Stats 1430 Notation

The smaller α (alpha) gets, the harder it is to reject Ho. a. True b. False

. True (alpha is your cutoff value to reject Ho

confidence interval for p

=phat+/-z sqrt(phat(1-phat)/n) - requires n large enough to meet conditions

confidence interval for mu x

=xbar +/- z(sigmax/sqrt(n)), if you know sigma - need X with normal distribution or CLT with large enough n

In this instance the parameter of interest is a. definitely between $27.60 and $36.40. b. the average amount spent on DVDs by all residents. c. 200 individuals. d. The Apex telephone directory.

b. the average amount spent on DVDs by all residents.

The owner of a restaurant claims that the time a customer takes to decide what they want on the menu (X) has a mean of 3.2 minutes. (Assume X has a normal distribution with standard deviation .8 minutes.) You believe the mean is more than 3.2 minutes. Your sample of 25 customers chosen at random has a mean time of 3.6 minutes. What is your p-value? a. 2.5 b. 0.9938 c. 0.0062 d. 0.05

c. 0.0062

The formula for a confidence interval for p involves a Z-value. Why is this? (Assume n is large.) a. Because the original distribution was a normal distribution .b. Because you always use Z in any confidence interval c. Because of the Central Limit Theorem d. All of the above

c. Because of the Central Limit Theorem

Bob's Z-score on an exam is 0.25. What is the correct interpretation? Circle one: a. Bob's score is 25 percentage points above the mean. b. Bob's score is at the 25th percentile. c. Bob's score is 0.25 standard deviations above the mean. d. Bob got a 25 on the exam.

c. Bob's score is 0.25 standard deviations above the mean.

X has some unknown distribution. What do we know about the distribution of Xbar? a. It has an exact normal distribution if the sample size n is large enough b. It has an approximate normal distribution for any sample size n. c. It has an approximate normal distribution if the sample size n is large enough. d. Since the distribution of X is unknown, the distribution of Xbar is also unknown.

c. It has an approximate normal distribution if the sample size n is large enough.

As n increases, what happens to muxbar a. It increases b. It decreases c. It stays the same

c. It stays the same

Suppose you take a random sample of size n and look at the average Xbar. As n increases, which of the following statements is true? a. The mean of Xbar decreases. b. The mean of Xbar increases. c. The mean of Xbar stays the same.

c. The mean of Xbar stays the same.

Which of the following is a test statistic? a. p-value = .02 b. xbar =15.10x c. Z=-2.67 d. More than one of these answers is correct.

c. Z=-2.67

Which of the following is a test statistic? a. p-value = .02 b. xbar=15.10 c. Z=-2.67

c. Z=-2.67

CLT conditions

np>=10 n(1-p)>=10

z- z=for pop z=for sample

standard deviation x-mu/sigma xbar-mu 0/sigma/sqrt(n)

Q1 and Q3 are

the 1st and 3rd quartiles of one sample of data

mux

the mean of the random variable X. Also known as the mean of the entire population

mu xbar

the mean of the random variable Xbar. Also known as the mean of all possible values of Xbar =to mu x the sample of the entire population

phat

the proportion of yeses in one sample

sigma x bar

the standard error of Xbar. Also known as the standard error of all possible values of Xbar - it is equal to the standard deviation of the population divided by square root of n.

sigma phat

the standard error of phat, the standard error of all possible values of phat =sqrt(p(1-p)/n)

test statistic when testing Ho about p is

z=(p-po)/sqrt((po(1-po))/n)

test statistic when testing Ho about mu x

z=(xbar-mu 0)/(sigma x/sqrt(n)) - need X with normal distribution or CLT with large enough n

Is pˆ the sample proportion or the population proportion? a. Sample proportion b. Population proportion

a. Sample proportion

. The Central Limit Theorem only applies to the SHAPE of the distribution of X-bar, not to its mean or standard error. a. TRUE b. FALSE

a. TRUE

. A p-value can change if you take a new sample. a. TRUE b. FALSE

a. TRUE (each sample gives a different test statistic and hence a different p-value)

Let X be the number of professional golfers that said YES to your survey question. What is the name of the distribution for X? a. The binomial distribution b. The normal distribution (exactly) c. Approximate normal distribution d. An unknown distribution

a. The binomial distribution

Suppose the time to serve a customer (X) has a normal distribution with mean 5 minutes and standard deviation 2 minutes. You want to investigate the 5% of customer service times that were the longest. What cutoff point are you looking for? a. 5th percentile for X b. 95th percentile for X

b. 95th percentile for X

Suppose your confidence interval for the percentage of all American families planning a vacation for the summer is 30% to 40%. Now suppose the media reported that 50% of American families go on vacation during the summer, would you agree or disagree with them, based on your data? a.Agree b. Disagree c.Not enough information to tell

b. Disagree

10. A p-value in hypothesis testing means the same thing as the sample proportion. a. TRUE b. FALSE

b. FALSE

Suppose your p-value in a hypothesis test is .055. Using the standards from this class what do you conclude? a. Reject Ho b. Fail to reject Ho c. Accept Hod. Either b or c can be used

b. Fail to reject Ho (for us, we use .05 as our cutoff value to reject Ho. This doesn't quite make it.)

Suppose your p-value in a hypothesis test is .055. Using the standards from this class what do you conclude? a. Reject Ho b. Fail to reject Ho c. Accept Ho d. Either b or c can be used

b. Fail to reject Ho (since the p-value .055 > significance level of .05.)

If you take a random sample of 50 M&M's and record the number of M&Ms of each color, you have a binomial distribution. a. True b. False

b. False

Let's say we have a random sample of n=61 and are testing a two sided hypothesis. The calculated z value is .04, is this sufficient evidence to reject the null hypothesis? Why or why not? a. True b. False

b. False (Z is the test-statistic, not the p-value. If Z is small, your data is close to the claim in Ho, so not much evidence against it.

If you are not able to prove the alternative hypothesis, this means the null hypothesis is correct. a. True b. False

b. False (just means you didn't have enough evidence against it)

If someone claims the population mean is 5 and you believe it's greater than 5, you write the following hypotheses: Ho: xbar= 5 and Ha: xbar>5 a. True b. False

b. False (x-bar is about data; need μ's)

If you want to estimate the population mean, which technique do you use? a. Report the mean of your sample b. Find a confidence interval for μ c. Conduct a hypothesis test for μ d. None of the above

b. Find a confidence interval for μ

If you increase n, what happens to the margin of error of your confidence interval for p? a. It increases b. It decreases c. It stays the same d. Not enough information to tell

b. It decreases

n this instance the sample is a. All residents of Apex, NC. b. The 200 individuals contacted .c. $32. d. The Apex telephone directory.

b. The 200 individuals contacted

If you roll a die 100 times and find the average, and I roll a die 200 times and find the average, who is more likely to have an average that is greater than 5? a. ME b. YOU c. SAME CHANCE FOR BOTH

b. YOU Because you roll fewer times, your results have a higher chance to be further away from the mean (3.5). The more times you roll the closer to 3.5 your results are likely to be.

You can use the normal distribution to approximate a binomial distribution when the following conditions are met: a. np ≥ 10 and np(1-p) ≥ 10. b. np ≥ 10 and n(1-p) ≥ 10. c. n ≥ 10 and p ≥ 10. d. n > 30

b. np ≥ 10 and n(1-p) ≥ 10.

Xbar=mux t/f

false, the mean of Xbar equals mux

sigma x

he standard deviation of X. Also known as the standard deviation of the entire population.

X

is a random variable that represents the individual values in the population. Varies from individual to individual.

Xbar

is a random variable that represents the sample mean of any sample of size n taken from the population. Varies from sample to sample.

xbar

is the mean of one sample of data

M

is the median of one sample of data

p

is the proportion of yeses in the entire population. Also known as the probability of getting a pyes in a binomial random variable with n trials.

s

is the standard deviation of one sample of data

xbar for all possible sample means

is the value of Xbar for one sample of size n from the population. (It represents the mean of one sample.)

x

is the value of for one single individual from the population.

CLT conditions

n has to be >30 and the xbar is normal

n k

n! / (k!)(n-k)!

normal distribution

n>30 or stated in the problem, in plot it is a straight line, in graph it is bell shaped

A survey is conducted to study the backgrounds of professional golfers. A random sample of 30 professional golfers was surveyed. The question they were asked was: "Did your parents play golf?" 10% of the golfers said yes. -The 10% in this problem is a population parameter. t/f

False

If you have a Z-value of Z = 0.6, that means 60% of the data lie below you. a. True b. False

False

You need the CLT to be able to say that the standard deviation of Xbar equals sigma/sqrt(n)

False CLT only applies to SHAPE

The mean of X is equal to Xbar T/F

False the mean of X equals the mean of Xbar

variance

SD^2

6. We use statistics to estimate population parameters, not the other way around. t/f

True

Suppose you have a confidence interval for the population mean. If the population standard deviation were to increase (and everything else stayed the same) then the margin of error for your confidence interval would: a) increase b) decrease c) not change

a) increase

A random variable X has a normal distribution with a mean of 40 and a variance of 25. Given that X = 20, its corresponding z- score is ____. a. -4.0 b. -0.8 c. 0.8 d. 4.0

a. -4.0

Suppose 1063 people out of a random sample of 2054 adults report that they play video games. What is the standard error of pˆ ? a. .0110 b. .0001 c..4997 d. .2496

a. .0110

suppose you want to estimate the percentage of all OSU students who will take classes this summer. You take a random sample of 200 OSU students and find that 50 of them will take classes this summer. What is the population in this problem? a. All OSU students b. The 100 OSU students who were sampled c.30% d. The percentage of all OSU students who will take classes this summer

a. All OSU students

The Milbert Marketing Group recently conducted a study of buying habits of the residents of Apex, North Carolina. From the Apex telephone directory they randomly selected 200 individuals and asked them how much they spent on purchases of DVD movies in the past month. They found that these individuals had spent an average of $32 with a margin of error of +/- $4.4 (constructed using 95% confidence.) In this instance the population of interest is a. All residents of Apex, NC. b. Milbert Marketing. c. The 200 individuals contacted. d. $32.

a. All residents of Apex, NC.

Suppose you have a multiple choice test and each question has 4 possible answers. If someone guesses, they would be expected to get 25% of the problems right in the long term. You believe your students did better than just guessing on your exam. If you conducted a hypothesis test for this, what would your hypotheses be? a. Ho: p = .25 and Ha: p > .25 b. Ho: p = .25 and Ha: p < .25 c. Ho: p > .25 and Ha: p = .25 d. Ho: p^ = .25 and Ha: p^ > .25

a. Ho: p = .25 and Ha: p > .25

Which of the following statements about margin of error is false? a. Increasing the sample size increases the margin of error. b. Increasing the population standard deviation increases the margin of error. c. Increasing the confidence level increases the margin of error.

a. Increasing the sample size increases the margin of error.

What happens to the standard deviation (aka standard error) of Xbar if you have to reduce the sample size? a. It increases. b. It decreases. c. It stays the same.

a. It increases.

The Central Limit Theorem is important in statistics because: a. It says for n ≥ 30, and any distribution that's not normal, the sampling distribution of Xbar is approximately normal. b. It says for any sample size and any distribution that's not normal, the sampling distribution of Xbar is approximately normal. c. It says for n ≥ 30 and any distribution that's not normal, the sampling distribution of Xbar is exactly normal. d. It says for any sample size, if X has a normal distribution, then the sampling distribution of Xbar is normal.

a. It says for n ≥ 30, and any distribution that's not normal, the sampling distribution of Xbar is approximately normal.

We collected some data and wanted to know if the data came from a normal distribution. We made a normal probability plot and it showed a straight line. What does this tell us? a. It tells our data comes from a normal distribution. b. It tells us our data does not come from a normal distribution. c. It doesn't tell us anything.

a. It tells our data comes from a normal distribution.

The Central Limit Theorem is important in statistics because it says: a. The distribution of is approximately normal, no matter what the distribution of X is, Xas long as n is large enough. b. The distribution of is approximately normal, no matter what the distribution of X is, and no Xmatter what the sample size is. c. The distribution of is normal if the distribution of X is normal.

a. The distribution of is approximately normal, no matter what the distribution of X is, Xas long as n is large enough.

The Central Limit Theorem is important in statistics because it says: a. The distribution of is X approximately normal, no matter what the distribution of X is, as long as n is large enough. b. The distribution of is X approximately normal, no matter what the distribution of X is, and no matter what the sample size is. c. The distribution of is normal if the distribution of X is normal.

a. The distribution of is approximately normal, no matter what the distribution of X is, as long as n is large enough.

A 95% confidence interval is wider than a 90% confidence interval if all else remains the same. a. True b. False

a. True

There is a 100% chance that your sample mean lies within your 95% confidence interval. a. True b. False

a. True

. A large p-value means you have little evidence against Ho. a. True b. False

a. True (large p value means small Z value, so your data is close to the value in Ho. Can't go against it.)

We may get different conclusions for the same problem if hypotheses are different. For example: conclusion for H0: μ=8 and HA: μ<8 might be different with conclusion for H0: μ=8 and HA: μ≠8. a. True b. False

a. True (not-equal-to Ha has a doubled p-value)

P(Z < -2.74) = P(Z > 2.74) a. Yes b. No

a. Yes

If you get a new sample, which of the following elements of a hypothesis test will change? a. Your p-value b. Your significance level c. Both a and b

a. Your p-value

As the population standard deviation increases, the margin of error: a. increase b. decrease c. does not change

a. increase

If X has a Normal Distribution, then the (sampling) distribution of Xbar a. is exactly normal for any n b. is exactly normal for n > 30 c. is approximately normal for n > 30 d. is approximately normal for any n

a. is exactly normal for any n

Suppose you want to estimate the percentage of all OSU students who will take classes this summer. You take a random sample of 200 OSU students and find that 50 of them will take classes this summer. What is the statistic in this problem? a.The percentage of all OSU students who will take classes this summer b. 50 c.200 d. 25%

d. 25%

A population has a mean and standard deviation of 45 and 9, respectively. A random sample of size 81 is taken from this population. The mean and standard deviation of Xbar are: a. 9 and 45 b. 45 and 9 c. 81 and 45 d. 45 and 1

d. 45 and 1

If X has a normal distribution, when does Xbar also have a normal distribution? a. The Central Limit Theorem is needed; n has to be large .b. The Central Limit Theorem is needed; n can be any size. c. The Central Limit Theorem is not needed; n has to be large. d. The Central Limit Theorem is not needed; n can be any size.

d. The Central Limit Theorem is not needed; n can be any size.

Suppose you want to estimate the percentage of all American families planning a vacation for the summer. Your confidence interval is 30% to 40%. What was your value of p^ ? a.30% b. 40% c.10% d. Unknown or none of the above

d. Unknown or none of the above

The normal distribution is used to approximate a binomial distribution only if: a. The sample size n is greater than 30 b. The population proportion p is close to 0.50 c. The underlying population is normal d. np and n(1 - p) are both greater than or equal to 10

d. np and n(1 - p) are both greater than or equal to 10

If someone claims the population mean is 5 and you believe it's greater than 5, you write the following hypotheses: Ho: xbar=5 and Ha: xbar>5 t/f

false (must use population mean mu NOT sample mean xbar)