Stats 1430 Final Exam

True (Large P value means small z value, so your data is close to the value in Ho. You cant go against it.

(True/False) A large P-value means that you have little evidence against Ho.

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

(True/False) A p-value can change if you take a new sample.

False

(True/False) A p-value in hypothesis testing means the same thing as the sample proportion.

False (H0:Mu=5, Ha:Mu>5)

(True/False) If someone claims the population mean is 5 and you believe that its greater that five, you write the hypothesis Ho: Xbar=5 and Ha: Xbar>5.

False (Just means that you didn't have enough evidence against it)

(True/False) If you aren't able to prove the alternative hypothesis, this means the null hypothesis is incorrect.

False (The Z value is how many std. deviations away from the mean)

(True/False) If you have a Z-value Z=0.6, that means 60% of the data lies below you?

False (Not binomial. It isn't a yes or no question. There are many colors of M&M's.

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

False (The mean of x is = to the mean of Xbar)

(True or false) The mean of X is equal to Xbar?

True

(True/ False) There is a 100% chance that your sample mean lives within your 95% confidence interval.

True

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

False (Z=.40 represents the number of std. deviations away from the mean not the percentile of std. normal (z) distribution.

(True/False) The 40th percentile of standard normal (z) distribution occurs at the number z=0.40.

True (Alpha is your cutoff to reject Ho)

(True/False) The smaller alpha gets the harder it is to reject Ho.

True

(True/False) The t-distribution is symmetric?

True ( this is true because "not equal" to Ha has a doubled P-value

(True/False) 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.

True

(True/False) We use statistics to estimate population parameters, not the other way around?

a. True b. False (false; Xbar is sample and Mu x is population)

(True/False) Xbar=Mu x

False (CLT only applies to shape)

(True/False) You need the CLT to be able to say that the std. deviation of Xbar = std. deviation / sq root of n.

a. Yes (inverse, probabilities are symmetric)

(Yes/No) P(Z < -2.74) = P(Z > 2.74)

True

(true/false) The central limit theorem only applies to the SHAPE of the distribution of Xbar, not its mean or standard error.

False

14. 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?

False

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. (True/False) The 10% in this problem is a population parameter.

a.) The binomial distribution (correct) b.) the normal distribution c.) approximate normal distribution d. an unknown distribution

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. Let X be the number of professional golfers that said YES to your survey question. What is the name of the distribution of X?

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

As a general rule, the normal distribution is used to approximate a binomial distribution only if:

a. It increases b. It decreases c. It stays the same (correct)

As n increases, what happens to Mu sub Xbar?

a.) Increases (Correct) b.) Decreases c.) Does not change

As the population standard deviation increases, the margin of error:

This doesn't have a normal distribution. This doesn't have a normal distribution due to the fact that if it did, the plot would be in a relatively straight line, which this doesn't show in the given normal probability plot.

Below is a normal probability plot of salaried for stat 133 students 5 years after they graduate from OSU. Does this data have a Normal distribution? Explain why or why not. (Picture is on 'Practice Problems 1' sheet.)

a.) Bob' 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. (Correct) d.) Bob got a 25 on the exam.

Bob's Z-score on an exam is 0.25. What is the correct interpretation.

a. Bob's score is 25 percentage points above the mean. b. Bob scored better than 25% of the other students. c. Bob's score is 0.25 standard deviations above the mean. (Correct) d. More than one of the above answers is correct.

Bob's Z-score on an exam is 0.25. What is the correct interpretation? Circle one:

(32-28)/(10/Squ root of 40)

For the following 6 problems: An internet magazine reports the monthly internet access fee for all households has a normal distribution with mean $28. You think the mean fee is actually more than that. You select a random sample of 40 households and find the average monthly internet access fee is $32. (Assume the population standard deviation is $10.) Calculate the test-statistic. Show formula and all calculations.

a.) No b.) X had an already normal distribution

For the following 6 problems: An internet magazine reports the monthly internet access fee for all households has a normal distribution with mean $28. You think the mean fee is actually more than that. You select a random sample of 40 households and find the average monthly internet access fee is $32. (Assume the population standard deviation is $10.) Did we need the Central Limit Theorem to do any calculations or draw conclusions in the above problems regarding the average monthly internet access fee? a. Circle one: YES/NO b. Explain why or why not (10 words or less is all we will grade.)

a.) P=.0057<.05=alpha. Reject the Ho because P=.0057<.05=alpha b.) We reject the claim that the monthly internet access fee is $28

For the following 6 problems: An internet magazine reports the monthly internet access fee for all households has a normal distribution with mean $28. You think the mean fee is actually more than that. You select a random sample of 40 households and find the average monthly internet access fee is $32. (Assume the population standard deviation is $10.) Suppose the p-value for this problem turns out to be .0057 (do not calculate or dispute). Based on this p-value, what do you conclude about Ho and about the magazine's claim? a. Conclusion about Ho (and explain why) b. Conclusion about magazine's claim (in common language - 10 words or less)

a.) Change b.) Stay the same c.) Stay the same d.) Increase e.) Stay the same

For the following 6 problems: An internet magazine reports the monthly internet access fee for all households has a normal distribution with mean $28. You think the mean fee is actually more than that. You select a random sample of 40 households and find the average monthly internet access fee is $32. (Assume the population standard deviation is $10.) Up to this point you were testing to see if the average fee is more than $28 per month. Now suppose you want to test whether or not the average fee is $28. (Assume all the other information given in the original problem stays the same.) What would happen to each of the following items under this new testing scenario? Circle your answers; no calculations or explanations needed. a. The alternative hypothesis would: change/stay the same b. The test statistic (Z) would: increase / decrease / stay the same c. The significance level would: increase / decrease / stay the same d. The p-value would: increase / decrease / stay the same e. Your decision about whether or not to reject Ho in this particular problem would: change / stay the same

Ho: Mu=28 Ha: Mu >28

For the following 6 problems: An internet magazine reports the monthly internet access fee for all households has a normal distribution with mean $28. You think the mean fee is actually more than that. You select a random sample of 40 households and find the average monthly internet access fee is $32. (Assume the population standard deviation is $10.) What are your null and alternative hypotheses? Label them clearly.

a.) is exactly normal for any n (correct) b.) is exactly normal for n>30 c.) is approximately normal for n>30 d.) is approximately normal for any n

If X has a normal distribution, then the (sampling) distribution of Xbar:

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 (Correct)

If X has normal distribution, when does Xbar also have a normal distribution?

False (it would be Mu, not Xbar)

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

9

If the sample size for a data set is 10, the degrees of freedom for a confidence interval involving t is____?

a.) Your p-value (Correct) b.) Your significance level - Not correct because your significance level stays the same once it is set ahead of time. c.) Both A and B

If you get a new sample, which of the following elements of a hypothesis test will change?

a.) it increases b.) it decreases (Correct) c.) it stays the same d.) not enough information to tell

If you increase your n, what happens to the margin of error of your confidence interval for p?

a.) ME b.) YOU (Correct) c.) Same chance for both

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. Report the mean of your sample b. Find a confidence interval for µ (correct) c. Conduct a hypothesis test for µ d. None of the above

If you want to estimate the population mean, which technique do you use?

sample proportion (p-hat)

P-hat is the sample proportion or the population proportion?

a.) 30% b.) 40% c.) 10% d.) Unknown or none of the above (Correct)

Suppose that you want to estimate the percentage of all American families planning a cation for the summer. Your confidence interval is 30% to 40%. What is your value of p-hat?

a. 5th percentile for X b. 95th percentile for X (correct)

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.) increase (correct) b.) decrease c.) not change

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:

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

Suppose you have a multiple choice test and each question has 4 possible answers. If someone guesses, they would expect 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 you hypothesis test be?

a.) it increases b.) it decreases c.) It stays the same (Correct) Mu x bar = Mu x

Suppose you take a random sample of size n and look at the average x bar. As n increases, which of the following statements is true about the mean of x bar.

a.) The mean of Xbar decreases b.) The mean of Xbar increases c.) The mean of Xbar stays the same (correct)

Suppose you take a random sample size of n and look at the average Xbar. As n increases, which of the following statements is true:

a.) all OSU students (correct) b.) The 100 OSU students who were sampled c.) 30% d.) The percentage of all OSU students who will take classes this summer.

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.) The percentage of all sou students who will take classes this summer b.) 50 c.) 200 d.) 25% (Correct)

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

a.) Agree b.) Disagree (correct) c.) Not enough info to tell

Suppose your confidence interval for the percentage of all American families planning a vacation for the summer id 30% to 40%. Now suppose you the media reported that 50% of American families go on vacation during the summer, would you agree of disagree with them bases on your data?

a.) Reject Ho b.) Fail to reject Ho (Correct) c.) Accept Ho d.) Either b or c can be used

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 (Correct. You would fail to reject Ho because p-value = .055 > .05 = alpha.) c.) Accept Ho d.) Either b or c can be used

Suppose your p-value in a hypothesis test is .055. Using the standards from this class what do you conclude?

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

The Central Limit Theorem is important in statistics because it says:

a. It says for n ≥ 30, and any distribution that's not normal, the sampling distribution of is approximately normal. (correct) b. It says for any sample size and any distribution that's not normal, the sampling distribution of is approximately normal. c. It says for n ≥ 30 and any distribution that's not normal, the sampling distribution of is exactly normal. d. It says for any sample size, if X has a normal distribution, then the sampling distribution of is normal.

The Central Limit Theorem is important in statistics because:

a.) all residents of Apex, NC. (Correct) b.) Milbert Marketing c.) The 200 individuals contacted d. $32

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.) definitely between $27.60 and $36.30. b.) The average amount spent on DVDs by all residents (correct) c.) 200 individuals d.) The apex telephone directory

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 parameter of interest is:

a.) All residents of Apex, NC b.) The 200 individuals contacted (Correct) c.) $32 d.) The apex telephone directory

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 sample is:

Because of the Central Limit Theorem

The formula for a confidence interval for p involves a Z-value. Why is this? (Assume in is large)

0

The t-distribution has a mean of ____?

Z (Std. Normal)

The t-distribution looks more and more like a _____ distribution as the degrees of freedom increase?

False (The mean of Xbar = Mu sub x, not Xbar itself)

True or false: Xbar=Mu sub x

It tells our data comes from a normal distribution

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 increases (Correct) b.) It decreases c.) It stays the same

What happens to the std deviation (aka the std error) of Xbar if you have to REDUCE the sample size:

P=(x=k)=(n k)P^k(1-P)^n-k

What is the binomial distribution formula?

a.) P-value = .02 b.) Xbar = 15.10 (Xbar is a sample statistic) c.) Z=2.67 (Correct, test statistic = Z value) d.) More than one of these answers is correct

Which of the following is a test statistic?

a.) p-value= .02 b.) Xbar=15.10 c.) Z=-2.67 (correct) d.) More than one of these answers is correct

Which of the following is a test statistic?

a.) increasing the sample size increases the margin of error (Correct; Increasing the sample size doesn't increase MOE) b.) increasing the population std deviation increases the margin of error c.) Increasing the confidence level increases he margin of error

Which of the following statements is FALSE:

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 (correct) d.) Since the distribution of X is unknown, the distribution of Xbar is also unknown

X has some unknown distribution. What do we know about the distribution of Xbar?

a.) np>=10 and np(1-p)>=10 b.) np>=10 and n(1-p)>=10 (correct) c.) n>=10 and p>=10 d.) n>30

You can use normal distribution to approximate a binomial distribution when the following conditions are met: