Stat 210 final

New Situation: Many meteorologists track named storms, particularly those that have the potential to make landfall; some meteorologists are more successful in predicting the track of the storm than others. Suppose all currently employed meteorologists are identified as either being employed by the U.S. National Weather Service, employed by a local television station within the United States, or employed in a country other than the United States. In this scenario, what is the population of interest?

All currently employed meteorologists

Of interest is for all earthquakes that have occurred between January 2015 and September 2017, to describe the relationship between the magnitude of the earthquake and the number of people killed by the earthquake. In this scenario, what is the population of interest?

All earthquakes that have occurred between January 2015 and September 2017

New Situation: For all named storms since 2000, of interest is to determine the proportion of these named storms that did make landfall in the United States. Based on this information, what is the population of interest?

All named storms since 2000

The relationship between the magnitude of the earthquake and the number of people killed is influenced by the country in which the earthquake takes place. Some countries have building codes that produce buildings that better withstand the damage of an earthquake than buildings in some other countries. In this scenario, the country in which an earthquake takes place is which of the following?

Lurking variable

One of the classes in the sample is a section of STAT 210 with 126 enrolled students. Using this data, if the value of 126 were removed from the data set, which of the following statistics is a measure of center that would be heavily influenced by the removal?

Mean

Based on the information in question 1, what is the parameter of interest?

Mu = The mean sustained wind speed of the storms at the time they made landfall

Consider the information in question 1. Based on this, using both the appropriate symbol and in words, what is the parameter of interest?

Mu = the mean number of enrolled students in all the classes being taught at VCU during the Fall 2022 semester

For all 2022 Veterans Day celebrations, of interest is to determine the mean number of people attending the celebrations. Based on this, using both the appropriate symbol and in words, what is the parameter of interest?

Mu = the mean number of people attending all 2022 Veterans Day celebrations

To select the sample described in question 9 the following was done. First, a random sample of 5 years between 2000 and 2017 was selected. Then for each of these 5 years, a random sample of 4 named storms was selected. What type of sampling procedure is this an example of?

Multistage random sampling

Is the population standard deviation sigma known?

No

What are the unusual features of the sampling distribution?

None

What is the shape of the sampling distribution?

Normal

Specific to this situation, what is the dependent variable?

Number of People killed

Suppose a sample of 25 named storms that have made landfall in the United States since 2000 is chosen. The sample is purposely selected such that all the storms made landfall in either Texas or Louisiana; storms that made landfall in other states are excluded from the sample. In this scenario, what type of bias could this cause?

Selection bias

In the current chapter covering statistical inferences on means, all of the procedures we have discussed (sampling distributions, confidence intervals and statistical tests) have involved two assumptions. What are those two assumptions?

Simple random sample and either the population is normally distributed or the sample size is large enough for the Central Limit Theorem to apply.

Earthquakes come in three main forms, depending on the plate movements that occur beneath the earth's surface. They could occur on a Convergent Boundary, on a Divergent Boundary or on a Transform Fault. The severity of the earthquake is classified as either mild, moderate, or major. Of interest is to determine if there is a relationship between the form of the earthquake and the severity of the earthquake. A random sample of 500 earthquakes was analyzed, and the following chart presents the conditional distributions of the severity of the earthquake for each form of earthquake.

Since the conditional distributions are significantly different, there is an association between the form of the earthquake and the severity of the earthquake.

What is the shape of the distribution?

Skewed Left

Earthquakes A random sample of 42 earthquakes that have occurred between January 2015 and September 2017 was selected and for each earthquake the magnitude of the earthquake and the number of people killed was recorded. The data appear in the scatterplot below.

Specific to this situation, what is the independent variable? Magnitude of Earthquake

A sample of 20 named storms since 2000 was selected. In this sample, 6 of the storms, or 30%, did make landfall in the United States. In this scenario, is 30% an example of a parameter or a statistic?

Statistic

This is a concept/definition question: which of the following sampling methods would give the highest likelihood of getting a sample of meteorologists that is representative of the number of meteorologists in the thee groups?

Stratified random sampling

Use the bar graph to describe the distribution for the flavor of cupcake for the sample of 40 cupcakes.

The cupcake ordered with the highest frequency is coconut (17) followed by strawberry-white chocolate (10), lemon (7), and chocolate-cream cheese (6)

Consider the information provided in questions 15 and 16. In this scenario, whigh of the following is the response variable?

The score ranging from 0 to 25 assigned for each predicted track of the named storm.

Which of the following is the correct conclusion for the hypothesis test?

There is insufficient evidence that the proportion of all people who went trick-or-treating who also had a pumpkin carved into a jack-o-lantern at their home is less than 0.62.

Based on the decision in question 10, which of the following is the correct conclusion?

There is sufficient evidence that the mean number of people attending all 2022 Veterans Day celebrations is different from 145 History people.

Which of the following are correct comparisons between the Z distribution and all t-distributions?

They have the same shape, mean and unusual features

Stem-and-leaf plots, histograms, and boxplots are all graphical methods for displaying quantitative variables.

True

Starting in 2000 and going through Hurricane Harvey in 2017, there have been 464 named storms in the past 18 years. Suppose we want to select a simple random sample of 12 named storms for further analysis. Each named storm is associated with a three-digit number between 001 and 464. The lists of numbers below are rows of a table of random digits; please start at the far left of the first row and select a simple random sample of 12 named storms out of the total of 464 named storms. All that is required is to simply give the numbers of the 12 named storms that were chosen using the rows of random digits below 135599 201944 313927 404838 545902 603410 752229 893865 911299057273 105820 298223 304367 459035 522957 632850 720854 829109 985767 059105 138502 248503 358239 447728 598347 603494

Using the lines of random digits provided, the list of 12 numbers selected is as follows: 135, 201, 313, 404, 410, 229, 299, 057, 273, 105, 298, 223

Using 95% confidence, suppose 64 out of 320 people received fruit in addition to candy. Which of the following is the correct interpretation of the confidence interval?

We have 95% confidence that the proportion of all people who went trick-or-treating who received fruit in addition to candy is between 0.15617 and 0.24383.

Instructions A different simple random sample of 16 classes being taught at VCU during the fall 2022 semester was selected and for each the number of enrolled students recorded. The data is given in the stem and leaf plot below. Formulas are given below the stem and leaf plot.

What is the value of the appropriate measure of center? Median = 102.5

Consider the information provided in questions 15 and 16. In this scenario, which of the following is the treatment variable?

Whether the meteorologist is employed by the U.S. National Weather Service, employed by a local television station within the United States, or is employed in a country other than the United States.

Which of the following values represents the weakest correlation between two variables?

r = 0.07

Which of the following values represents the strongest correlation between two variables?

r= -0.92

What is the correct value of the test statistic?

t = 3.341

If 64 out of 320 people received fruit in addition to candy what are the 95% confidence interval values?

(0.15617, 0.24383)

A simple random sample of 270 people who went trick-or-treating is selected, and 162 of them also had a pumpkin carved into a jack-o'-lantern at their home (and the other 108 did not). Use this information to test if the proportion of all people who went trick-or-treating who also had a pumpkin carved into a jack-o'-lantern at their home is less than 0.62 at the a = 10 level of significance. What is the value of the test statistic Z?

-0.68

For the data below, calculate the correlation coefficient between X and Y. You may use the calculator to find the answer, or you can use the totals provided to aid in the calculation by hand.

-0.798

Suppose we have a t-distribution with 22 degrees of freedom. Find the value of t22 such that the probability of being less than that value is .975.

2.074

Calculate the standard deviation of the data.

26.56

Calculate the IQR of the data.

27.5

Suppose the goal is to estimate the proportion of all people who went trick-or-treating who ate all of their candy in one night using a 95% confidence interval with margin of error no larger than 0.048. What is the minimum number of trick-or-treaters that would need to be selected to allow the calculation of a 95% confidence interval with margin of error no larger than 0.048? It can be assumed for this problem only that the proportion of all people who went trick-or-treating who ate all of their candy in one night is 0.24 and this number can be used for this problem.

305

Now suppose of interest is to estimate the mean number of children attending all 2022 Veterans Day celebrations. For this problem only, assume that the standard deviation of the number of children attending all 2022 Veterans Day celebrations is 21. What is the minimum number of 2022 Veterans Day celebrations that would need to be selected for the sample to allow the calculation of a 98% confidence interval with margin of error no larger than 8.

38

Rhiannon made her first sky dive while in college. Based on a normal distribution with mean 52.8 years and standard deviation 10.3, what must the age of a skydiver be to fall in the bottom 11.12% of the distribution?

40.232

Calculate the median of the data.

45.5

On May 16, 2017, Verdun Hayes of Somerset, Great Britain set a new Guinness World Record: the oldest ever skydiver. The World War II veteran, who fought on the beaches of Normandy in 1944, set a new record when he skydived at age 101. Suppose the ages of all skydivers follow a normal distribution with mean 47.8 years and standard deviation 12.6 years. Based on this distribution, how old must a skydiver be to fall in the top 2.62% of the distribution?

72.242

The regression line that gives the linear relationship between the magnitude of the earthquake and the number of people killed is predieted mmbar of people billed - 114 • 35,4 (magnitude of the earthquake), In 2017 a 5.8 magnitude earthquake was centered in Louisa County, Virginia; use the regression line to prediet the number of people killed for a magnitude earthquake

91.32

For a given set of data, a relative frequency histogram is more likely to be skewed than a frequency histogram.

False

What are the unusual features?

15 is an outlier

What is the probability that a standard normal variable will be equal to -0.68?

0

What is the p-value?

0.0018

Aaliyah is 24 years old. Based on a normal distribution with mean 52.8 years and standard deviation 10.3, what is the probability that a skydiver will be 24 years of age or less?

0.0026

Suppose we have a t-distribution with 22 degrees of freedom. Find the probability that t22 is greater than 2.508.

0.01

What is the standard deviation of the sampling distribution? (round to 4 decimal places)

0.0382

Bryse is 62 years old. Based on a normal distribution with mean 49.3 years and standard deviation 11.8, what is the probability that a skydiver will be 62 years of age or more?

0.1409

If 64 out of 320 people recgived fruit in addition to candy what is the value for P hat?

0.2

What is the p-value of the test? (Z table is provided at the beginning of the test if needed)

0.2492

Riana Miren and Trinh are 52 and 64 years old, respectively. Based on a normal distribution with mean 47.8 years and standard deviation 12.6, what is the probability that a skydiver will be between 52 and 64 years of age?

0.2702

What is the mean of the sampling distribution? (round to 3 decimal places)

0.373

A simple random sample of 270 people who went trick-or-treating is selected, and 162 of them also had a pumpkin carved into a jack-o'-lantern at their home (and the other 108 did not). Which of the following is the correct value for p ?

0.6

Consider the scatterplot above. Which of the following is the best guess of what the correlation coefficient r is equal to?

0.6

What is the standard deviation of a standard normal distribution?

1

What z value should be used to calculate a 95% confidence interval? (Use the t table provided at the beginning of the test)

1.960

The regression line that gives the linear relationship between the magnitude of the earthquake and the number of people killed is predicted number of people killed = -114 + 35.4(magnitude of the earthquake). Which line best represents this equation?

Black

Suppose a 95% confidence interval was computed based on a sample of 320 trick-or-treaters. If the sample size were increased to 640, what impact would this have on the margin of error and width of the confidence interval?

Both the margin of error and the width would decrease

Instructions A simple random sample of 16 classes being taught at VCU during the fall 2022 semester was selected and for each the number of enrolled students recorded. The data is given in the stem and leaf plot below. Formulas are given below the stem and leaf plot.

Calculate the mean of the data. 48

For all named storms since 2000, it is recorded for each whether it made landfall in the United States or not (yes or no). Whether a named storm made landfall in the United States or not is what type of characteristic?

Categorical variable

A random sample of 85 undergraduate level classes was selected and the number of enrolled students during the fall 2017 semester was recorded for each. The data is displayed in the boxplot below. Use this boxplot to completely describe the distribution of the number of enrolled students in this sample of 85 undergraduate level classes.

Center of 65, Skewed left, Spread (IQR) 25, 10 is an outlier

Consider the information presented in question 1. What type of characteristic is the mean sustained wind speed of the storms at the time they made landfall?

Continuous Quantitative Variable

Each year the proportion of named storms that make landfall in the United States is calculated. Based on this, the proportion of named storms that make landfall in the United States is what type of characteristic?

Continuous quantitative variable

The amount of damage done by a named storm is impacted in part by the number of days the storm stays over land once it makes landfall. What type of characteristic is the number of days that a storm stays over land once it makes landfall?

Discrete quantitative variable

Suppose we wanted to predict the number of people killed for a magnitude 10.0 earthquake. Using the regression line presented in question 4 to do this would be an example of which of the following?

Extrapolation

Using a significance level a = .10 what would your decision be?

Fail to reject the null hypothesis

Situation Veterans Day is an official United States public holiday that honors military veterans who served in the United States Armed Forces. It is observed annually on November 11 and coincides with other holidays, including Armistice Day and Remembrance Day, celebrated in other countries that mark the anniversary of the end of World War I. Major hostilities of World War I were formally ended at the 11th hour of the 11th day of the 11th month of 1918, when the Armistice with Germany went into effect. The United States previously observed Armistice Day. The U.S. holiday was renamed Veterans Day in 1954.

For all 2022 Veterans Day celebrations, of interest is to determine the mean number of people attending the celebrations. Based on this, what is the population of interest? All 2022 Veterans Day celebrations

Budget Redesign VCU recently moved to a new budget model called University Budget Redesign, a new budget process and model designed to enhance VCU's mission, vision, core values and strategic direction. The budget redesign allows VCU to make focused investments over time in our strategic plan and priorities. It enables departments, schools and the college to adopt an entrepreneurial spirit and take calculated, well-informed risks to advance and support our goals. It also allows central support units to collaborate more effectively. One key aspect of the University Budget Redesign is to return a significant portion of the tuition revenue to the unit that teaches the classes. Hence tracking class size (number of enrolled students) is an important metric for all involved.

For all VCU classes being taught during the fall 2022 semester, of interest is to estimate the mean number of enrolled students in all the classes. In this scenario, what is the population of interest? all VCU classes being taught during the fall 2022 semester

Stimulus Hurricane Harvey was an active tropical cyclone that became a category 4 hurricane late on August 25, 2017 and then made landfall near Rockport, Texas, causing unprecedented and catastrophic flooding in southeastern Texas. It was the first major hurricane to make landfall in the United States since Wilma in 2005, ending a record 12-year period with no major hurricanes making landfall in the United States. Harvey was also the first hurricane to hit the state of Texas since Ike in 2008, and the strongest to hit the state since Carla in 1961. In addition, it was the strongest hurricane in the Gulf of Mexico since Hurricane Rita in 2005 and the strongest to make landfall in the United States since Hurricane Charley in 2004. It joined Matthew as one of only two U.S. hurricanes to cause an extreme wind warning to be issued, indicating "tornado-like winds" within the storm, including isolated tornadoes.

For all named storms that have made landfall in the United States since 2000, of interest is to determine the mean sustained wind speed of the storms at the time they made landfall. In this scenario, what is the population of interest? All named storms that have made landfall in the United States since 2000

Situation and Formulas Halloween is a celebration observed in a number of countries on October 31, the eve of the Western Christian feast of All Hallows' Day. Halloween activities include trick-or-treating, attending Halloween costume parties, carving pumpkins into jack-o-lanterns, lighting bonfires, apple bobbing, divination games, playing pranks, visiting haunted attractions, telling scary stories, and watching horror films. [Source: Wikipedia]

For all people who went trick-or-treating, of interest is to determine the proportion who received fruit in addition to candy. Based on this, what is the population of interest? All people who went trick or treating

Is the proportion of all people who went trick-or-treating who received fruit in addition to candy in the confidence interval computed in question 9?

I don't know

What is the value of the appropriate measure of spread?

IQR = 29.5

The regression line that gives the linear relationship between the magnitude of the earthquake and the number of people killed is predicted number of people killed = -114 + 35.4(magnitude of the earthquake). Which of the following is the correct interpretation of the slope of this regression line?

If the magnitude of the earthquake increases by 1, then the predicted number of people killed increases by 35.4

The regression line that gives the linear relationsnip between the magnitude or the earnquake and the number or people killed is predicted number of people killed = -114 + 35.4(magnitude of the earthquake). Which of the following is the correct interpretation of the intercept of this regression line?

If the magnitude of the earthquake is 0, then the predicted number of people killed is -114

Sampling Distribution Suppose it is known that among all people who went trick-or-treating, 37.3% also visited a haunted attraction. If a simple random sample of 160 people who went trick-or-treating is selected and the proportion of this sample who also visited a haunted attraction determined, if appropriate describe completely the sampling distribution of p hat

In the situation described above, is there a simple random sample? Yes

Using the data above, which of the following statistics is a measure of spread that would be resistant to the removal of the observation of 126 for STAT 210?

Interquartile Range

Of interest is to determine if the employer of the meteorologist is associated with how well they track the storm. A random sample of 10 meteorologists employed by the U.S. National Weather Service was selected; a random sample of 10 meteorologists employed by a local television station within the United States was selected; and a random sample of 10 meteorologists employed in a country other than the United States was selected. Each was asked to predict the path of a named storm, and a score between 0 and 25 was assigned for each prediction. Of interest is to compare the mean score for the three groups of meteorologists. As described, is this an example of a controlled experiment or an observational study?

Observational Study

One earthquake was magnitude 3.8 and resulted in the death of 260 people. You should be able to identify this earthquake on the scatterplot. This observation represents which of the following?

Outlier

Which of the following is the point estimate of the parameter stated in question 2?

P hat

Consider the information presented in question 1. Suppose it is known that among all named storms that have made landfall in the United States since 2000, 31% of them stay over land for 3 or more days once they make landfall. In this scenario, is 31% an example of a parameter or a statistic?

Parameter

Based on the information in question 7, what is the parameter of interest?

Pi = The proportion of all named storms since 2000 that did make landfall in the United States

For all people who went trick-or-treating, of interest is to determine the proportion who received fruit in addition to candy. Using both the appropriate symbol and in words, what is the parameter of interest?

Pi = the proportion of all people who went trick or treating who received fruit in addition to candy

Consider the scatterplot above. Use this scatterplot to describe completely the relationship between the magnitude of the earthquake and the number of people killed.

Positive, moderate, linear

Based on the p-value in questron 9 and using a significance level a = 0.05, which of the following is the correct decision?

Reject the null hypothesis

This is a definition question: having 10 meteorologists of each type in the sample, as opposed to only 1 of each type, is referred to as which of the following?

Replication

Consider the information in question 9 and the sampling procedure described in question 10. Suppose one of the years selected was 2006, and the meteorologist tracking storms that year was not accurate in identifying whether the storm made landfall in the United States or not. What type of bias could this cause?

Response bias

Hypothesis Test Consider the previous information. It is conjectured that the mean number of people attending all 2022 Veterans Day celebrations is 145, and of interest is to test this conjecture versus the alternative that the mean number of people attending all 2022 Veterans Day celebrations is different from 145 people. To test the hypothesis, a simple random sample of 41 Veterans Day celebrations was selected and the number of people attending each was recorded. The mean number of people attending for this sample of 41 celebrations was 157 people, with a standard deviation of 23 people. The distribution of the data was bimodal. If appropriate, use this information to test the hypotheses stated in question 5 at the a = .05 level of significance.

Which of the following are the appropriate null and alternative hypothesis? H0 : Mu = 145, HA: mu /= 145

Hypothesis Test It is conjectured that the proportion of all people who went trick-or-treating who also had a pumpkin carved into a jack-o-lantern at their home is 0.62. Of interest is to test this claim versus the alternative that the proportion of all people who went trick-or-treating who also had a pumpkin carved into a jack-o'-lantern at their home is less than 0.62. A simple random sample of 270 people who went trick-or-treating is selected, and 162 of them also had a pumpkin carved into a jack-o-lantern at their home (and the other 108 did not). If appropriate, use this information to test if the proportion of all people who went trick-or-treating who also had a pumpkin carved into a jack-o-lantern at their home is less than 0.62 at the a = .10 level of significance.

Which of the following provides both the correct null and the correct alternative hypothesis for the situation described above? H0: pi = 0.62 Ha: pi < 0.62

What is the point estimate of the population mean mu?

X bar

A simple random sample of 270 people who went trick-or-treating is selected, and 162 of them also had a pumpkin carved into a jack-o'-lantern at their home (and the other 108 did not). Is there a simple random sample?

Yes

A simple random sample of 320 people who went trick-or-treating was selected, and it was determined that 64 out of these 320 people received fruit in addition to candy. Do we have a simple random sample?

Yes

A simple random sample of 320 people who went trick-or-treating was selected, and it was determined that 64 out of these 320 people received fruit in addition to candy. Is the sample size large enough for the central limit theorem to apply?

Yes

In the situation described above, is the sample size large enough for the Central Limit Theorem to be applied?

Yes because .373*160 =59.68 and (1-373)*160 = 100.32 are both greater than 10

Are the assumptions met?

Yes, because there is a simple random sample and the sample size is large enough for the Central Limit Theorem