Exam 2 Quiz Questions

A

What is the definition of the p-value? A. the probability that we would see a test statistic this extreme or more if the null hypothesis were true. B. the probability that we would see a test statistic this extreme or more if the alternative hypothesis were true. C. the probability that the alternative hypothesis is true. D. the probability that the null hypothesis is true.

2.539 (First, find the degrees of freedom, n-1. Use the t table and look up the degrees of freedom and the confidence level.)

What is the value of the t score for a 98% confidence interval if we take a sample of size 20?

p: unknown p-hat: 0.6697 po: 0.5

What proportion of students who take Intro Stats at the University of Florida have never taken Statistics before? Is it more than half of them? A study of STA 2122 students found that 438 out of 654 students had never taken a Statistics course before. Match the following symbols with the correct answer. p: p-hat: po: Options: unknown, 0.5, 0.6697

(4.58, 7.10), (Formula: x-bar +/- t*s / sqrt(n) In this problem, n is large, so you can use the z critical value rather than t.)

A study on students drinking habits asks a random sample of 60 male UF students how many alcoholic beverages they have consumed in the past week. The sample reveals an average of 5.84 alcoholic drinks, with a standard deviation of 4.98. Construct a 95% confidence interval for the true average number of alcoholic drinks all UF male students have in a one week period.

16 (Formula: Set z*s / sqrt(n) equal to the desired margin of error and solve for n. Make sure you use the correct value of z, and remember to round to the next largest integer.)

A study on students drinking habits wants to determine the true average number of alcoholic drinks all FSU undergraduate students have in a one week period. We know from preliminary studies that the standard deviation is around 2. How many students should be sampled to be within 1 drink of population mean with 95% probability?

(0.0910, 0.1238), (Remember that you have to have at least 15 observed successes and 15 observed failures. The formula for the confidence interval is phat +/- z * sqrt(phat *(1-phat)/n).)

In 2004, the General Social Survey (which uses a method similar to simple random sampling) asked, "Do you consider yourself athletic?" For this question, 255 people said that that they did out of 2373 randomly selected people. What is the 99% confidence interval for the proportion of all Americans who consider themselves athletic?

0.0064 (The standard error for a CI for p is sqrt((p-hat * (1 - p-hat)/n)))

In 2004, the General Social Survey (which uses a method similar to simple random sampling) asked, "Do you consider yourself athletic?" For this question, 255 people said that that they did out of 2373 randomly selected people. What is the standard error of the confidence interval?

It's p-value will be larger than .05. (TRUE - since the 95% CI DOES include 6 hours, we would NOT reject Ho: mu = 6 at alpha = .05, hence the p-value must be larger than .05.)

In 2004, the General Social Survey asked 2,664 respondents how many minutes or hours a week they spent sending email. The 95% confidence interval for the resulting data is (5.58 hours, 6.18 hours).What can we conclude about the significance test of Ho:mu=6 vs. Ha: mu does not equal 6?

-4.47 (To find the test statistic, TS = (x-bar - #in Ho) / (s / sqrt(n) ).)

A researcher was interested in studying Americans email habits. She suspected that Americans spend less than 7 hours a week answering their email. The General Social Survey in 2004 included a question that asked about the number of hours that the respondent spend on email per week. The General Social Survey in 2002 asked 1,264 respondents this question. The sample mean number of hours was 6.02 and the sample standard deviation was 7.80. Find the test statistic.

False (As you increase n, this causes the width of the interval (z times sqrt(p*(1-p)/ n) or t* s /sqrt(n) ) decreases. Think: Larger sample -- More information -- Smaller interval.)

As you increase n (assuming everything else remains the same), the width of the confidence interval increases. True or False?

It's p-value will be larger than .05

Suppose that you had consumer group wanted to test to see if weight of participants in a weight loss program changed (up or down). They computed a 95% confidence interval of the result (-4.977, 2.177). Suppose that we had a significance test with the following hypothesis: Ho: population mean weight loss = 0 Ha: population mean weight loss does not equal 0 What do we know about the p-value for the test?

w: -1.79; x: 0.0367; y: strong; z: population proportion

Suppose that you were trying to determine if the percentage of Americans that speak a second language is less than 30% . In 2016, the General Social Survey had a question that asked its participants if they spoke a second language. Out of 2867, 816 said yes. The hypotheses being tested are: Ho: p = 0.30 versus Ha: p < 0.30. a) The test statistic is ___w___ b) The p-value is __x__ c) So we have (strong/weak) statistically significant evidence that the ____z___ of Americans in 2016 who speak a second language is less than 30%.

1.94 (This question is asking for the test statistic only. TS = (phat - po )/ stderr. The stderr is sqrt(po*(1-po)/ n).)

Suppose that you were trying to determine if the population proportion of Americans that believe the government is doing too little to protect the environment is more than 50%. You decide to test the null hypothesis Ho: p = 0.50 versus Ha: p > 0.50. In 2010, the General Social Survey included a question that asked its participants if they felt that the US government was doing too little to protect the environment. Out of the 1304 surveyed, 687 said yes. What is the value of the test statistic for this problem?

A

The bootstrap method of constructing confidence intervals can be used to estimate: A. any parameter B. a population mean C. a population median D. a population standard deviation

A, C, D

The results of a confidence interval and significance test should agree as long as (Choose all that apply): A. we are making inferences about means B. we are making inferences about proportions C. the significance test is two-sided D. both are conducted on the same data set

6147 (Recall n= (p-hat)(1-p-hat)z^2/m^2 gives the minimum sample size needed for the desired confidence level and margin of error.)

We would like to estimate the proportion of UF students who owns a scooter to within 1% of the truth, with 95% confidence. We believe around 20% of students do. How many students should be sampled?

B (we always need to assume this), C (Yes - that makes it a problem about the proportion of successes), E ((This is necessary for the distribution of p-hat to be fairly symmetric (not too extreme in either direction)),

When we make inferences about ONE POPULATION PROPORTION, what assumptions do we need to make? Mark all that apply. A. Sample Size is 30 or more. B. Data must be from a simple random sample. C. Data is categorical. D. Counts of successes and failures at least 5 each. E. Counts of successes and failures at least 15 each F. Data is quantitative. G. The data must have a Normal Distribution.

at alpha=0.05

When looking at the results of a 95% confidence interval, we can predict what the results of the two-sided significance test will be:

17.94 (To find the standard error, find the standard deviation of the data set and then divide by the square root of n.)

You want to make a confidence interval for the true average price of calculators in Gainesville. A random sample of 5 calculators reveals the following prices: 10.95, 15.95, 103.95, 17.95, 12.95. What is the standard error of the sample mean, x-bar? IMPORTANT: Keep all significant digits in your calculator until the very end.

No (since a plot of the data shows an outlier.)

You want to make a confidence interval for the true average price of four function calculators in Gainesville. A random sample of 5 calculators reveals the following prices: 10.95, 15.95, 103.95, 17.95, 12.95. Can we use the t table to make this confidence interval? a) yes b) no

p: parameter we wish to make inferences about; p-hat: estimator used in conducting a significance test

What proportion of students who take Intro Stats at the University of Florida have never taken Statistics before? Is it more than half of them? A study of STA 2122 students found that 438 out of 654 students had never taken a Statistics course before. Match the following symbols with the correct answer. p: parameter we wish to make inferences about/estimator used in conducting a significance test p-hat: parameter we wish to make inferences about/estimator used in conducting a significance test

A, B, C

Which of the following are assumptions for the Significance Test for the Proportion? A. Data is from a random sample. B. npo and n(1-po) are both greater than 15 C. Data is Categorical. D. Data is Quantitative. E. Data is from a convenience sample. F. Data is from a Normal Distribution. G. nphat and n(1-phat) are both greater than 15

sample statistic (For the sampling distribution, we take repeated samples, compute the average for each one, and then look at the distribution of THOSE AVERAGES. OR For the sampling distribution, we take repeated samples, compute the proportion of successes for each one, and then look at the distribution of THOSE PROPORTIONS. The sample proportions and the sample averages are statistics.)

A sampling distribution refers to the distribution of a:

The average temperature of coffee in the population, which is unknown.

A coffee company wants to make sure that their coffee is being served at the right temperature. If it is too hot, the customers could burn themselves. If it is too cold, the customers will be unsatisfied. The company has determined that they want the average coffee temperature to be 65 degrees C. They take a sample of 20 orders of coffee and find the sample mean to be equal to 70.2 C. What does mu represent for this problem?

Ho: p = 0.33 Ha: p >0.33 (Hypothesis statements are about the population proportion(p), not the sample proportion (p-hat).By just random chance, someone would pick the cup with the ball under it 1/3 of the time. The researcher in this case is interested in determining if the ball is selected more often than suggested by chance.)

A researcher is interested in determining if a psychic really has power to predict. The researcher takes three cups and puts a ball under one of the cups. After mixing the cups up many times, the researcher asks the psychic which cup has the ball under it. The researcher records if the psychic was correct or not. The researcher does this one hundred times. If the psychic really has special abilities then he should pick the location of the ball more often then if it was by chance alone. The researcher is interested in determining if the correct cup is selected significantly more often then chance would suggest. What would be the null and alternative hypothesis for this case?

Ho: mu = 350; Ha: mu does not equal 350

A restaurant decides to test their oven's thermostat to see if it is working properly, that is, if the actual temperature inside the oven is the same as the temperature to which the thermostat was set. Twenty times, the oven was set at 350 degrees and then the temperature was measured with a thermometer. The chef wants to know if the average oven temperature is different from 350, when the thermostat is set at 350. What is the correct null and alternative hypothesis for this test?

mu= the true mean time spent by teenagers playing computer games this year

A scientist who studies teenage behavior was interested in determining if teenagers spend more time playing computer games then they did in the 1990s. In 1990s, the average amount of time spent playing computer games was 10.2 hours per week. Is the amount of time greater than that for this year? What is the parameter?

between 0.05 and 0.10 (Since this is a hypothesis test for the population mean and you have a small sample size, you must use the t table. Look at the n-1 degrees of freedom row on the table. Where does the test statistic fall in the row of critical values? There are three possibilities.*Does it fall between two critical values in absolute value?What is the area to the right of each of those critical values? Look at the subscripts at the top. Your p-value is between these probabilities.*Does it fall larger that all of the critical values listed in the table in absolute value?If your test statistic is less than all the critical values, then its p-value is greater than 0.10.*Is the test statistic smaller than all listed critical values in absolute value?If your test statistic is larger than all of the critical values, your p-value is smaller than 0.001.)

A scientist who studies teenage behavior was interested in determining if teenagers spend more time playing computer games then they did in the 1990s. In 1990s, the average amount of time spent playing computer games was 10.2 hours per week. Is the amount of time greater than that for this year? Twenty students were surveyed and asked how many hours they spent playing video games. The test statistics is equal to 1.39. What is the p-value?

(3.24, 4.08), (Formula: x-bar +/- t*s / sqrt(n)In this problem, n is large, so you can use the z critical value rather than t.)

A study on students drinking habits asks a random sample of 124 "non-greek" UF students how many alcoholic beverages they have consumed in the past week. The sample reveals an average of 3.66 alcoholic drinks, with a standard deviation of 2.82. Construct a 90% confidence interval for the true average number of alcoholic drinks all UF "non-greek" students have in a one week period.

A (TRUE - That is what "95% confidence" means), E (TRUE - This says the same thing as A), F (TRUE - As long as we talk about the probability of AN interval, not THIS interval.), G (TRUE: We are trying to estimate the population mean.)

A study reports that college students work, on average, between 4.63 and 12.63 hours a week, with confidence coefficient .95. Which of the following statements are correct? MARK ALL THAT ARE TRUE. There are four correct answers. You must mark them all to get credit. A. The interval was produced by a technique that captures mu 95% of the time. B. 95% of all college students work between 4.63 and 12.63 hours a week. C. 95% of all samples will have x-bar between 4.63 and 12.63. D. The probability that mu is between 4.63 and 12.63 is .95. E. 95% of samples will produce intervals that contain mu. F. The probability that mu is included in a 95% CI is 0.95. G. We are 95% confident that the population mean time that college students work is between 4.63 and 12.63 hours a week.

B (In order to use large sample confidence interval formula ((phat +/- z * sqrt(p*(1-p)/n with no additional values added), you must have at least 15 observed successes and 15 observed failures. If you don't have at least 15 observed successes and 15 observed failures, a small sample confidence interval can be computed by adding two successes and two failures.)

A survey asked 30 people if they believed that private enterprise could solve US problems 14 said yes. Which of the following statements correctly describes how the confidence interval for the population proportion of people that agree that private enterprise can solve US problems should be computed? A. There are not 15 successes and 15 failures. A confidence interval can not be done. B. There are not 15 successes and 15 failures. A confidence interval can be computed by adding 2 successes and 2 failures. C. There are not 15 successes and 15 failures. A confidence interval can be computed by adding 1 success and 1 failure. D. There are at least 15 successes and 15 failures. A large sample confidence interval for the population proportion can be computed (phat +/- z * sqrt(p*(1-p)/n) with no additional values added.

a) will not; b) will not; c) will not

A test of Ho:mu=0.36 vs Ha: mu not=0.36 resulted in a p-value of 0.004. We can predict that, using the same data set: a) the 90% CI for mu (will/ will not) include 0.36 b) the 95% CI for mu (will/ will not) include 0.36 c) the 99% CI for mu (will/will not) include 0.36

0.2033

A water treatment plant needs to maintain the pH of the water in the reservoir at a certain level. To monitor this, they take 2 oz. of water at 37 locations every hour, measure the pH at each of those locations, and find their average. If the pH level of the reservoir is ok, the results at each location will have varying results, with an average pH of 8.5 and a standard deviation of 0.22. If the pH level of the reservoir is ok, what is the probability that the sample average is LESS than 8.47?

normal (The sampling distribution of p-hat is approximately normal with a mean of p and a standard error of sqrt(p(1-p)/n) as long as np and n(1-p) greater than or equal to 15.)

If np is greater than or equal to 15 and n(1-p) is greater than or equal to 15, what is the approximate shape of the sampling distribution of the sample proportion?

b (p, the true population proportion that would have answered yes to this question)

In 1996, the General Social Survey (which uses a method similar to simple random sampling) asked, "On the whole, do you think it should be the government's responsibility to provide decent housing for those who can't afford it?" For this question, 240 people said that it definitely should out of 1572 randomly selected people. We will make a 90% confidence interval for: a) mu b) p c) p-hat d) sigma

0.0164 (margin of error = z*stderr)

In 2004, the General Social Survey (which uses a method similar to simple random sampling) asked, "Do you consider yourself athletic?" For this question, 255 people said that that they did out of 2373 randomly selected people. We will make a 99% confidence interval for p. What is the margin of error of the confidence interval?

(0.0910, 0.1238), (Remember that you have to have at least 15 observed successes and 15 observed failures. The formula for the confidence interval is phat +/- z * sqrt(phat *(1-phat)/n))

In 2004, the General Social Survey (which uses a method similar to simple random sampling) asked, "Do you consider yourself athletic?" For this question, 255 people said that that they did out of 2373 randomly selected people. What is the 99% confidence interval for the proportion of all Americans who consider themselves athletic?

p-value greater than .1: : we are not convinced that the person is guilty; p-value between .01 and .1: we are pretty sure the person is guilty; p-value smaller than .01: we are almost absolutely certain the person is guilty

In testing, we give the null hypothesis the benefit of the doubt, and don't believe the alternative unless we have overwhelming evidence for it. Our judicial system operates under a similar principle: A defendant is considered "innocent until proven guilty", and it is the job of the prosecutors to prove that guilt "beyond a reasonable doubt". This amounts to testing Ho: innocent vs Ha: guilty. In this context, match the following p-values with the correct interpretation. p-value greater than .1: p-value between .01 and .1: p-value smaller than .01: Options: we are not convinced that the person is guilty, we are almost absolutely certain the person is guilty, we are pretty sure the person is guilty,

A, C, E, F, H

MARK ALL THAT ARE TRUE!! We can use the Normal (Z) table to find probabilities about: A. individuals, if the population is Normal B. individuals, if the population is NOT Normal C. averages based on small n, if the population is Normal D. averages based on small n, if the population is NOT Normal E. averages based on large n, if the population is Normal F. averages based on large n, if the population is NOT Normal G. count of successes out of n independent trials H. sample proportion of successes out of n independent trials, when np and n(1-p) is large enough

No (we can't really check this assumption since we don't have the whole population, but the t distribution is robust to modest departures from Normality, so we can use it if a plot of the data has no major outliers.)

One of the assumptions we sometimes need to make when performing statistical inferences is that the response variable in the population has a Normal distribution. Is it possible to check that this assumption is satisfied?

0.0192 (To find the p-value, draw a picture of the normal curve. Mark off the test statistic and shade in the direction of the alternative. Find the shaded area in the normal table.)

Suppose we are testing Ho: p=.20 vs Ha: p does not equal .20 and TS=2.34. What is the p-value?

C (REMEMBER: Reject Ho if the p-value less than alpha)

Suppose you conduct a test and your p-value is equal to 0.002. What can you conclude? A. Reject Ho at alpha=0.05 but not at alpha=0.10 B. Reject Ho at alpha=0.10 but not at alpha=0.05 C. Reject Ho at alpha equal to 0.10, 0.05, and 0.01 D. Do not reject Ho at alpha equal to 0.10, 0.05, or 0.01

b

The sampling distribution of the sample mean is approximately normal with a mean of mu and a standard error of sigma/sqrt(n) as long as a) n is less than or equal to 30 b) n is greater than or equal to 30 c) n is less than or equal to 15 d) n is greater than or equal to 15

0.106 (Remember that np and n(1-p) must be greater than or equal to 15 for you to be able to complete the problem. Draw the picture. Mark off the mean and the value of interest. Create a z-score. (phat - p)/sqrt(p(1-p)/n). Use the z-score and the z-table to find the correct probability.)

Twenty-nine percent of Americans say they are confident that passenger trips to the moon will occur in their lifetime. You randomly sample 200 Americans and ask if they believe passenger trips to the moon will occur in their lifetime. What is the probability that less than 25% of the people sampled will answer Yes to the question?0.

1.70 (To find the z value for a (1-alpha)100% CI you need to figure out which z value has alpha/2 area to the right of it. For example, for a 95% CI alpha=1-0.95=0.05, so alpha/2=0.025. If you look up 0.025 in the middle of the Z table it corresponds to z=-1.96. That means the area to the left of z=1.96 is 0.025. So the area to the right of z=1.96 is also 0.025 by symmetry. So the answer would be z=1.96.)

What value of z should we use when making a 91% confidence interval for p?

a

the distribution of p-hat will ONLY be approximately Normal if np and n(1-p) are a) greater than or equal to 15 b) less than or equal to 15 c) greater than or equal to 30 d) less than or equal to 30