if the z* value is negative

Which of the following are true about a Discrete Random variable: - outcomes are not generated randomly - outcomes are not mutually exclusive - outcomes are independent - all of these statements are true

outcomes are independent outcomes are generated randomly and are mutually exclusive, so only independent is correct

For the confidence interval you completed above, the confidence interval statement will be one that professes a level of confidence that the ____________ is between 2 numbers - sample mean - population mean

population mean We are 100% sure the CI includes the sample mean because it is in the center of the interval. The CI is used to say were we think the actual true population mean occurs - it is a statement of inference about the population using sample data

What is the name of of a display showing discrete random outcomes that often can not be used for empirically collected data? - probability function - probability distribution - probability histogram

probability function if there is not some mathematical relationship among the probabilities (like rolling a die and all outcomes are equally likely) - e.g., empirically collected data (data from very large samples) then it can't be shown as a probability function

What is the name of of a display showing discrete random outcomes as a mathematical relationship? - probability distribution - probability function - probability histogram

probability function mathematical relationships → probability function

You sample 100 students to find out the average number of apples they eat each week. You want to know if the U of MD average is significantly less than the US average of 3.2 apples/week. Which is the correct ALTERNATIVE hypothesis for this question?

the population mean is less than 3.2

true or false: As sample size increases, a randomly selected sample will have a sample mean that is closer to the true population value in part because the impact of a single outlier is decreased

true

true or false: As sample size increases, the variability in the value of the possible sample means will decrease

true

true or false: For t-tests will small sample sizes (compared to large sample sizes), there is a greater burden of proof in terms of needing a t*value that is further from zero before you can reject the null hypothesis

true

true or false: If the population is normally distributed, then the sampling distribution of sample means will also always be normally distributed

true

true or false: Not rejecting the null hypothesis is considered a 'not statistically significant result'. Because of this, you will need to have a very large sample size and very small error bars for your results to be considered correct.

true

true or false: The null hypothesis is the hypothesis that is directly statistically tested

true

true or false: The p-value in your conclusion statement is the probability that you made a Type I error in your study.

true

true or false: The rule for using a normal approximation for a binomial probability is that the distribution is roughly unimodal and symmetric and this is met when n*p > 5

true

true or false: The standard normal curve is always symmetric around a value of zero

true

true or false: When sample size is small, the t-distribution will be less peaked and more spread out compared to the z-distribution

true

true or false: Your confidence interval is a statement about your confidence that some parameter falls in an interval of values

true

true or false: Alpha is always set prior to your statistical analysis

true it is part of the study design and must be set (usually to standards in your field) prior to any data analysis.

true or false: If you reject the null hypothesis, and that accurately reflects what is happening in the population, then you had sufficient statistical power to do so

true statistical power is the ability to reject the null hypothesis when it is really false in the population, so a correct rejection of the Ho is statistical power.

When can you assume the sampling distribution of sample means is normally distributed? - when n is greater than 30 - when n is equal to 30 - always - never

when n is greater than 30

For the previous question what are the degrees of freedom for the test? - 99 - 100 - not applicable (no df used)

99 f for 1 population t tests is n-1 = 99

Which of the following is a possible binomial event as described? - Measuring the number of eggs in a nest where possible answers are zero through 6 - Answering the question: Are you a Washington Capitals fan when the answers are Yes or No - Rolling a single Die and recording the number of dots showing - Recording attendance at lecture as Present awake, present asleep or absent

Answering the question: Are you a Washington Capitals fan when the answers are Yes or No being a Caps fan or not has only 2 possible outcomes → binomial

For the Standard normal distribution, what is the P(z > 1.39)?

0.0823

The probability of having a pet is 60% in some population. For 6 randomly chosen people, what is the probability that exactly 2 have a pet in any order?

0.14 6!/2!4! * .6^2 * .4^4 = .138

The probability of liking Peach Sherbet in some population is 20%. For 8 randomly chosen people, what is the probability that exactly 3 like peach sherbet in any order?

0.15 = 8!/3!5! * .2^3 * .8^5 = 0.147

A population is normally distributed with a mean of 20 and a standard deviation of 6. What is the probability of randomly sampling and finding a sample mean of 22 or more? Assume the sample size is 9

0.16

A population is normally distributed with a mean of 100 and a standard deviation of 10. What is the probability of random sampling and getting a value between 105 and 115?

0.2417 z for 115 = (115-100)/10 = 1.5, the area for 1.5 is .4332 z for 105 is (105-100)/10 = .5 area for .5 is .1915. But you want the difference between these 2, the area from 105 to 115, so subtract the larger from the smaller to get .2417

For the standard normal distribution, what is the probability that z is between 0 and 1.2?

0.3849 You need the area from the mean (0) to +1.2 - which from table 3 is 0.3849

The probability of liking chocolate ice cream in some population is 80%. For 8 randomly chosen people, what is the probability that 7 or more like chocolate ice cream in any order?

0.5 This is probability of 7 or more so need to do 2 calculations = P(7 out of 8) and add to P(8 out of 8) (since mutually exclusive outcomes) P(7 of 8) = 8!/7!/1! * .8^7 * .2^1 = .336 P(8 out of 8) = 8!/8!0! * .8^8 * .2^0 = .168 add together = .336 + .168 = .504

A population is normally distributed with a mean of 50 and a standard deviation of 8. What is the probability of randomly sampling this population and getting a value between 44 and 58?

0.6147

The probability of getting the flu this year is 0.2. You randomly chose 100 people from a population. What is the probability that 18 or more will have the flu this year, in any order?

0.6915

You randomly sample 30 individuals from a population that is normally distributed with a mean of 40 and a standard deviation of 10. What is the probability that a sample mean will have a value of 41 or less?

0.7088

For some reason you have 7 tennis balls and 6 golf balls and wonder how many unique ways you can lay out these balls from left to right. For example it could be (t = tennis, g = golf) t t t t t t t g g g g g g How many unique sorts of tennis and golf balls are there?

1,716 unique sorts = the binomial coefficient = n!/x!(n-x)! = 13!/7!6! = 1716

You take a sample of size 17, get a sample mean of 15.2 and a sample standard deviation of 1.2. For a 95% confidence interval for the mean, what will the UPPER limit value be? Assume the * value you need for the calculation is 2.12.

15.8 95% confidence interval - upper limit: sample mean + 2.12 (1.2/sqrt of 17) = 15.2 + (2.12* 0.29) = 15.2 + .62 = 15.8

A population is normally distributed with a mean of 100. If the probability of a value in this population being greater than 105 is 40%, what is the population standard deviation.

20 This is solving for an unknown. You need to determine the z score for a value of 105. +z = 105-100/sigma, the z value is the one that is at 10% above the mean, so using the z table backwards, you can find that a value of 0.1000 is closest to a z value of .25, and it is positive since it is above the mean of zero. So now: .25 = (105-100)/sigma and I can use an algebra calculation (if needed) to find the unknown sigma of: 20

true or false: As sample size increases, the distribution of the population will look more normal

false

true or false: The standard error is a measure of the mistakes made in sampling the population

false

true or false: There are an infinite number of standard normal curves.

false

true or false: If you reject the null hypothesis, you could have made a Type 1 correct decision

false If you reject the Ho, you could have made a type B correct decision (your sample data matches the true population and you did reject the Ho correctly) or a Type I error (your sample data does not match the true population values and you rejected the Ho when it was really not false in the population).

true or false: Depending on the statement of the original question, the equal sign may be in the null hypothesis or in the alternative hypothesis

false The equal sign is always in the null hypothesis, the alternative hypothesis is always a statement of a significant effect ex: Ho mu = 11, Ha mu not equal to eleven Ho: Mu less than or equal to 11, Ha: mu greater than 11

true or false: Continous random variables always follow a normal distribution if you know the population distribution.

false The population distribution doesn't change with sample size, just the sampling distribution of sampling means (SDSM) which will look normal is the sample size is large enough

true or false: A confidence interval is an example of a point estimate

false it is an interval statement. Point estimates are single numbers: e.g., a sample mean is a point estimate for the population mean

true or false: The t-distribution is identical to the z distribution when the sample size (n) is greater than 30

false it isn't identical until n > 100

true or false: The sampling distribution of sample means is always symmetric around a value of zero

false it will be symmetric around the population mean

true or false: If your sample results match to the hypothesized value then you should accept the null hypothesis.

false you never accept the null, you either reject the null or do not reject the null. It is never a statement saying 'you accept the null'

What is considered a rare event? - if the probability is less than 5% - if the probability is less than or equal to 5% - it has not been defined

if the probability is **less** than 5% must be less than 5%, equal to 5% is not considered rare or unusual