Math 2510 Final Review

The first 200 CU students to walk into the UMC are selected. The 200 students' average GPA is 3.1. What is a statistic of this study?

the average GPA of the 200 students selected at CU

Which of the following is an assumption when testing goodness of fit?

the expected value is at least 5 for each cell

For each of the following situations, determine if you could calculate the probability using the binomial distribution. If you cannot, choose the reason why. You have one bag of hard candy, containing 6 Lemon, 3 Orange, and 4 Cherry flavors. You reach in and draw three candies, one at a time, and set them aside after each draw. Find the probability that none of the candies are Lemon

this situation is not binomial since the trials are not independent

For each of the following situations, determine if you could calculate the probability using the binomial distribution. If you cannot, choose the reason why. You have three bags of hard candy, each containing 6 Lemon, 3 Orange, and 4 Cherry flavors. You draw one candy from each bag and set it aside. Find the probability that two candies are Cherry and one is Lemon.

this situation is not binomial since there are more than two possible outcomes

The number of deaths each day due to COVID in a 30-day period would be a

time series graph

A t-distribution has thicker tails than a normal distribution. (T or F)

true

As n increases the t-distribution approaches the standard normal distribution.(T or F)

true

Like the t-distribution, there is a different chi-square curve for each unique value of degrees of freedom. (T/F)

true

The chi-square distribution is for a Goodness of Fit test. (T/F)

true

The chi-square distribution is non-symmetrical, especially for small values of the degrees of freedom. (T/F)

true

The shape of a t-distribution depends on its degrees of freedom. (T or F)

true

The test statistic for any chi-square test is always greater than or equal to zero (T/F)

true

When the degrees of freedom value is less than 9, the curve is highly skewed to the right. (T/F)

true

Two truck dealerships, Peterbilt and Kenworth, have both launched the same new warranty program for their customers. Peterbilt had 352 of the 891 customers purchase the warranty while Kenworth had 226 of their 578 customers purchase the warranty. At the 95% confidence level, are Peterbilt customers more likely to purchase the warranty than Kenworth customers. interval

two sample p interval

A random sample of 35 Airbus jet planes have a mean speed of 740 mph with a standard deviation of 57 mph. A random sample of 38 Boeing 747 jet planes have a mean speed of 898 mph with a standard deviation of 44 mph. Do Boeing 747 jet planes tend to have a higher mean speed than the Airbus jet planes? intervals

two-sample t interval

A random sample of 35 Airbus jet planes have a mean speed of 740 mph while a random sample of 38 Boeing 747 jet planes have a mean speed of 898 mph. The standard deviation for both aircrafts are known to be 57 mph and 44 mph, respectively. Do Boeing 747 jet planes tend to have a higher mean speed than the Airbus jet planes? interval

two-sample z interval

You are trying to determine if the mean time Bruce Willis spends running in his movies is different than 27 seconds. After surveying 31 Bruce Willis movies, he runs for an average of 12 seconds. Which type of test is this?

two-tailed

If the null hypothesis is that seatbelts are safe and we conclude seatbelts are unsafe when they are, in fact, safe is a ______ error

type 1

We reject the null hypothesis, but the null hypothesis was true is a ______ error

type 1

We fail to reject the null hypothesis, but the alternate hypothesis was true is a _______ error

type 2

beta is a ____ error

type 2

A poll was conducted to determine the public's opinion on an upcoming ballot issue. A 95% confidence interval from the results was 0.5301 < p < 0.6877, where p is the true proportion of those in favor of the issue. What conclusion can we make from this interval? Assume an issue passes if it is approved by 50% or more of voters.

we are 95% confident the issue will pass

Which of the following is the correct conclusion for a hypothesis test with Ho: µ1 - µ2 = 0 and Ha: µ1 - µ2 < 0 if we determine that we should Reject Ho ?

we have enough evidence to conclude u1< u2

Which of the following is the correct conclusion for a hypothesis test at a significance level of 0.05 Ho: µ1 - µ2 = 0, Ha: µ1 - µ2 ≠ 0 and a p-value of 0.007?

we have evidence that u1 doesn't equal u2

If a null hypothesis is rejected at the 0.02 level of significance, would it also be rejected at the 0.08 level of significance?

yes

See M5 2A question 3, 4, & 5

yuh

See homework module 5 1-B problem 1 & 2

yuh

see M5 2C question 2

yuh

see all of m7 1a & question 1 1b

yuh

see m5 2c problem 4

yuh

see m5 test question 5 & 7

yuh

see m6 1B problem 1

yuh

see m6 2a question 4 and 5

yuh

see m6 exam question 9 and 15

yuh

see m7 1c question 1, 3

yuh

A population is normally distributed with mean 44 and standard deviation 1.5. A sample of size 25 is taken from the population. Find the probability that the sample mean will be larger than 44.21.

0.242

An urn contains 8 Red balls, 14 Green balls, 11 Yellow balls. If you randomly draw one ball, what is the probability it is Red?

0.2424

Suppose the runners' ages in a local 10K race are normally distributed with mean 45 and standard deviation = 12.78, what percentage of runners were between 38 and 59?

0.5714

Assume that the scores on a placement exam are normally distributed with a mean of 73.4 and standard deviation of 7.45. If 9 scores are chosen at random, what is the probability that the sample mean will fall between 67 and 76?

0.8475

Based on a sample of size 86, a mean is calculated to be 14.3 and the standard deviation is calculated to be 2.13. What is the upper bound on the 90% confidence interval for the true mean?

14.6820

The monthly number of patients admitted to the Pike County Mental Hospital is normally distributed. Before the COVID-19 pandemic, an average of 57.2 patients were admitted per month. Since the pandemic, 9 months of data have been collected, with a sample mean of 65 monthly patients and a sample standard deviation of 8. Find a P-value to test if there are now significantly more than 57.2 monthly patients admitted.

0.0096

The average length of a population of bamboo sections is 26 cm with standard deviation 3.8 cm. If a biologist finds a section in her plot that is 25.8 cm long, what z-score should she report?

-0.0526

The weights of avocados are normally distributed with mean 7.61 ounces and standard deviation 1.40 ounces. Suppose you randomly select 11 avocados and compute their mean weight to be 7.20 ounces. What is the z-score for your computed sample mean?

-0.9713

Consider a standard deck of 52 cards. What is the probability of a card being Red given it is a Black?

0

Event A and Event B are mutually exclusive. If P(A) = 0.374 and P(B) = 0.523, calculate P(A and B)?

0

A population is normally distributed with mean 73 and standard deviation 1.6. Find P(63.92 < x < 67.28).

0.0002

All Billy Goats Gruff must cross the troll bridge some time in the spring. Across 20 years of April data, an average of 185 goats crossed during that month. Across 22 years of May data, an average of 227 goats crossed during that month. The number of crossings is known to be normally distributed with a population standard deviation of 43 for each month. At the 1% level of significance, find a P-value to test whether there is a difference between the number of April crossings compared to May.

0.0016

Suppose we have a population with an unknown standard deviation. We are testing H0: µ = 20, Ha: µ > 20 at the level of significance α = 10%. We collect a random sample of size 36 and find that x̄=21 and the sample standard deviation is 1.9. What is the p value for our test?

0.0016

Suppose we have a population with a known standard deviation of 2.1. We are testing: H0: µ = 25, Ha: µ > 25 at the level of significance α = 5%. We collect a random sample of size 37 and find that x̄=26. What is the p value for our test?

0.0019

In a newly released murder mystery, the author decides to secretly print two different versions of the book with different endings. In 1 out of every 8 books, the butler is the murderer. Suppose 6 friends each buy a copy of the book. Find the probability of each of the following events occurring: At least 4 read that the butler did it:

0.0030

Suppose the weight of a chocolate bar is normally distributed with a mean of 7.2 ounces and standard deviation of 0.03 ounces. Using this information, you can find the probability that a single chocolate bar weighs more than 7.23 ounces. (Hint: use the normal distribution). Now, If you were to purchase 8 chocolate bars, what is the probability that at least 5 of the bars will weigh more than 7.23 ounces? (Hint: use the binomial distribution). Express your answer as a probability with four decimals (12.34% would be entered as 0.1234).

0.0037

Consider a standard deck of 52 cards. Suppose you draw 5 cards without replacement. What is the probability that the last two cards are Aces, given that the first three are not Aces?

0.0051

The length of a meter stick produced for general use is normally distributed with mean 1,011 cm and standard deviation 21.99 cm, what percentage of meter sticks produced were less than 958 cm in length?

0.008

Suppose A and B are events with P(A) = 0.659, P(B) = 0.197, and P(A and B) = 0.093. Find P((A or B)c)

0.237

Suppose events A and B are independent with P(A) = 0.312 and P(B) = 0.763. Find P(A and B)

0.2381

In a newly released murder mystery, the author decides to secretly print two different versions of the book with different endings. In 1 out of every 8 books, the butler is the murderer. Suppose 6 friends each buy a copy of the book. Find the probability of each of the following events occurring: More than 2 read that the butler did it

0.0291

You set up a colorful candy bag for your friend with 8 Cherry, 12 Orange, 11 Lemon, 13 Grape, and 9 Sour Raspberry, hard candies. When they pull out two of them, one for each of you, what is the probability they are both Lemon?

0.0399

An earth-conscious clothing store offers a 15% discount if you bring in a bag full of old clothing to recycle the fabric. The probability that each bag brought in will contain fabric that can actually be recycled is 69%. In a given day, if there are 22 bags of fabric brought in to recycle, calculate the following: The probability that at most 11 bags will contain fabric that can be recycled

0.0486

A random sample of 75 gourds have a mean circumference of 4.35 inches. The standard deviation of the circumference for the gourd species is known to be 0.79 inches. Testing the claim that the mean circumference of this species of gourd is less than 4.5 inches at a 5% significance level, what is the associated p-value? Round your answer to 4 decimal places.

0.0501

You set up a colorful candy bag for your friend with 4 Cherry, 8 Orange, 2 Lemon, 8 Grape, and 6 Sour Raspberry, hard candies. When they pull out two of them, one for each of you, what is the probability they draw 1 Cherry and 1 Sour Raspberry in either order?

0.0635

My brother's trick coin lands on heads 31% of the time. If I flip it 53 times what is the probability that I will get exactly 13 heads?

0.0736

An earth-conscious clothing store offers a 15% discount if you bring in a bag full of old clothing to recycle the fabric. The probability that each bag brought in will contain fabric that can actually be recycled is 69%. In a given day, if there are 22 bags of fabric brought in to recycle, calculate the following: The probability that fewer than 13 bags will contain fabric that can be recycled

0.1104

The incubation period for a virus (time from exposure until first symptom) is normally distributed with mean 6 days and standard deviation 2 days. A researcher wishes to see how rare a certain group's average incubation time is, so a sample of 8 people is taken. What is the probability of that sample's mean incubation time being less than 5.2 days?

0.1289

David has been claiming that a higher proportion of hits are home runs in his Dominican baseball league than across the border in his friend's Haitian league. Last year in his league there were 819 hits and 71 of them were home runs. In his friend's league there were 417 hits and 29 home runs. At the 5% level of significance, find the P-value to test David's claim. Round your answer to 4 decimal places.

0.148

Find the P-value for an appropriate test for the following scenario: A recent survey showed an increase in alcohol use among local college students compared to the national proportion. Suppose that a survey of 98 local college students and 217 national college students is conducted to see if the proportion of alcohol use is higher locally than nationally. Locally, 55 college students reported drinking alcohol within the past month, while 108 national college students reported drinking it. Test the claim that alcohol use among college students is higher locally than it is nationally. Use a significance level of 0.05.

0.1481

Suppose events A and B are mutually exclusive with P(A) = 0.58 and P(A or B) = 0.73. Find P(B)

0.15

Consider a binomial experiment with n = 33 trials and the probability of success on each trial is p = 19%. Compute the probability of exactly 6 successes.

0.1762

Assume that the scores on a placement exam are normally distributed with a mean of 73.7 and standard deviation of 6.04. If 3 scores are chosen at random, what is the probability that the sample mean will be less than 71?

0.2194

A box contains 14 blue blocks, 11 yellow blocks, 4 blue spheres, and 5 yellow spheres. What is the probability you draw a sphere given it is blue?

0.2222

Suppose events A and B are events with P(A) = 0.395, P(B) = 0.299, and P(A or B) = 0.471. Find P(A and B).

0.223

Suppose events A and B are independent with P(A) = 0.631 and P(B) = 0.443. Find P(A and B).

0.2795

In order to estimate the length of wolves in a forest, 8 wolves are selected to be studied by some researches. The lengths of the wolves, in feet, are 4.90, 4.75, 5.54, 3.63, 5.11, 4.83, 5.00, 4.50. Find the variance of the lengths of the selected wolves.

0.3077

Suppose events A and B are independent with P(A) = 0.257 and P(A or B) = 0.487. Find P(B)

0.3096

Suppose events A and B are mutually exclusive with P(A) = 0.352 and P(B) = 0.316. Find P((A or B)c)

0.332

In order to find the lengths of wolves in a small animal preserve, all the wolves are measured, and their lengths, in feet, are 4.44, 4.61, 4.78, 5.57, 5.30, 4.89, 4.68, 4.83. Find the standard deviation of the lengths of the wolves in the entire animal preserve.

0.3484

A friend made a claim that economics majors were more likely than business majors to have framed versus unframed posters in their residence halls. I decided to investigate further and found that 30 of 44 economics majors had framed posters and 39 of 77 business majors had framed posters in their residence halls. Construct a 95% confidence interval for the difference in these samples (economics - business) and record the upper bound of this interval.

0.3526

A pack of Pokemon cards contains 12 fire type, 8 poison type, and 11 water type cards. If you randomly draw one card what the probability it is a water type?

0.3548

An earth-conscious clothing store offers a 15% discount if you bring in a bag full of old clothing to recycle the fabric. The probability that each bag brought in will contain fabric that can actually be recycled is 69%. In a given day, if there are 22 bags of fabric brought in to recycle, calculate the following: The probability that more than 15 bags will contain fabric that can be recycled

0.4532

You have a bag containing 17 green balls, 6 red balls, and 16 purple balls. If you draw out three balls, one at a time and without replacement, what is the probability that the third ball is green given that the first two are red?

0.4595

Suppose events A and B are mutually exclusive with P(A) = 0.188 and P(B) = 0.313. Find P(A or B).

0.501

5 Ravenclaw, 12 Slytherin, 9 Hufflepuff, and 20 Gryffindor students are the only ones to enter their names in the tri-wizard tournament. If only one name is drawn, what is the probability it is not a Gryffindor student?

0.5652

Consider a sample of 112 Nintendo and 91 PlayStation game systems. If 21 Nintendo and 11 PlayStation game systems are defective and one is randomly selected from the sample, find the probability that the game system is Nintendo or defective?

0.6059

A bag of mystery jewels contain 13 genuine rubies, 20 imitation rubies, 10 genuine sapphires, and 8 imitation sapphires. What is the probability you draw an imitation stone given it is a ruby?

0.6061

Suppose events A and B are mutually exclusive with P(A) = 0.151 and P(A or B) = 0.826. Find P(B)

0.675

A correlation analysis is performed on x = price of gold, against y = proportion of men with a facial hair. If the value of r2 = 0.69, it would be stated that:

0.69 of the variation in proportion of men with a facial hair can be explained by variation in price of gold.

Find the P-value for an appropriate test for the following scenario: You are trying to determine if the proportion of people that have traveled outside of the country is less than 40%. After surveying 91 people, 39 said they have traveled outside of the country. Test the claim at the 0.01 significance level.

0.711

Suppose events A and B are independent with P(A) = 0.272 and P(B) = 0.519. Find P(A^c).

0.728

We toss a coin with an unknown probability of heads 35 times and we get 21 heads. Construct a 95% confidence interval for the true probability of heads for this coin. What is the upper bound of this confidence interval?

0.7623

Consider a sample of 52 Nintendo and 80 PlayStation game systems. If 22 Nintendo and 24 PlayStation game systems are defective and one is randomly selected from the sample, find the probability that the game system is Playstation or defective?

0.7727

Suppose events A and B are independent with P(A) = 0.377 and P(B) = 0.464. Find P((A and B)^c)

0.8251

A group of 200 students are randomly selected from CU. The 200 students' average GPA is 3.1. What is the sample in this study?

the 200 selected students at CU

In a newly released murder mystery, the author decides to secretly print two different versions of the book with different endings. In 1 out of every 8 books, the butler is the murderer. Suppose 6 friends each buy a copy of the book. Find the probability of each of the following events occurring: No more than 1 read that the butler did it

0.8835

An urn contains 3 Red balls, 13 Green balls, 10 Yellow balls. If you randomly draw one ball, what is the probability it is not Red?

0.8846

Assume the weight of a bag of peanut M&Ms is normally distributed with a mean of 112.7 grams and standard deviation of 23.3 grams. Considering a random sample of 12 bags, what is the z-score for an average weight of 119?

0.9366

A population is normally distributed with mean 67.5 and standard deviation 1.5. Find P(x < 69.95).

0.9488

In a newly released murder mystery, the author decides to secretly print two different versions of the book with different endings. In 1 out of every 8 books, the butler is the murderer. Suppose 6 friends each buy a copy of the book. Find the probability of each of the following events occurring: Fewer than 3 read that the butler did it

0.9709

An assembly line machine produces a defective widget 20% of the time, the rest of the time it produces a widget correctly. If the assembly line produces 33 widgets, compute the probability that at least 3 of those widgets are defective?

0.9732

An earth-conscious clothing store offers a 15% discount if you bring in a bag full of old clothing to recycle the fabric. The probability that each bag brought in will contain fabric that can actually be recycled is 69%. In a given day, if there are 22 bags of fabric brought in to recycle, calculate the following: The probability that at least 9 bags will contain fabric that can be recycled

0.9984

Event A and Event B are mutually exclusive. If P(A) = 0.387 and P(B) = 0.234, calculate P((A and B)c)

1

Suppose the visitors to an amusement park are known to have a mean age of 23.31 years, and a standard deviation of 7.45 years. We then take a random sample of 54 visitors to the park, and find that their mean age is 21.51 years. If we were to take repeated samples of size 54 and calculate their means, what would we anticipate the standard deviation of the sample means to be?

1.0138

In order to ignite some competition, a second candle company, "Wax Poetic", opens in order to rival "At Wick's End." Taking a sample of 120 candles from each company, the candles from "At Wick's End" had mean length 7.23 inches, and standard deviation 1.2 inches. The candles from "Wax Poetic" had mean length 6.65 inches, and standard deviation 3.5 inches. Find the upper bound of the 88% confidence interval for the difference in the population mean candle lengths for the companies. (Use the difference "At Wick's End" - "Wax Poetic").

1.1082

For a standard normal distribution find the value z so that 5% of the area is to the right of z.

1.6449

Suppose a person's temperature is normally distributed with mean 98.77 and standard deviation 2.16. Find the temperature cut off that will put a person's temperature in the top 11%.

101.4193

Given a sample mean of 9.10, sample size of 44, and a margin of error 3.12, determine the associated confidence interval for the population mean. What is the upper bound of this confidence interval?

12.22

Assume the weight of a bag of peanut M&Ms is normally distributed with a mean of 130.34 grams, and a standard deviation of 21.2 grams. What would be the lowest weight, on average, of 32 randomly sampled M&M bags, in order for that weight to be in the 88th percentile of all possible 32-bag averages?

134.74

A certain distribution is mound shaped with a mean of 43 and standard deviation of 6. Approximately what percentage of the data will be greater than 49?

16%

The weights of adult females are normally distributed with mean 129 pounds and standard deviation 18.7 pounds. What is the the weight (in pounds) of an adult woman corresponding to the z-score 2.16?

169.39

Data was collected from 51 random students on the number of hours spent studying for the final and their corresponding exam score in a statistics class. If a 94% confidence interval for β resulted in (3.63, 6.59), what is the least you would expect the exam score to increase by if the student studied an extra 5 hours?

18.15

Given a sample mean of 15.64, sample size of 70, and a margin of error 2.93, determine the upper bound of the associated confidence interval for the population mean.

18.57

Calculate the mode of the following: 3, 25, 4, 33, 10, 2, 2, 13, 27, 2, 30, 7.

2

The heights of adult females are normally distributed with mean 61 inches and standard deviation 2 inches. What is the z-score for an adult woman with height 65.14 inches?

2.07

The birth weights of babies in the United States are normally distributed with mean 3.362 kilograms and standard deviation 0.58 kilograms. What is the z-score for a baby with birth weight 4.844 kilograms?

2.5552

A random sample of 39 bookstores in Colorado were sampled to determine the mean cost of bookmarks sold. With an average of $2.91 bookmark and a standard deviation of $0.33, find a 90% confidence interval for the true mean cost of bookmarks sold in Colorado bookstores. What is the upper bound of the associated confidence interval?

2.9991

Calculate the mean of the following: 8, 16, 14, 34, 14, 26, 12, 37, 22. Round your answer to 4 decimal places.

20.3333

Suppose a Binomial random variable has a 0.34 probability of success on a single trial. What is the expected value when performing 72 trials?

24.48

Suppose X is a normal random variable with mean 23 and standard deviation 3.46. Find c such that P(X<c) = 0.776.

25.6253

Suppose we have a sample of size 31 from a normally distributed population with an unknown standard deviation. Given that the sample mean is 28, and the sample standard deviation is 4, construct a 93% confidence interval for the true population mean. What is the upper bound of the associated confidence interval?

29.3499

Assume approximately 12% of all people are left-handed. If you select a group of 249 people, what is the expected value of those selected that are left handed?

29.88

Suppose you have a data set with n = 32 points. What would be the degrees of freedom for t-critical in order to construct a 91% confidence interval for the slope of the best fit line?

30

Researchers are interested in estimating the percentage of Americans who will get a flu shot this year. How many Americans should be surveyed to be 80% confident that the sample proportion of Americans who will get a flu shot this year is within 0.11 of the population proportion? Assume we have a prior estimate of 40%.

33

A candy manufacturer has replaced 9.17% of their chocolate bars with a new mystery flavor. Find the mean and the standard deviation for the number of mystery bars in a random sample

34.5709, 5.6036

Suppose we have a sample of size 25 from a normally distributed population with a known standard deviation of 2. Given that the sample mean is 36, construct a 90% confidence interval for the true population mean. What is the upper bound of the associated confidence interval?

36.6579

Find the median of the following: 38, 37, 6, 30, 40, 40, 76, 35, 50, 65

39

Suppose you want to estimate the mean number of times an average American has traveled outside the country. Assuming you know the population standard deviation is 3.79, how many people must you sample in order to be at least 93% confident that the mean will be within 0.344 of the true value?

399

Suppose X is a normal random variable with mean 40 and standard deviation 1.89. Find c such that P(X>c) = 0.407

40.4447

Find the mean of the following: 18, 52, 43, 42, 34, 17, 39, 71, 54, 52, 45

42.4545

Suppose you collect 500 samples of size 74 from a population with parameter p = 0.303. If you construct a 85% confidence interval for each sample, how many intervals would you expect to contain the parameter p?

425

SAT Math scores are normally distributed with a mean of 476 and a standard deviation of 97. What is a student's SAT Math score if the z-score is -0.43?

434

The SARS (Severe Acute Respiratory Syndrome) epidemic of 2002 has the distinction of being the first new communicable disease of the 21st century. How many SARS patients would need to be studied to be 95% confident that the mean incubation time is within 2.95 days of the population mean? Assume the population standard deviation incubation time is 10 days.

45

Suppose you have a population with an unknown distribution with mean 50 and standard deviation 10. What is the smallest interval that is guaranteed to contain at least 95% of the population?

5.27 < x < 94.73

The five number summary of a data set is 11-35-49-72-86. What percent of the data lies between 35 and 72 (assuming there are no repeated values)?

50%

A physicist is testing a new device that produces photon waves. The wavelengths of photons produced with this method are known to be normally distributed with standard deviation 2.5 microns. If he/she measures 22 waves that were produced and gets a sample mean 50 microns, what upper bound would be reported for the 96% confidence interval for the mean wavelength in microns?

51.0947

Suppose you have a normally distributed population with a mean of 57.32, standard deviation of 2.13. Consider the sampling distribution with sample size of 17. There is an interval (Lower, Upper) centered at 57.32 that contains 85% of the sampling distribution. Find the Upper bound of this interval.

58.0637

Calculate the median of the following: 76, 36, 74, 77, 69, 5, 43, 53, 72, 9.

61

Suppose you constructed a frequency table from a data set with 8 classes, class width of 7, and minimum value of 8. Assuming the data set only contains whole numbers, what is the largest possible value in the data set?

63

We are conducting a study on the typing speed of court reporters. If we have a sample of n = 70, and wanted to find our margin of error using t-critical, what would be our degrees of freedom, assuming the distribution of typing speeds is approximately normally distributed?

69

Calculate the 5-number summary for the following set of data: 7, 7, 8, 8, 11, 16, 17, 17, 19, 19, 21

7, 8, 16, 19, 21, 11

A candle company, "At Wick's End," produces a line of candles that are supposed to be 8 inches long. Taking a sample of 90 candles, their mean length was found to be 7.66 inches, with a sample standard deviation of 0.64 inches. Find the upper bound of the 92% confidence interval.

7.7795

A biologist is tasked with finding a 90% confidence interval for the mean weight of adult seals based on a random sample of 35 adult seals that was collected in the study region. Adult seal weights are known to have standard deviation of 13 kg. If the average weight within that sample was 70 kg, what is the upper bound of the associated confidence interval would be reported.

73.6144

Suppose you collect 1000 samples of size 80 from a population with parameter p = 0.770. If you construct a 76% confidence interval for each sample, how many intervals would you expect to contain the parameter p?

760

Researchers are interested in estimating the percentage of Americans who will get a flu shot this year. How many Americans should be surveyed to be 94% confident that the sample proportion of Americans who will get a flu shot this year is within 0.103 of the population proportion?

84

Do you think more children are born on a Friday? Or a Saturday? Or do you think every day of the week (Monday to Sunday) has the same chance to having a child born on that day? To test this theory, a researcher randomly sampled the records of 660 children, what would be the expected frequency for Monday?

94.2857

The amount of snow (measured in inches) that Boulder, CO receives per year is approximately normal with mean 71 and standard deviation 8. Using the empirical rule, what is the probability that Boulder will get more than 47 inches of snow in a given year?

99.85

Describe the properties of normal distribution

Approximately 68% of the data will fall within +/- 1 standard deviations of the mean, he area under the curve is 1, Approximately 95% of the data will fall within +/- 2 standard deviations of the mean, symmetrical

Our friend gives us a set of data we know nothing about except that the mean is 100 and the standard deviation is 5. Regardless of how the data set is distributed, we know that at least 75% of the data falls between 90 and 110. Which of the following would support this line of reasoning?

Chebyshev's Theorem

A study is done to see if CU students are getting enough sleep. 20 CU students are interviewed. The mean sleep time is calculated to be 7.2 hours with sample standard deviation 2.4 hours. Z or T test and why?

Does not apply

A correlation analysis is performed on x = number of books read per month, against y = IQ score. If a confidence interval for the slope of the regression line (beta) is reported to be (1.3, 3.2), it would be stated that:

For every additional book read, we can expect that between 1.3 and 3.2 more IQ points are scored.

An instructor claims the exam scores for all sections of a course are normally distributed with µ= 78.1 and σ= 6.8. Which of the following would be the appropriate null and alternative hypothesis to test whether the scores fit the claimed distribution?

H0: The scores are normally distributed with u= 78.1 and o= 6.8. H1: The scores are not normally distributed with u= 78.1 and o= 6.8.

A medical researcher is interested in whether the average recovery time from a virus is over 3 weeks. The null and alternate hypotheses that would be used are:

H0: µ = 3 H1: µ > 3

describe the assumptions when testing the significance of the correlation coefficient

Homogeneity of variance of the y-values at each x-value. The y-values are normally distributed about any given x. There is a linear relationship in the population.

Across the Nintendo game space, various game regions are reporting a positive Pixelitus test rate of 10 percent, with a standard deviation of 3 percent. In Hyrule the rate is 15 percent and in Mushroom Kingdom the rate is 6 percent. Assuming the distributions are approximately normal, which region's result is more rare?

Hyrule's is more rare because the z-score is further from zero, meaning it is more standard deviations from the mean.

Counties across the nation are reporting a positive COVID test rate of 10 percent, with a standard deviation of 3 percent. In Clarkston County the rate is 12 percent and in Kingston County the rate is 7 percent. Assuming the distributions are approximately normal, which county's result is more rare?

Kingston County's is more rare because the z-score is further from zero, meaning it is more standard deviations from the mean.

A study is done to see if CU students are getting enough sleep. 20 CU students are interviewed. The mean sleep time is calculated to be 7.2 hours with sample standard deviation 2.4 hours. Is it appropriate to perform a hypothesis test for means?

No, the distribution is not known to be approximately normal and our sample size is less than 30 so CLT does not apply.

A staple gun misfires 25% of the time, the rest of the time it staples correctly. If I try to staple something 20 times and letting r represent the number of times the stapler misfires, what would be the correct notation to indicate the probability that exactly 5 of those times the stapler misfires?

P(r=5)

A tire repair shop is able to patch 75% of air leaks. When the repair shop is unable to patch a leak, they have to replace the tire. If 20 tires are brought in with an air leak and r represents the number of tires that can be patched, what would be the correct notation to indicate the probability that more than 5 of the tires are able to be patched?

P(r>5)

Consider a hypothesis test with: H0: ρ = 0, Ha: ρ ≠ 0 ; p-value = 0.0063; and α = 0.01. Which of the following is the correct conclusion?

Reject H0 and conclude that there is significant relationship between x and y; the correlation coefficient is significantly different from zero.

A researcher wants to know if male CU students are shorter than the national average height of 175.4 cm. After randomly sampling a group of CU students the researcher conducts a hypothesis test at a level of significance of α = 0.01 and calculates a p-value of 0.0077. What should the researcher conclude?

Since p<α, the researcher should reject the null hypothesis and conclude that male CU students are shorter than the national average.

Public health officials are interested in determining if vaccination rates are higher in Marin County than in Kings County. After randomly sampling 1101 and 1053 health records in each county, respectively, a hypothesis test with a level of significance of α = 0.1 was conducted and a p-value of 0.0777 was found. What should the researcher conclude? (Consider Marin to be the first population).

Since p<α, the researcher should reject the null hypothesis and conclude that vaccination rates in Marin County are higher than in Kings County.

Out of 80 people surveyed, 4 said they don't like eating ice cream. Would it be appropriate to run a proportion test, with approximating with the normal distribution, to see if less than 10% of people don't enjoy eating ice cream?

Since the hypothesized number of successes and failues (8, 72) are both greater than 5, the test is appropriate.

Suppose you have a data set of size 17, with mean 20 and standard deviation 3. If you add 20 to every data value, how will the mean and standard deviation change?

mean will increase and standard deviation will stay the same

A recent survey showed an increase in alcohol use among local college students compared to the national proportion. Suppose that a survey of 98 local college students and 216 national college students is conducted to see if the proportion of alcohol use is higher locally than nationally. Locally, 54 college students reported drinking alcohol within the past month, while 109 national college students reported drinking it. Would it be appropriate to run a proportion test, with approximating with the normal distribution, to test this claim?

Since the hypothesized number of successes and failures (50.9, 47.1, 112.1, 103.9) are all greater than 5, the test is appropriate.

A study was done to determine if bulldogs sleep more hours in a day than pugs do. Let μ1 be the true mean number of hours bulldogs sleep per day, and μ2 be the same for pugs. Suppose after samples were collected, the 85% confidence interval was 0.3478 < μ1 - μ2 < 0.9871 What can you conclude from this interval?

Since the interval contains only positive numbers, we can conclude with 85% confidence that the true mean number of hours slept by bulldogs is more than the true mean number of hours slept by pugs in a day.

A study was done to determine if people with Apple phones are more likely to regularly play games on it than those with Android phones. Let p1 be the true proportion of people with an Apple phone that regularly play games on their phone, and p2 be the same for those with Android phones. Suppose after samples were collected, the 90% confidence interval was -0.1702 < p1 - p2 < 0.0936. What can you conclude from this interval?

Since the interval contains positive and negative numbers, we cannot conclude that the proportion of people that play games on Apple phones is different than the proportion of people that play games on Android phones.

A car company claims their new model of car has gas mileage of 33 mpg. After test driving 40 cars, the mean mileage was 32.1 mpg, with a 95% confidence interval of 31.01 < μ < 33.19. Based on this information, what can we conclude?

Since the interval contains the claimed population mean, we cannot conclude that the company's claim is incorrect.

If we have a correlation coefficient of r = 0.31, and r2 = 0.0961, then which of the following would be accurate?

The amount of unexplained variation is 0.9039 and the explained variation is 0.0961.

When performing a Z hypothesis test for means, we must have that:

The distribution is normal OR the sample size is at least 30. Also, the population standard deviation is known.

In the 70's, film giant Kodak conducted a study which showed (p < 0.001) a very strong positive linear correlation (r > 0.9) between film sales and the incidence of pick-pocketing and purse-snatching. The information came from a large sample of sales and police data collected from a range of locations worldwide. Which of the following would have been a valid conclusion from the study?

The levels of film sales and criminal activity are positively correlated but neither causes the other. They are both positively correlated to another factor such as the level of tourism.

A significance level for a hypothesis test is given as α = .01. Interpret this value

The probability of making a Type I error is .01.

A study conducted at a local cheer camp found a positive correlation between the average number of showers taken each week and the amount of deodorant used. What can be said about this?

There is a relationship between deodorant usage and showering. As showering increases, deodorant usage increases.

A hypothesis test results in rejecting the null hypothesis at the 5% level of significance. What can be said for the same hypothesis test at the 1% level of significance?

There is not enough information, the P-value would need to be provided in order to make a conclusion.

When performing a hypothesis test for a non-zero population correlation coefficient between HAQ (healthcare access quality index), and SDI (socio-demographic index), a P-value is found to be 0.0074. At the 1% level of significance, it would be stated that:

There is significant evidence that HAQ and SDI are correlated.

The age of an elephant is what kind of variable?

quantitative

Events in the same sample space can add up to be more than 1 (T or F)

True, if they are not mutually exclusive

Describe a 95% confidence interval for the unknown mean of a population

We are 95% confident that the unknown population mean is contained in the interval. The method used to generate this interval will correctly generate other intervals that contain the true sample mean 95% of the time. 95% of the confidence intervals calculated using this method will contain the true population mean. If you produced 100 confidence intervals using the same method, we would expect that approximately 95 of them will contain the true population mean.

A study is conducted to determine if a fishery is catching and selling tuna with weights below the standard of 70 pounds. A sample 80 tuna are collected, having a mean of 68.2 pounds. A test is performed at a 0.05 significance level to see if the mean weight of tuna by the fishery is below 70 pounds, resulting in a P-value of 0.0781. Choose the correct interpretation of this result.

We do not have enough evidence to conclude at the 0.05 significance level that the true mean weight of tuna caught by the fishery is less than 70 pounds.

A study is conducted to determine if a fishery is catching and selling tuna with weights below the standard of 70 pounds. A sample 80 tuna are collected, having a mean of 68.2 pounds. A test is performed at a 0.05 significance level to see if the mean weight of tuna sold by the fishery is below 70 pounds, resulting in a p-value of 0.03271. Choose the correct interpretation of this result.

We have enough evidence to conclude at the 0.05 significance level that the true mean weight of tuna caught by the fishery is less than 70 pounds.

Consider a scenario similar to that discussed above where we rolled a die 81 times to test if it were fair. Hypothetically, if we found a p-value of 0.0338, at the 0.05 significance level we would conclude the following:

We reject the null hypothesis in favor of the alternative.

Consider a scenario similar to that discussed above where we rolled a die 81 times to test if it were fair. Hypothetically, if we found a p-value of 0.0338, at the 0.05 significance level we would conclude the following:

We reject the null hypothesis in favor of the alternative. There is evidence that the die is unfair.

Which of the following would be a correct conclusion following an ANOVA test comparing three different means at a 5% significance level and p-value of 0.0152.

We reject the null hypothesis. There is sufficient evidence at the 0.05 significance level to suggest that at least one pair of means are not equal.

Reporting the average response for each question on a survey where the respondents select a number 1-5 would be a

bar graph

A census in Colorado is taken by randomly selecting the first 2,000 residents on a voting roster is called

a convenience

what must occur for a graph to be considered a time series graph

a measure of time is on the x-axis

A recent study on coffee consumption surveyed residents of Colorado and residents of Florida. The study found that Colorado residents drank an average of 6.1 ounces of coffee per day while Florida residents drank an average of 11.7 ounces of coffee per day. If we wish to test whether the mean coffee consumptions in these two states are different, what assumptions must be met to use the standard normal distribution (i.e., a z-test)?

both samples need to greater than or equal to 30 or the populations need to be approximately normal Both the population standard deviations are known.

A poll is conducted by randomly choosing 8 telephone number prefixes of an area code (eg 634-XXXX) and calling all numbers with those prefixes.

cluster

The first 200 names in the local phone book are selected for a poll.

convenience

What are two examples of quantitative variables?

daily temp and volume of a liquid

As n increases, the tails in the t-distribution become "fatter". (T or F)

false

Like the standard normal distribution (z), there is a different chi-square curve for each unique value of degrees of freedom (T/F)

false

The chi-square distribution is used for a comparison of two means (T/F)

false

The chi-square distribution is used for a test on a correlation coefficient. (T/F)

false

The chi-square distribution is used for an ANOVA test. (T/F)

false

There is more probability in the tails for a normal distribution (T or F)

false

We will always use a student's t distribution when we are given raw data to analyze, regardless if we know the population standard deviation or not. (T or F)

false

A die is rolled 33 times. If we want to test the claim that the die is fair (i.e., that the percentages of 1's, 2's, ....6's rolled are equal) which of the following would be the correct null and alternative hypothesis?

ho: dice is fair hi: dice is unfair

We want to test the significance of the correlation coefficient to decide whether there is a linear relationship in the sample data that is strong enough to use to model the relationship in the population. The line of best fit is: ŷ = -31 + 1.7x with r = 0.6451 and n=13 data points. What would be the appropriate null and alternative hypothesis?

ho: p=0 ha: p=/ 0

Select the appropriate null and alternate hypotheses for the following scenario: A recent survey showed an increase in alcohol use among local college students compared to the national proportion. Suppose that a survey of 98 local college students and 216 national college students is conducted to see if the proportion of alcohol use is higher locally than nationally. Locally, 54 college students reported drinking alcohol within the past month, while 109 national college students reported drinking it. *Denote the proportion of local college students who drink alcohol as pL and the proportion of national college students who drink alcohol as pN. Test the claim that alcohol use among college students is higher locally than it is nationally. Use a significance level of 0.05.

ho: pl=pn ha; pl> pn

You are trying to determine if the mean time Tom Cruise spends running in his movies is less than 30 seconds. After surveying 31 Tom Cruise movies, he runs for an average of 24 seconds.

ho: u = 30 ha: u <30

Which of the following is an assumption when testing the significance of the correlation coefficient?

homogeneity of variance

A person's year of birth is an

interval

Assume the weight of groundhogs are approximately normally distributed, with a mean weight of 8.6 pounds, and standard deviation of 1.1 pounds. If you take a random sample of 5 groundhogs, what is the probability the sample mean will be less than 9 pounds? How would you shade the graph representing the scenario above?

left-tailed including mean

Suppose you have a data set of size 11 with no repeated values, and that the mean and median are both 15. If you remove the two largest values from the data set, how will the mean and median change?

mean and median will decrease

Suppose you have a data set of size 11 with no repeated values, and that the mean and median are both 15. If you remove the smallest value and largest value from the data set, how will the mean and median change?

mean and median will stay the same

Suppose you have a data set of size 12, with mean 30 and standard deviation 4. If you multiply every data point by 4, how will the mean and standard deviation change?

mean and standard deviation will increase

Suppose you have a data set of size 40, with mean 34 and standard deviation 5. If you add two data points, both 15, to the data set, how will the mean and standard deviation change?

mean will decrease and standard deviation will increase

Suppose you have a data set of size 8, with mean 20 and standard deviation 3. If you add two data points, both 10, to the data set, how will the mean and standard deviation change?

mean will decrease and standard deviation will increase

Suppose you have a data set of size 11 with no repeated values, and that the mean and median are both 15. If you remove the value 15 from the data set, how will the mean and median change?

mean will stay the same and median cannot be determined

Suppose you have a data set of size 40, with mean 34 and standard deviation 5. If you add two data points, both 34, to the data set, how will the mean and standard deviation change?

mean will stay the same and standard deviation will increase

Geese are known to have an average weight of 12 pounds. A flock of geese from the northeast part of the country has an average weight of 7 pounds per animal. Find mu

mu= 12

Suppose x is a random variable from a very right-skewed distribution. In order to compute a 92% confidence interval, from a sample of size n = 9 with s = 5.3, determine which distribution (standard normal or Student's t) you would use, and what the corresponding critical value would be.

neither distribution applies

Suppose we want to create a confidence interval for population proportion, p. We take a sample of n=31 and compute that p̂ = 0.97. Is it reasonable to say that the distribution for the proportion (p) is approximately normal? Why or why not?

no, nq is less than 5

State two ANOVA assumptions

normality and homogeneity of variance

When studying the difference in the mean weights of two populations of study subjects, one which was given a weight loss pill and the other which was given a placebo, a 90% confidence interval is calculated to be (-1.55, 2.35). At this confidence level, we can:

not necessarily conclude the pill worked because the zero is in the interval

Which assumptions must be satisfied for a 1-sample proportion interval?

np and nq must be greater than 5

The total number of tornados that have touched down as of a given week in a 3-month time span would be an

ogive

A recent flyer claimed that 2 out of every 9 trucks sold at a local dealership are manufactured by Peterbilt. Find a 95% confidence interval for those who shop at this dealership that will purchase a Peterbilt truck. interval

one sample p interval

A random sample of 54 hot dog stands were sampled to determine the mean price of hot dogs in New York. The selected stands had a mean price $4.51 per hot dog and a standard deviation of $0.43 per hot dog. Find a 90% confidence interval for the true mean price of hot dogs in New York. interval

one sample t interval

A random sample of 36 apple trees were sampled to determine the average yielding an apple orchard. The average yield was 834 pounds per tree. The population standard deviation for this particular species of tree is 113 pounds. Find a 95% confidence interval for the mean weight of apples produced. interval

one sample z interval

Choose the correct null and alternate hypotheses for the following scenario: You are trying to determine if the proportion of people that have traveled outside of the country is more than 34%. After surveying 100 people, 30 said they have traveled outside of the country. Test the claim at the 0.01 significance level.

p = 0.34, p > 0.34

Top 3 complaints made when looking to where to focus customer service would be a

pareto graph

What are two examples of qualitative variables?

person's hair color and different types of investment options

How much time do you spend on social media apps? A statistician claims that college students spend an average of 15 hours per week on social media apps. She knows from a prior study that the population standard deviation is 6.7 hours. Assuming that all conditions are met, which test is appropriate?

z. test for one mean

You roll two 6-sided dice 12 times, and record the number of times the sum is 8. What is the sample space?

{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

You roll two 4-sided dice, and record the largest of the two numbers. What is the sample space?

{1, 2, 3, 4}

You roll two 4-sided dice, and record their sum. What is the sample space?

{2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

You flip 3 fair coins, recording each outcome in order. What is the sample space?

{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

You have an urn containing 1 white ball, 4 black balls, and 3 red balls. You randomly pull out two balls at the same time from the urn and record the colors. What is the sample space?

{WB, WR, BB, BR, RR}

Which assumptions must be satisfied to construct a 1-sample z-interval coming from a heavily left-skewed distribution (i.e., the distribution is not approximately normal)?

σ is known and n ≥ 30