Psych 10 final

Suppose the distribution of family incomes of all the US households is positively skewed with mean 71,000 and standard deviation 15,000. Based on the central limit theorem, what is the probability that the average income of some 2000 families is below 70,000? Let's assume the sample size is large enough so that the central limit theorem works well.

.14

Assume that cans of cola are filled so that the actual amounts are normally distributed with a mean of 12.00 oz and a standard deviation of 0.11 oz. We use X to denote the weight of a can of cola, so X ~ N(µ = 12, σ = 0.11). A supermarket sells this type of cola in boxes, and each box has 36 cans. We consider each box as a random sample of size n = 36. If we randomly pick a box from the supermarket, what is the probability that the average weight of the 36 cans in this box exceeds 12.05 oz? Hint: use the central limit theorem.

.32

A supermarket sells peaches in boxes, and each box has 16 peaches. The peaches vary in size, but all the boxes have the same label that says the net weight of the box is 64 oz and the price is $7. Suppose workers at this supermarket never weight the boxes, but just randomly put 16 peaches in each box. Some customers worry that selling peaches in this way is unfair, because they may get a box that weights much less than 64 oz but they pay the same price. The supermarket manager tries to dissuade their concern. Suppose weight of individual peaches in the population follow X ~ N(4, 0.2). If we randomly pick a box, what is the probability that the weight of the box is less than 62 oz (ie, 2 oz less than what the label says)?

.62

Suppose the weight of adults follow a normal distribution with mean 160 lbs and standard deviation 20. A certain scenic boat tour company operates on a small boat that has a capacity of 10 people only. To ensure safety, every passenger is required to have their weight measured before getting on the boat. If the total weight of the 10 passengers on the boat exceeds 1750 lbs, the boat is overweight and not allowed to operate. Assuming tourists all randomly come to the boat, how often will the boat be overweight? We want to know the probability of the total weight of the 10 people in the boat exceeding 1750 lb. This is equivalent to the probability of the average weight exceeding 175 lb. The probability is ________%.

.89%

Assume that cans of cola are filled so that the actual amounts are normally distributed with a mean of 12.00 oz and a standard deviation of 0.11 oz. We use X to denote the weight of a can of cola, so X ~ N(µ = 12, σ = 0.11). If we randomly pick a box of 36 cans from the supermarket, what is the probability that the average weight of the 36 cans in this box is less than 11.80 oz?

0

The standard normal distribution is a normal distribution with a mean of ______ and standard deviation of _______. 0;1 1;0 Any value; any positive value Any positive value, any value

0,1

IQ scores in the population follow N (100,15). We randomly pick a sample of 50 people from the population. Based on these 50 people,we will have _______ sampling distribution(s) of sample means. 1 50 Infinitely many 0

1

If we wish to form a 75 % confidence interval using normal distribution, what is the z-score we should use in the confidence interval formula? 0.75 1.15 37.5 0.2734

1.15

In the population, what percent of SAT scores are ABOVE 750? 2.28% 1.16% 22.7% 98.84 %

1.16%

Suppose the weight of adults follow a normal distribution with mean 160 lbs and standard deviation 30. A small private plane can carry 10 passengers only, and it cannot operate if the total weight of the 10 passengers exceeds 1800 lbs. Suppose passengers of this plane all randomly come from the population of adults. The probability that the total weight of 10 passengers exceeds 1800 lbs is

1.74 percent

Assume that the population of heights of men (in inches) has a normal distribution N(69.5, 2.4). If we draw a random sample of 100 men from the population, what is the probability that the mean height of the sample is less than 69.0 inches?

1.88

If Y~N (10,3), what is the mode of Y? 10 5 0 There is not enough information

10

In a normal distribution, what % of raw scores have a z-score that is larger than 1.20?

11.51

Texas has roughly 225,000 farms, more than any other state in the US. The actual mean farm size is µ = 582 acres, and the standard deviation is σ = 150. Suppose the size of these farms follows a normal distribution. For random samples of n = 100 farms. If I random select a sample of 100 farms, what is the probability that the sample mean is greater than 600 acres?

11.51

Scores of a certain test follow a normal distribution whose µ and σ are unknown. We know exactly 50% of the scores are below 120, and the other 50% are above 120. Then what is the mean of this normal distribution? 100 120 60 All of the above are possible values for µ, depending on the σ value

120

From a certain population I randomly draw a sample: (1,2,2,2,3,110). If I want to avoid making mistakes in the long term, what is my best guess of the population mean? 2 20 2.5 3

2

If variable Y follows N(20,5), what is the median of Y? 10 20 10.5 9.5

20

We have a random sample of n = 100 and the sample mean X = 25.7-. We also know o= 5. Give a 95 percent confidence interval for the population mean. Pick the closest answer if there is no exact match. 24.72 and 26.68 15.9 and 35.5 25.29 and 26.11 25.61 and 25.79

24.72 and 26.68

Suppose the weight of adults follow a normal distribution with mean 160 lbs and standard deviation 30. A small private plane can carry 10 passengers only, and it cannot operate if the total weight of the 10 passengers exceeds 1800 lbs. Suppose passengers of this plane all randomly come from the population of adults. The probability that an individual passenger's weight exceeds 180 lbs is

25.14 percent

Individual X scores in the population have a standard deviation of 15. For all the possible samples with sample size n = 25, their sample means have a standard error of __.

3

Assume that cans of cola are filled so that the actual amounts are normally distributed with a mean of 12.00 oz and a standard deviation of 0.11 oz. We use X to denote the weight of a can of cola, so X ~ N(µ = 12, σ = 0.11). If we randomly pick a can of cola from the production line, what is the probability that this can weights less than 11.80 oz?

3.44

Assume that cans of cola are filled so that the actual amounts are normally distributed with a mean of 12.00 oz and a standard deviation of 0.11 oz. We use X to denote the weight of a can of cola, so X ~ N(µ = 12, σ = 0.11). If we randomly pick a can of cola from the production line, what is the probability that the weight of this can will be larger than 12.05 oz?

32.28

The population has 50,000 athletes. We randomly assign these athletes to buses, and each bus takes 45 people. Within each bus, we calculate the average weight of the athletes. In the sampling distribution of mean weights, each data point is based on _______ athlete(s).

45

Numerous random samples of sample size n=4 are drawn from the population N(u=80, o=10). What is the standard error in the sampling distribution of sample means? 2.5 5 4 10

5

Suppose I draw many samples from a population and each sample has 64 students. In the sampling distribution of sample means, each data point is based on ________ students. 1 64 63 Numerous

64

In the population, what percent of SAT scores are BELOW 555? 38.30% 69.15% 19.15% 50%

69.15%

In a normal distribution, what percent of data are above Z = -0.84 (negative 0.84)?

79.95

Jerry's ACT score is higher than 85% of all the students' scores. So Jerry's ACT score is on the ______ percentile. 85th 15th 30.23rd 80.23rd

85th

Given a certain sample, we compute a 90% confidence interval for u as (55, 66). What is the confidence level of this interval? 0 percent or 100 percent 10 percent 90 percent 1.65

90 percent

Consider the statement "I collected a sample of 200 scores, and formed a 90 percent confidence interval for u as (12, 16)" Which of the following is INCORRECT? The probability that u falls within (12, 16) is either 0 percent or 100 percent 90 percent of the time, u is between 12 and 16 The width of this interval is 4. If I had a formed a 70 percent confidence interval instead, the interval should have been narrower.

90 percent of the time, u is between 12 and 16

Jack's SAT is 780. He did better than ______ of all the SAT test takers. 25.4% 2.54 % 99.46% 0.54%

99.46%

We can use a normal distribution to approximately describe the following data EXCEPT that The heights of 2000 randomly selected adult women The brain volumes of 250 randomly selected adult males A histogram that has two distinctive peaks (modes) The number of white blood cells of 500 randomly selected adult women

A histogram that has two distinctive peaks (modes)

Jerry got 680 on SAT. If he took ACT instead, what score would he have got? About 20.8 About 28.65 About 68 About 25.6

About 28.65

IQ scores in the population follow N(100, 15). If we calculate the z-score for each IQ raw score in the population, then all these z-scores will follow a ________ distribution. Exactly normal Standard normal Approximately normal Positively skewed

Approximately normal

Suppose the distribution of family incomes of all the US households is positively skewed with mean 71,000 and standard deviation 15,000. If I draw numerous samples from the US and each sample has 2000 families. For each sample I calculate the average income of the families in that particular sample. What would the sampling distribution of average family incomes look like? Postively skewed Negatively skewed Normal Approximately normal

Approximately normal

The time length of movies (eg, "Zootopia" is 104 minutes long, "Frozen" is 102 mins long, etc) follows a positively skewed distribution in the population. If we draw a random sample of 100 movies and make a histogram of the time lengths of these 100 movies, what would the histogram look like? Normal Positively skewed Approximately normal None of the above

Approximately normal

Consider the following two statements. Are they true or false? 1. If we draw numerous random samples of sample size n = 50 from a population and calculate each sample's mean, we will have numerous sampling distributions of sample means. 2. If we draw a sample size of n= 1,000,000 from a population and calculate the sample mean, we will have a sampling distribution of sample means. Both 1 and 2 are true Both 1 and 2 are false 1 is true, 2 is false 1 is false, 2 is true

Both 1 and 2 are false

Sam and Marilyn are both interested in the mean SAT score of all the students in Arizona. Sam randomly picked n = 80 students and got sample mean X= 522. Marilyn randomly picked n=150 students and got sample mean X= 530. Based on the Central Limit Theorem, are the following two statements true or false? 1. In the long run, as long as they always use X to estimate u, neither Sam or Marilyn will make mistakes in their estimation. 2. Sam's estimation is more reliable than Marilyn's, because the X in Sam's sample has a smaller standard error. Both 1 and 2 are true Both 1 and 2 are false 1 is true, 2 is false 1 is false, 2 is true

Both 1 and 2 are true

Assume that cans of cola are filled so that the actual amounts are normally distributed with a mean of 12.00 oz and a standard deviation of 0.11 oz. We use X to denote the weight of a can of cola, so X ~ N(µ = 12, σ = 0.11). Which case is more likely to appear, (a) a can weights over 12.05 oz, or (b) the average weight of 36 cans is over 12.05 oz? -Case (a) -Case (b) -It depends on the standard error - They are about equally likely

Case (a)

As sample size increases, the variability of X from sample to sample will Increase Decrease Remain the same Either A or B

Decrease

If we draw a sample with sample size 500,000 from a population, we will have a sampling distribution of sample means because the sample size is so large. True False

False

Which of the following statements about normal distribution is NOT correct? The normal distribution is a family of distributions There are infinitely many normal distributions To identify a normal distribution, we need to know two things about this distribution If a normal distribution is perfectly symmetric, it called standard normal distribution.

If a normal distribution is perfectly symmetric, it called standard normal distribution.

Based on the properties of normal distribution, which of the following is correct? The T-shirt size (S,M,L, etc) of people roughly follow a normal distribution The salaries of all NBA players roughly follow a normal distribution If the data is bimodal, the data do not follow a normal distribution If the data's mean is a lot smaller than the median, the data follow a normal distribution

If the data is bimodal, the data do not follow a normal distribution

Tom collected a sample of size n = 100, and formed a 90% confidence interval for µ as [4, 6]. Suppose later he find out that µ = 7 in the population. Which of the following statements is correct? Tom must have done something wrong in collecting data. Tom's interval was too wide. Tom must have made a mistake in calculation. It does not necessarily mean Tom made a mistake. Sometimes this can happen in practice.

It does not necessarily mean Tom made a mistake. Sometimes this can happen in practice.

Tom collects samples using n=100 and Jerry collects samples using n= 200. They are both form 90 percent confidence intervals for u. In the long run, for all the possible intervals Tom and Jerry could calculate, whose intervals will cover u more often? Tom's Jerry's The same All of the above are possible

Jerry's

Texas has roughly 225,000 farms, more than any other state in the US. The actual mean farm size is µ = 582 acres, and the standard deviation is σ = 150. Suppose the size of these farms follows a normal distribution. For random samples of n = 100 farms, what is the sampling distribution of sample means? N(582, 150) N(582, 15) N(582, 100) N(0, 1)

N(582, 15)

Are the following two statements true/possible or false/impossible? 1. Tom's SAT score is on the 10th percentile. Therefore, his score is among the top 10%. 2. Eric's SAT is on the 80th percentile and Sarah's SAT is on the 120th percentile. Sarah's SAT score is higher than Eric's Only 1 is true/possible Only 2 is true Both 1 and 2 are true Both 1 and 2 are false

Only 2 is true

The time length of movies (eg, "Zootopia" is 104 minutes long, "Frozen" is 102 mins long, etc) follows a positively skewed distribution in the population. We draw numerous random samples and each sample has 100 movies. For each sample we calculate the average time length X. What would the sampling distribution of X look like? Normal Positively skewed Approximately normal None of the above

Positively skewed

Suppose the distribution of family incomes of all the US households is positively skewed with mean 71,000 and standard deviation 15,000. I randomly pick 2000 families in the US and make a histogram of the incomes of these 2000 families. What would the histogram look like? Postively skewed Negatively skewed Normal Approximately normal

Postively skewed

When we draw several random samples from a population X will differ from sample to sample, because there is ___________. Standard error Sampling error Sampling distribution Random sampling

Sampling error

Sarah collects samples using sample size n = 100 and forms 90 percent confidence intervals for u. Eric collects samples using sample size n= 200 and forms 80 percent confidence intervals for u. In the long run, for all the possible intervals Sarah and Eric could calculate, whose intervals will cover u more often? Sarah's Eric's The same All of the above are possible

Sarah's

The variability of sample mean X is ________ the variability of individual scores X. Smaller than Larger than Roughly equal to Unrelated to

Smaller than

The standard error in the sampling distribution of sample means is ___________. Standard deviation also called sampling deviation sampling error standard deviation of individual X scores

Standard deviation

The distribution that is normal with mean 0 and standard deviation of 1 is called Regular normal distribution Standard normal distribution Perfect normal distribution Ideal normal distribution

Standard normal distribution

Which is correct about the normal distribution? The larger the standard deviation, the flatter and wider the normal distribution is THere is only one normal distribution Standard normal distribution is denoted as N(1,1) Some normal distributions are positively skewed

The larger the standard deviation, the flatter and wider the normal distribution is

Tom collects samples using sample size n =100 and Jerry collects samples using sample size n =200. They both form 90% confidence intervals (CIs) for µ. In the long run, for all the possible 90% CIs Tom could form, and all the possible 90% CIs Jerry could form, whose CIs will include µ more often? Toms Jerrys The same All of the above are possible

The same

The sampling distribution of sample means consists of All the scores contained in a sample All the scores contained in the population The sample means for all the possible samples The difference between sample mean and population mean

The sample means for all the possible samples

Anna studies smoking behaviors by asking people "How many cigarettes do you smoke per day?" We use X to denote this number, and X follows a positively skewed distribution in the population. Which of the following is a correct application of the Central Limit Theorem? If Anna collects a very large sample, the z-scores of people in her sample will follow a normal distribution The sampling distribution of sample means X is probably positively skewed If Anna collects a very large sample, the distribution of individual scores X in her sample is approximately normal The sampling distribution for X is approximately normal if Anna's sample size is large enough

The sampling distribution for X is approximately normal if Anna's sample size is large enough

Data in the population are positively skewed. Based on the central limit theorem. Which of the following is guaranteed to resemble a normal distribution? Data in a random sample Data in the population The sampling distribution of sample means, if n is large All of the above

The sampling distribution of sample means, if n is large

The standard deviation in the sampling distribution of sample means is usually called The sampling error of mean The standard error of mean The sample mean The central limit mean

The standard error of mean

hich is correct about the normal distribution? The larger the mean, the flatter the normal distribution will be There are infinitely many normal distributions Standard normal distribution is denoted as N(1, 1) Some normal distributions are positively skewed all of the above none of the above

There are infinitely many normal distributions

Suppose the distribution of family incomes of all the US households is positively skewed with mean 71,000 and standard deviation 15,000. If I randomly pick a family in the US, what is the probability that this family's income is below 70,000? 7% 47.21% 2.79 % There is not enough information

There is not enough information

Exam scores of a very easy test follow a negatively skewed distribution. Theses scores have u = 50 and o - 15. Eric got 61 on this exam. Which of the following statements must be correct? 50% of the class got scores above 50 ERic did better than 76.73 % of his classmates Eric did better than 73% of his classmates There is not enough information to calculate probabilities

There is not enough information to calculate probabilities

We have calculated an 80 percent confidence interval to be (86, 93). Suppose later someone who has access to the entire population tells us that the population mean is u=100. Which of the following statement is necessarily correct? This can happen in practice about 20 percent of the time. There's nothing wrong with u=100 falling outside of this particular interval (86,93) We must have made mistakes in calculation THe interval (86, 93 is to wide) Our sample size is too small

This can happen in practice about 20 percent of the time. There's nothing wrong with u=100 falling outside of this particular interval (86,93)

In a certain test, scores follow N(µ = 100, σ = 30). Which of the following statements is correct? The median of the data is 50 These test scores follow a standard normal distribution If we randomly pick a student, the probability of seeing this student's score below 70 is 34.13% Tom got 130 on this test. He is better than 84.13% of the test-takers.

Tom got 130 on this test. He is better than 84.13% of the test-takers.

Tom took ACT and got 29.8. Jerry took SAT and got 680. Whose score is better? Tom's 29.8 on ACT Jerry's 680 on SAT They are about the same There is not enough information

Tom's 29.8 on ACT

Which of the following statement is correct? Within a sample, it is reasonable to use X to estimate u because random sampling guarantees that X= u in this particular sample. We cannot avoid making mistakes when we estimate u based on a certain sample. Eric collects a sample and calculate an 80 percent Cl for u as (2, 6). Suppose later Eric finds out that the true population mean is in fact u=7. Then Eric must have made some mistakes in calculation. In inferential stats, we usually care how well we do in a given sample more than our overall performance in the long term

We cannot avoid making mistakes when we estimate u based on a certain sample.

Given a certain sample, we compute a 90 percent confidence interval for u as (55, 66). Which of the following is correct? The probability 90 percent is about this particular interval (55, 66). We do not know whether u is in the interval (55, 66) as u is unknown The probability that u falls within this interval (55, 66) is 90 percent U must be a value between 55 and 66

We do not know whether u is in the interval (55, 66) as u is unknown

If we draw numerous random samples of sample size n = 50 from a population, we will have numerous sampling distributions of sample means. True False

false

Due to ___________, different random samples are somewhat different from each other. standard error sampling error random sampling sampling distribution

sampling error

The sampling distribution of sample means is ____________ the population mean the mean of the distribution of the sample the distribution of sample means over all possible samples The distribution of data in a sample

the distribution of sample means over all possible samples

Given a particular sample, we compute a 95% confidence interval for µ as [112, 118]. Which of the following is INCORRECT? the probability 0.95 is about all the confidence intervals based on all the possible samples, not about this particualr one [112, 118]. we don't know whether this interval includes µ because µ is unknown. if this interval includes µ, then µ is somewhere between 112 and 118. we cannot say there is 0.95 probability that µ falls within [112, 118], because µ is not a random variable but a fixed value. the probability that µ falls within [112, 118] is 0.95.

the probability that µ falls within [112, 118] is 0.95.

In a random sample, every case in the population has an equal chance of being selected. True False

true

Which of the following is an incorrect method for point estimation? use sample mean to estimate population mean use sample median to estimate population median use sample variance to estimate population variance all of the above are correct methods for point estimation

use sample median to estimate population median

Consider the sampling distribution of sample means. With a large sample size and a small population variance, all the possible sample means will be close to the population mean. will slightly underestimate the population mean. will slightly overestimate the population mean. will equal the population mean.

will be close to the population mean.

Tom's SAT score is on the 80th percentile. So Tom did better than 80% of the students who took SAT. True False

true