Stats 3 Exam
In spring 2017, data was collected from a random selection of STA 2023 students. One of the questions asked how much sleep they had gotten the previous night. The 95% confidence interval comparing underclassmen to upperclassmen was (-0.233, 1.1250) Interpret the interval. We are 95% confident that the ___________________ hours of sleep for underclassmen is between 0.233 ______________ to 1.1125 _______________ that upperclassmen.
1. population mean 2. less 3. more
An instructor was interested in seeing if there was a difference in the average amount of time that men and women anticipate studying for an Introduction to Statistics course in the summer. A group of men and women were randomly selected from the University of Florida. The Minitab results are below. What is the best interpretation of the results below? Difference= mu(F) - mu(M) T-Test of difference= 0(vs not =): T-Value= 0.23 P-value= 0.817 DF=46 A. with a p-value of 0.817, there is no statistically significant evidence of a difference in the average anticipated amount of time studying between the men and women. B. with a p-value of 0.817, there is statistically significant evidence of a difference in average anticipated amount of time studying between men and women. C. with a p-value of 0.23, there is statistically significant evidence of a difference in average anticipated amount of time studying between men and women. D. with a p-value of 0.23, there is no statistically significant evidence of a difference in average anticipated amount of time studying between men and women. E. we are 81.7% confident that there is no statistically significant evidence of a difference in average anticipated amount of time studying between men and women. F. we are 23% confident that there is no statistically significant evidence of a difference in average anticipated amount of time studying between men and women.
A
Should we focus on the p-value instead of the alpha level? A. Yes- alpha is arbitrary, while the p-value gives a better representation of the amount of evidence we have to reject the null. B. No answer text provided. C. No-there is no relationship between alpha and the p-value. D. doesn't matter- alpha and the p-value are the same thing.
A
in 2010 and 2012, Gallup asked the same 50 people how many hours they had worked at a job in the past 7 days. Is there a difference in the population mean amount of hours worked at a job between 2010 and 2012? Would this be an example of independent or dependent samples? A. dependent samples B. independent samples
A
Which of the following are assumptions for the confidence interval for the different between two population means? Select all that apply. A. data is quantitative. B. there are at least 15 successes and 15 failures. C. data is from a convenience sample. D. both sample sizes are greater than 30 or the data from a normal distribution, E. random sample F. data is categorical
A, D, E
An agricultural field test compares two varieties of corn, silver queen and country gentlemen. The researchers take 10 plots and divide each of these plots in half. Each plot has similar amount of sun light, shade, quality of soil and irrigation. The variety of corn is randomly chosen for each half of a plot. After the harvest, the yield of corn is measured for each half plot at each location. The yield from silver queen was compared to the yield of country gentlemen. Note: Differences were taken by taking Variety A- Variety B. The 95% CI for the mean is (-0.223, 0.988) What is the correct interpretation of this interval? A. there is convincing evidence that variety A has a higher population mean yield than variety B, at 95% confidence. B. there is not enough evidence to say that variety A has a different mean yield than variety B, at 95% confidence. C. we have sufficient evidence to show that variety B has a higher population mean yield than variety A, at 95% confidence. D. there is convincing evidence that population mean yield of variety A is different from variety B, at 95% confidence.
B
An agricultural field test compares two varieties of corn, silver queen and country gentlemen. The researchers takes 10 plots and divides each of these plots in half. Each plot has similar amount of sun light, shade, quality of soil and irrigation. The variety of corn is randomly chosen for each half of a plot. After the harvest, the yield of corn is measured for each half plot at each location. The yield from silver queen was compared to the yield of country gentlemen. Note: Differences were taken by taking Silver Queen-Country Gentlemen. The 95% CI for the mean is (-0.223, 0.988) What can we expect will be the p-value for a two sided test using this data? A. the p-value should be smaller than 0.95 B. the p-value should be higher than 0.05 C. the p-value should be smaller than 0.05 D. the p-value should be higher than 0.95
B
An education specialist was studying SAT math scores at a local university. She found that the following 95% confidence interval for the population mean score for SAT math: (450, 550). Suppose that a significance test at Ho: population mean equals 345 versus Ha: population mean does not equal 345. The p-value for this test was 0.0007. Which of the following statements accurately describes this situation? A. the population mean score for SAT Math is statistically (but not practically) different from 475. B. The population mean score for SAT Math is statistically and practically different from 345. C. The population mean score for SAT math is practically (but not statistically) different from 345. D. The population mean score for SAT math is NOT statistically and practically different from 345.
B
Doctors are interested in seeing what type of arch support helps the most to alleviate foot pain. 25 volunteers are asked to wear one type of arch support for one week and rank their level or pain on a scale from one to ten. The next week, they wear another type of arch support and once again rank their pain. The type of arch support that each participants used the first week was randomly selected from the two types. Which arch support is better? What type of test would they conduct to test this claim? A. comparing proportions from 2 independent samples B. comparing means from dependent samples C. one proportion D. comparing proportions from dependent samples E. one mean F. comparing means from two independent samples
B
Go to artofstat.com and select the WebApp called Errors and Power in Significance Tests. Use the following settings. Select null hypothesis value po: 0.5 Type of alternative hypothesis: greater Show: Type 1 error True value of p: 0.65 Sample size n: VARIES Type 1 Error alpha: 0.05 Notice that since the true value of p=0.65 and the value of po we are testing against is 0.5, in this case the null hypothesis is FALSE. So the correct decision is to Reject Ho. Now change the value of n and notice what happens to the Type 1 and Type II errors. Which of the following is the best description of the effect of increasing n? A. Probability of Type I error does not change- that is given by alpha. But as the sample size n increases, the probability of a type II error decreases, making it easier to make a correct decision- Fail to Reject Ho. B. probability of Type I error does not change- that is given by alpha. But as the sample size n increases, the probability of a type II error decreases, making it easier to make a correct decision to reject Ho. C. probability of Type II error does not change- that is given by alpha. But as the sample size n increases, the probability of a type I error decreases, making it easier to make a correct decision to reject Ho.
B
In 2012, the general social survey included a question that asked respondents if they had "often/sometimes" been treated rudely at work. Out of 614 men, 62 said yes they had "often/sometimes" been treated rudely at work. Out of 589 women, 79 said yes they has "often/sometimes" been treated rudely at work. What is the pooled proportion for the null hypothesis Ho: p1-p2=0 vs. alternative hypothesis Ha: p1-p2 does not equal 0? A. unknown B. 0.117 C. 0.0739 D. 0.134 F. 0.101
B
in spring 2017, data was collected from a random selection of STA 2023 students. One of the questions asked how many hours they had volunteered in the past 24 hours. For the 39 randomly selected upperclassman, the sample mean was 0.12 and the sample standard deviation was 0.42. For the 35 randomly selected underclassmen, the sample mean was 0.34 and the sample standard deviation was 0.87. What is the point estimate of the difference in the population mean volunteered between underclassmen and upperclassmen? A. -0.45 B. -0.22 C. unknown D. 0 E. 4
B
A social scientist is interested in determining if there is a significant difference in the proportion of republicans between two areas of town. He takes independent random samples of 200 families in each area of town and a significance test was conducted. The p-value was 0.106. What should be our conclusions? A. the evidence is very strong- there is a difference in the proportion of republicans between the two areas of town. B. the evidence is very strong- there is NO difference in the proportion of republicans between the two areas of town. C. we do not have enough statistical evidence to say that there is a significant difference in the proportion of republicans between two areas of town.
C
When conducting a significance test to determine if there is a difference between two treatments, with a quantitative response variable, treatments, with a quantitative response variable, treatments are given to different experimental units, we summarize the data by: A. comparing the difference in the responses for each experimental unit under both treatments, and then finding the mean and standard deviation of the differences. B. computing the difference in the proportion of the sample that reacted better to treatment one and the proportion of the sample that reacted better to treatment two. C. computing the mean and standard deviation of each treatment group separately. D. computing the proportion of the sample that reacted better to treatment one than treatment two
C
A major grocery store chain is trying to cut down on waste. Currently, they get peaches from two different distributers, Wholefruits and GreenGrocer. out of two large shipments, the manager randomly selects items from both suppliers and counts the number of items that are not sell-able due to bruising, disease or other problems. She then makes a confidence interval. Is there a significant difference in the quality of the peaches between the two distributers? 95% CI for pW-pG:(-0.156, -0.064) A. we are 95% confident that the proportion of non sell-able items for WholeFruits is anywhere between 0.064 LOWER and 0.156 HIGHER than the proportion of non sell-able items for Green Grocer. B. we are 95% confident that the proportion of non sell-able items for Whole Fruits is anywhere between 0.064 and 0.156 HIGHER than the proportion of non sell-able items for Green Grocer. C. we are 95% confident that the proportion of non sell-able items for Whole Fruits is anywhere between -0.064 and -0.156 D. we are 95% confident that the proportion of non sell-able items for WholeFruits is anywhere between 0.064 and 0.156 LOWER than the proportion of non sell-able items for Green Grocer. E. we are 95% confident that the proportion of non sell-able items for Whole Fruits is anywhere between 0.064 and 0.156
D
A significance test is conducted to determine if the majority of students at UF have a paying job at some time during the year. Ho: p=0.5 vs Ha: p>0.5 What would a type I error mean in this setting? A. determining that it is NOT more than half of students in the population who have a job when in fact, it really is more than half. B. determining that it is NOT more than half of students in the population who have a job when in fact, it really is NOT more than half. C. determining that it is more than half of students in the population who have a job when that is the truth about the population. D. determining that it is more than half of students in the population who have a job when in fact, it is really not.
D
Do less republicans (group A) than Democrats (group B) favor the government investing billions of dollars to improve the country's train system? One thousand Republicans and one thousand democrats were asked if they favored spending billions to improve the country's train system. How would we write the alternative hypothesis? A. Ha: pA-pB=0 B. Ha: pA-pB does not equal 0 C. Ha: pA-pB > 0 D. Ha: pA-pB < 0
D
Do less republicans (group A) then democrats (group B) favor the government investing billions of dollars to improve the country's train system? One thousand republicans and one thousand democrats were asked if they favored spending billions to improve the country's train system. How would we write the alternative hypothesis? A. Ha: pA-pB > 0 B. Ha: pA-pB does not equal 0 C. Ha: pA-pB = 0 D. Ha: pA-pB < 0
D
Do students from UF tend to spend less time texting than students at FSU? A random sample of 100 students was taken from both schools. Let muf be the population mean number of text messages sent per day at UF and let mufsu be the population mean number of text messages sent per day at FSU. How should we write the alternative hypothesis? A. Ha: mufsu - muf < 0 B. Ha: mufsu - muf = 0 C. Ha: mufsu - muf does not equal 0 D. Ha: mufsu - muf > 0
D
What is the definition of Type 1 error? A. rejecting the null hypothesis when the null hypothesis is really false. B. failing to reject the null hypothesis when the null hypothesis is really true. C. failing to reject the null hypothesis when the null hypothesis is really false. D. rejecting the null hypothesis when the null hypothesis is really true.
D
in 2012, Gallup asked participants if they had exercised more than 30 minutes a day for three days out of the week. Suppose that random samples of 100 respondents were selected from both Vermont and Hawaii. From the survey, Vermont had 65.3% who said yes and Hawaii had 62.2% who said yes. What is the value of the population proportion of people from Vermont who exercised for at least 30 minutes a day for 3 days a week? A. 0.653 B. 0.6375 C. 0.622 D. unknown
D
Doctors are interested in determining if the human body temperature is really 98.6 degrees. He selects 30 students and records their temperature using a digital thermometer. What type of test would they conduct to test this claim? A. comparing means from dependent samples B. comparing means from 2 independent samples C. comparing proportions from 2 independent samples D. comparing proportions from dependent samples E. one proportion F. one mean
F
The issue of capital punishment is a hotly debated topic. Do more republicans than democrats support capital punishment? A researcher randomly selects 100 republicans and 100 democrats and asks them if they support or do not support capital punishment. In this problem, we want to make inferences about: A. comparing means from two independent samples B. comparing means from dependent samples C. Comparing proportions from dependent samples D. one proportion E. one mean F. comparing proportions from two independent samples
F
is there a difference in the amount of time that college students spend reading or watching the news as they go through college? One hundred students were asked as freshman and as senior how many minutes a day they spent reading or watching the news?
Means from dependent samples
What proportions of Americans believe in climate change?
One proportion
Do college students change their view on climate change as they go through college? One hundred freshman are asked if they believe in climate change. The same students are asked 4 years later if they also believe in climate change?
Proportions from dependent samples
is there a difference in the amount of time that republicans and democrats spend watching or reading the news?
Two independent means
Is there a difference in the proportion of men and women who believe in climate change?
Two independent proportions
Do people improve their timing on an online crossword puzzle with an additional attempt? Twenty people were timed to complete a crossword puzzle online. After a twenty minute break, they were asked to complete the crossword puzzle online again. Was there an improvement in their time? (first-second) The p-value was 0.12. Interpret. With a p-value of 0.12, we have______ statistically significant evidence that the _______________ time to complete the puzzle has improved.
no population mean
What is the average amount of time that americans spends watching or reading the news a day?
one mean
When we make inferences about the difference of two independent population proportions, what assumptions do we need to make? Mark all that apply. A. random samples B. sample size must be greater than or equal to 30. C. counts of successes and failures at least 15 each for each group. D. Normal distribution of the response variable. F. the sum of the counts of successes and failures must be greater than 30.
A, C
A small county has two property appraisers, Tim and Julie. Does Tim appraise property differently on average than Julie? Each appraiser looks at 20 properties and each independently determines the value of the property. (Tim-Julie) How should we write the alternative hypothesis? (mud is the population mean difference) A. Ha: mud=0 B. Ha: mud does not equal 0 C. Ha: mud > 0 D. Ha: mud < 0
B
A teacher wants to see if a new unit on factoring is helping students learn. She has five randomly selected students take a pre-test and a post test on the material. The scores are out of 20. Has there been improvement? (pre-post) What value of t would you use for the 95% CI? Student: 1 2 3 4 5 Pre-test: 12 14 11 12 13 Post-Test: 15 17 15 20 13 A. 2.105 B. 2.776 C. 1.96 D. 2.571 E. 2.132
B
A teacher wants to see if a new unit on fractions is helping students learn. She has five randomly selected students take a pre-test and a post test on the material. The scores are out of 20. Suppose than you are about to compute a confidence interval for mud, how do you check for normality? A. you don't have to check for normality for this type of data. B. find the difference between the two scores for each subject. Make a plot of the differences and check for outliers. C. make a plot of the pre and post test scores and see if there are any outliers. D. you don't have to check for normality since the values are large enough.
B
A teacher wants to see if a new unit on taking square roots is helping students learn. She has 5 randomly selected students take a pre-test and post test on the material. The scores are out of 20. Has there been improvement? (pre-post) Pre-test: 11 9 10 14 10 Post-Test: 18 17 19 20 18 The test statistic is -14.9. What is the p-value? A. p-value > 0.01 B. p-value < 0.002 C. p-value < 0.001 D. p-value > 0.02
C
