Math Bio. Stats. Final

-Who is the shortest, relative to their age group? Show your work to compare the z-scores. A. Amber (6 years old) is 43.5 inches tall. 6-year-old girls have a mean height of 45.3 inches with a standard deviation of 2.1 inches. B. Logan (8 years old) is 47.5 inches tall. 8-year-old boys have a mean height of 50.4 inches with a standard deviation of 2.2 inches. C. Darren Sproles (31 years old) is 66 inches tall. Adult men have a mean height of 69.0 inches with a standard deviation of 2.8 inches.

-Logan is the shortest, relative to his age group. A. Amber: z = -0.86 B. Logan: z = -1.32 C. Darren Sproles: z = -1.07

A sample of 30 children with Tourette Disorder is selected from the practice of a pediatric neurologist in Birmingham, Alabama. Of the 30 children, 21 were boys and 9 were girls. If two study participants are randomly selected, what is the probability that both are girls?

0.083

In the world population, approximately 10% of all people are left-handed. What is the probability of randomly selecting 20 people who are not left-handed?

0.122

What sample size is needed to estimate the white blood cell count (in cells per microliter) for the population of adults in the United States? Assume you want 99% confidence that the sample mean is within 0.2 of the population mean. Assume the population standard deviation is 2.5.

1037 adults

First, second, and third prizes are to be awarded to three different people. If there are 15 eligible candidates, how many outcomes are possible?

2730

Find the GPA for the following student. An A is 4.0 points, a B is 3.0 points, a C is 2.0 points, and an F is 0.0 points. Round your answer to the nearest hundredth of a point. #of credits-Grade 3-A 3-A 5-B 3-B

3.43

On a physics exam there are 15 questions to choose from, but you must complete only 5 of them. How many different possibilities exist?

3003

The following data represent the number of sets played, X, in the men's singles final match for the years 1968 to 2011. x-Frequency 3-19 4-12 5-13 A. Construct the probability model for the random variable X, the number of sets played in the Wimbledon men's singles final match. B. Compute the mean of the random variable X. C. Compute the standard deviation for the random variable X.

A. x-Probability 3-0.4318 4-0.2727 5-0.2955 B. 𝜇𝑥=3.8637 sets (tech: 3.8636 sets) C. 𝜎𝑥=0.849 sets (tech: 0.8418 sets)

A pair of dice are thrown. A. What is the probability of the sum of the dice being 13 or more?

A. 0

The probability the Orioles win is 55%. If we sample the next 6 games, find the following probabilities. A. The Orioles win all 6 games. B. The Orioles win no more than 3 games. C. The Orioles win at least 3 games. D. The Orioles win exactly 3 games. E. The Orioles will not win any games. F. Find the mean of this distribution. G. Find the variance of this distribution. H. Find the standard deviation of this distribution.

A. 0.0277 B. 0.5585 C. 0.7447 D. 0.3032 E. 0.0083 F. 3.3 games G. 1.485 games2 H. 1.219 games

The waist circumference of males 20 to 29 years old is approximately normally distributed, with a mean of 92.5 cm and a standard deviation of 13.7 cm. A. What is the probability of randomly selecting a 20 to 29 year old male whose waist is larger than 108 cm? B. What is the maximum waist measurement for males with the smallest 4% of waists? Round to the nearest hundredth. C. What are the waist measurements for the middle 85% of 20 to 29 year old males? Round to the nearest hundredth. D. What is the probability of selecting a simple random sample of 8 males aged 20 to 29 years whose mean waist measurement is larger than 108 cm?

A. 0.1292 (tech: 0.1289) B. 68.53 cm (tech: 68.52 cm) C. 72.77 - 112.23 cm (tech: 72.78 - 112.22 cm) D. 0.0007

28. Look at table to complete questions. MEN (nonsmoker 339, occasional smoker 33, regular smoker 61, heavy smoker 34, total 467) WOMEN (nonsmoker 337, occasional smoker 32, regular smoker 84, heavy smoker 36, total 529) TOTALS (nonsmoker 716, occasional smoker 65, regular smoker 145, heavy smoker 70) TOTAL OF ALL 996 A. What is the probability of randomly selecting a survey participant who is a regular smoker? B. What is the probability of randomly selecting a survey participant who is a man, given that the person is a regular smoker? C. What is the probability of randomly selecting a survey participant who is a regular smoker, given that the person is a man? D. Did you use the Empirical Method, the Classical Method, or the Subjective Method to calculate the probability in Question #28?

A. 0.146 B. 0.421 C. 0.131 D. Empirical Method

A random number generator on a calculator is set up to generate numbers between 10 and 20. The resulting numbers follow a continuous uniform distribution. A. What is the likelihood a number between 15 and 17 will be generated? B. What is the likelihood a number greater than 12.405 will be generated? C. What is the likelihood a number less than 16.9 will be generated?

A. 0.2 B. 0.7595 C. 0.69

According to a study conducted by CESI Debt Solutions, 80% of married people hide purchases from their mates. Data is collected from a random sample of 15 married people. A. Find the probability that exactly 13 of the 15 people hide purchases from their mates. B. Find the probability that at least 13 of the 15 people hide purchases from their mates. C. Find the probability that fewer than 13 of the 15 people hide purchases from their mates. D. The Empirical Rule says that if an observation is not within two standard deviations of the mean, it is an unusual value. Using the Empirical Rule, would it be unusual to find that 8 of the 15 people hide purchases from their mates?

A. 0.2309 B. 0.3980 C. 0.6020 D. Yes, unusual

On a standardized test, the resulting scores follow a normal distribution, with a mean score of 512 points and a standard deviation of 109 points. A. What is the probability of randomly selecting a test-taker who scored below 480? B. If a simple random sample of 40 test-takers is selected, what is the standard error of the mean? Round to the nearest tenth. C. What is the probability of randomly selecting a simple random sample of 40 test-takers, where the mean score for the sample is below 480? Page 9 of 12 D. What is the probability of randomly selecting a simple random sample of 40 test-takers, where the mean score for the sample is greater than 550? E. What is the probability of randomly selecting a simple random sample of 40 test-takers, where the mean score for the sample is between 480 and 550?

A. 0.3859 (tech: 0.3845) B. 17.2 points C. 0.0314 (tech: 0.0317) D. 0.0136 (tech: 0.0137) E. 0.9550 (tech: 0.9546)

A simple random sample with is drawn. The sample mean is found to be 19.4 and the sample standard deviation is 3.7. A. What is the point estimate of the mean? B. Construct the 95% confidence interval if the sample size n is 30. Round the upper and lower bounds to the nearest hundredth. C. Construct the 95% confidence interval if the sample size n is 71. Round the upper and lower bounds to the nearest hundredth. D. Construct the 98% confidence interval if the sample size n is 30. Round the upper and lower bounds to the nearest hundredth. E. Increasing the sample size causes the margin of error to increase or decrease? F. Increasing the level of confidence causes the margin of error to increase or decrease? G. If the sample size is 12, what conditions must be met in order to compute the confidence interval?

A. 19.4 B. (18.02, 20.78) C. (18.52, 20.28) D. (17.74, 21.06) E. Increasing the sample size causes the margin of error to decrease. F. Increasing the level of confidence causes the margin of error to increase. G. If the sample size is 12, the sample must be normally distributed with no outliers.

Find the t-values. A. Find the t-value such that the area in the right tail is 0.0025 with 28 degrees of freedom. B. Find the t-value such that the area in the right tail is 0.20 with 33 degrees of freedom. C. Find the t-value such that the area in the left tail is 0.05 with 19 degrees of freedom. D. Find the critical value that corresponds to 98% confidence with 15 degrees of freedom. E. Find the critical value that corresponds to 50% confidence with 26 degrees of freedom.

A. 3.047 B. 0.853 C. -1.729 D. 2.602 E. 0.684

On a standardized test, the resulting scores follow a normal distribution, with a mean score of 512 points and a standard deviation of 109 points. A. What percent of the test takers earned a score above 700? B. What percent of the test takers earned a score below 700? C. What percent of the test takers earned a score above 245? D. What percent of the test takers earned a score between 500 and 650? E. What was the minimum score for the test takers who earned the top 8% of scores? F. If 25,000 people took the test how many can be expected to earn a score better than 750? G. Ninety-one percent of all test takers earned a score less than how many points? H. What are the scores to be in the middle 60%?

A. 4.27% (tech: 4.23%) B. 95.73% (tech: 95.77%) C. 99.29% (tech: 99.28%) D. 44.18% (tech: 44.11%) E. 665.69 (tech: 665.15) F. 365 people (tech: 362 people) G. 658.06 (tech: 658.14) H. 420.44 - 603.56 (tech: 420.26 - 603.74)

The typical rent in Sussex County is $684. Assume the distribution of rent follows the normal distribution, with a mean of $684 and a standard deviation of $254. A. What percent of households spend between $250 and $700 per month on rent? B. What percent of households spend between $650 and $720 per month on rent? C. What percent of households spend between $800 and $2200 per month on rent? D. What is the minimum amount needed to be in the top 18% of renters? E. What is the minimum amount needed to be in the 35th percentile of renters?

A. 48.03% (tech: 48.14%) B. 10.74% (tech: 10.96%) C. 32.28% or 32.27% (tech: 32.39%) D. $917.68 (tech: $916.50) E. $584.94 (tech: $586.13)

You are given a test consisting of 2 multiple-choice questions, each with 3 possible answers (a, b, or c) and you have to answer both of the test questions. The test is written in Sanskrit so the only part you can read is the letter of each possible answer. A. What is the sample space for the results of this test? B. Are the events "answering the first question correctly" and "answering the second question correctly" independent? C. What is the probability of getting the first answer correct? D. What is the probability of getting the second answer correct? E. What is the probability of getting both answers correct? F. What is the probability of getting both answers wrong? G. What is the probability of getting at least one answer wrong?

A. {aa, ab, ac, ba, bb, bc, ca, cb, cc} B. Yes, independent C. 1/3 D. 1/3 E. 1/9 F. 4/9 G. 8/9

According to the CDC, 19.6% of all children aged 6 to 11 years are overweight. A school nurse thinks the percentage of 6- to 11-year olds who are overweight is higher in her school district. A. What is the null hypothesis? B. What is the alternative hypothesis? C. Explain what it would mean to make a Type I error for this hypothesis test. D. Explain what it would mean to make a Type II error for this hypothesis test.

A. 𝐻0: 𝑝=19.6% (We use the symbol p because this is a hypothesis test for a proportion, not a mean.) B. 𝐻0: 𝑝>19.6% C. Type I error means to reject H0 incorrectly. A Type I error would be if we said the evidence supports the claim that the percentage of overweight 6- to 11-year olds is higher than 16.9%, when the actual population proportion is 16.9%. D. Type II error means to fail to reject H0 incorrectly. A Type II error would be if we said the evidence does not support the claim that the percentage of overweight 6- to 11-year olds is higher than 16.9%, when the actual population proportion actually is higher than 16.9%.

A coffee machine dispenses coffee into paper cups. You're supposed to get 10 oz. of coffee, but the amount varies slightly from cup to cup. The table below shows the amounts measured in a random sample of 20 cups. Use a significance level of 0.01 to test the claim that the machine is shortchanging customers. 10.5, 10.1, 10.0, 9.9, 10.0, 9.4, 9.6, 9.5, 10.6, 9.9, 10.0, 9.8, 9.7, 10.2, 9.5, 10.1, 9.8, 10.1, 9.8, 9.9, A. What is the null hypothesis? B. What is the alternative hypothesis? C. Calculate the test statistic. D. What is your conclusion about the null hypothesis? Why? E. Write a sentence that summarizes your conclusion about whether or not the evidence supports the alternative hypothesis. Be specific about the alternative hypothesis.

A. 𝐻0: 𝜇=10 B. 𝐻0: 𝜇<10 C. 𝑡0=−1.159 D. Fail to reject the null hypothesis. Classical method: −1.159 is not in the critical region, which is in the left tail, bounded by 𝑡=−2.539. P-value method: The P-value is between 0.10 & 0.15 (tech: 0.1305), so the P-value is greater than 0.01 (which is α). E. The evidence does not support the hypothesis that the coffee machine is shortchanging customers.

A football coach claims that the average weight of all the opposing teams' members is more than 225 pounds. To test the hypothesis, a sample of 50 players is taken from all the opposing teams. The mean is found to be 230 pounds, and the standard deviation is 15 pounds. At a significance level of 0.01, test the coach's claim. A. What is the null hypothesis? B. What is the alternative hypothesis? C. Calculate the test statistic. D. What is your conclusion about the null hypothesis? Why? E. Write a sentence that summarizes your conclusion about whether or not the evidence supports the alternative hypothesis. Be specific about the alternative hypothesis.

A. 𝐻0: 𝜇=225 Page 5 of 5 B. 𝐻1: 𝜇>225 C. 𝑡0=2.357 D. Fail to reject the null hypothesis. Classical method: 2.357 is not in the critical region, which is in the right tail, bounded by 𝑡=2.403. P-value method: the P-value is between 0.01 & 0.02 (tech: 0.0112), so the P-value is greater than 0.01 (which is α). E. The evidence does not support the claim that the average weight of the opposing teams is more than 225 pounds.

The national average starting salary for nurses is $35,000 but a local professional nurses' organization believes the starting salary for nurses in the Minneapolis area is different. A simple random sample of 10 nurses' starting salaries in Minneapolis results in a mean of $33,450 and a standard deviation of $500. The sample appears to have a normal distribution with no outliers. Use a 0.05 level of significance to test the hypothesis that starting nurses' salaries in Minneapolis are different from the national average. A. What is the null hypothesis? B. What is the alternative hypothesis? C. Calculate the test statistic. D. What is your conclusion about the null hypothesis? Why? E. Write a sentence that summarizes your conclusion about whether or not the evidence supports the alternative hypothesis. Be specific about the alternative hypothesis.

A. 𝐻0: 𝜇=35000 B. 𝐻1: 𝜇≠35000 C. 𝑡0=−9.80 D. Reject the null hypothesis. Classical method: -9.80 is in the critical region, which consists of two tails. The left tail is bounded by t=−2.262 and the right tail is bounded byt=2.262 . P-value method: the P-value is less than 0.0010 (tech: 0.00000422), so the P-value is less than 0.05 (which is α). E. The data support the claim that the average starting salary for nurses in Minneapolis is not $35,000.

A pair of dice are thrown. B. What is the probability of the sum of the dice being odd?

B. 1/2

A pair of dice are thrown. C. What is the probability of the sum of the dice being less than 5?

C. 1/6

A pair of dice are thrown. D. What is the probability of the sum of the dice being greater than or equal to 5?

D. 5/6

A pair of dice are thrown. E. What is the probability of the sum of the dice being less than 5 AND even?

E. 1/9

A pair of dice are thrown. F. What is the probability of the sum of the dice being less than 5 OR even?

F. 5/9

A pair of dice are thrown. G. What is the probability of the sum of the dice being less than 5, if you know the first die was a 2?

G. 1/3

A long time ago, Mrs. Sirkis' IQ was measured at the 75th percentile. Just yesterday, Mrs. Sirkis scored 75% on a grammar test. Explain the difference between these two scores in a way that demonstrates your understanding of the term "percentile".

Mrs. Sirkis scored higher than 75% of her age group. She answer 75% of the grammar test questions correctly.

An urn contains 20 colored golf balls: 8 white, 6 red, 4 blue, and 2 yellow. A child is allowed to draw balls until he gets a yellow one. The number of draws required is recorded. Does this result in a binomial distribution? If not, why not?

Not a binomial distribution because the number of trials is not fixed.

Is this a probability model? If not, what requirement has not been satisfied? Color-Probability Silver- 0.215 Gold- -0.042 Hot Pink- 0.673 Purple- 0.154

Not a probability model because P(gold)<0. Probabilities have to be between 0 and 1.

Is this a probability model? If not, what requirement has not been satisfied? Cookie Type-Probability Thin Mints- 0.25 Samoas- 0.19 Tagalongs- 0.13 Do-Si-Dos- 0.11 Trefoils- 0.09

Not a probability model because the sum of all the probabilities has to be 1. For this chart, Σ𝑃(𝑥)=0.77

The following data represent the vehicle repair costs for 2009-model mini- and micro-cars resulting from crash tests at 6 miles per hour. Treat these data as a simple random sample of low-impact crashes from a normally distributed population. Find the point estimate and construct a 90% confidence interval for the mean. Round to the nearest cent. 1480, 1071, 2291, 1688, 1124, 3476, 3701, 631, 1370, 929, 3345, 3648, 2057, 3148,

Point estimate: $2139.93; confidence interval (1612.46, 2667.40) tech: (1612.5, 2667.4)

In a simple random sample of 14 hospital patients' blood pressures, the mean for the sample is 134 mmHg. Assume the population standard deviation is 10 mmHg. Find the point estimate of the population mean and construct a 60% confidence interval. Round the upper and lower bounds to the nearest tenth.

Point estimate: 134 mmHg; confidence interval (131.8, 136.2) tech: (131.8, 136.3)

Based on interviews with 81 SARS patients, researchers found that the mean incubation period for the sample was 4.6 days, and the population standard deviation is 15.9 days. Based on this information, find the point estimate for the mean incubation period of the SARS virus and construct an 82% confidence interval for the mean incubation period of the SARS virus. Round the upper and lower bounds to the nearest tenth.

Point estimate: 4.6 days; confidence interval (2.2, 7.0)

Body temperatures were measured for 24 healthy people. It is safe to assume body temperatures are normally distributed. The results were a sample mean of 98.20°F, with a sample standard deviation of 0.62°F. Find the point estimate and construct a 99% confidence interval for the mean. Round the upper and lower bounds to the nearest hundredth. What does your confidence interval suggest about the usual assumption that healthy people's body temperature is 98.6°F?

Point estimate: 98.20°F; confidence interval (97.84, 98.56) tech: (97.85, 98.56). Since we are 95% confident the actual population mean is between 97.84°F and 98.56°F, the data suggests the assumed value of 98.6°F is not accurate.

determine if the variable is qualitative or quantitative. If the variable is quantitative, determine if it is discrete or continuous. State the level of measurement of the variable (nominal, ordinal, interval, ratio). Brand name on a pair of running shoes

Qualitative, nominal

determine if the variable is qualitative or quantitative. If the variable is quantitative, determine if it is discrete or continuous. State the level of measurement of the variable (nominal, ordinal, interval, ratio). Video game rating system by the Entertainment Software Rating Board (EC, E, E10+, T, M, AO, RP)

Qualitative, ordinal

determine if the variable is qualitative or quantitative. If the variable is quantitative, determine if it is discrete or continuous. State the level of measurement of the variable (nominal, ordinal, interval, ratio). Time to complete the 500-meter race in speed skating

Quantitative, continuous, ratio

determine if the variable is qualitative or quantitative. If the variable is quantitative, determine if it is discrete or continuous. State the level of measurement of the variable (nominal, ordinal, interval, ratio). The number of surface imperfections on a camera lens

Quantitative, discrete, ratio

Construct a stem and leaf chart (12, 22, 27, 3, 25, 30, 32, 37, 27, 31, 11, 16, 21, 32, 22, 46, 51, 55, 59, 16, 36, 30, 9, 24) B. Find the median for the number of grams of fat in breakfast meals offered at McDonald's. Round to the nearest tenth if necessary.

Stem-Leaf 0-39 1-1266 2-1224577 3-0012267 4-6 5-159 B. 27 grams

Explain why hypothesis testing cannot prove that the high-school dropout rate in Delaware is exactly 8.5%.

The null hypothesis is that the high-school dropout rate is 8.5%. In order to prove this is true, you would need data on every member of the population. This is not possible to achieve by using a sample. Therefore, hypothesis testing is not applicable. If you wanted to prove this claim, you would need to take a census.

A prospective graduate of the Dental Hygienist program would like to know if he can expect to earn more than $45,000 per year at his first job. He collects data a simple random sample of starting salaries for dental hygienists in Sussex County, performs a hypothesis test, and calculates the P-value to be 0.04. He collects data a simple random sample of starting salaries for dental hygienists in Kent County, performs a hypothesis test, and calculates the P-value to be 0.005. In which county is he more likely to earn a starting annual salary greater than $45,000? Justify your decision.

The prospective graduate is more likely to earn a starting salary higher than $45,000 in Kent County. The lower P-value means the evidence in Kent County more strongly supports the hypothesis that the mean starting salary is greater than $45,000 per year.

A dentist sampled patients to determine the length of time spent in the waiting room. The responses are below in minutes: 2, 12, 14, 16, 3, 5, 4, 10, 12,10, 12, 20, 18, 20, 4, 6, 8, 6, 8, 0, 2, 4, 12, 12 18. Prepare a grouped frequency distribution for the dentists' patients' waiting room time, using a class width (interval) of 3, and the first interval's lower limit of 0. (You may not need to use all the rows or columns.) B. Using the results from your frequency distribution on Problem #18, find the mean. Round to the nearest tenth if necessary. DO NOT USE THE RAW DATA, IT WILL BE MARKED WRONG IF YOU DO. C. Is this calculation (answer to #19) a parameter or a statistic?

Wait Time Frequency [0 - 2, 3] [3 - 5, 5] [6 - 8, 4] [9 - 11, 2] [12 - 14, 6] [15 - 17, 1] [18 - 20, 3] B. 9.3 minutes C. Statistic

In a survey conducted by the Gallup organization, 1100 adult Americans were asked how many hours they worked in the previous week. Based on the results, a 95% confidence interval for the mean number of hours worked had a lower bound of 42.7 hours and an upper bound of 44.5 hours. What does this mean?

We can be 95% confident that the actual mean hours worked in the previous week was between 42.7 hours and 44.5 hours.

According to a study, 16% of property crimes reported in the U.S. in 2006 were cleared by arrest or exceptional means. Twenty-five property crimes from 2006 are randomly selected and the number that was cleared is recorded. Does this result in a binomial distribution? If not, why not?

Yes, binomial distribution

homework is weighted at 10%, quizzes are weighted at 10%, the final exam is weighted at 20%, and tests are weighted at 60%. a. Calculate the current course grade for the following Biomedical Statistics student who has not yet taken the final exam. Round to the nearest tenth of a percent. On the test, you would have to show all work. b. Is it possible for this student to get an B, with a course average of at least 82.5%? Is it possible for her to get an A, with a course average of at least 91.5%? Assume you can replace the lowest test grade with the final exam. Test Grades ( 99%, 54%, 67%, 79%, 75%) Quiz Grades (93% 100%, 76%, 100%, 94%, 81%, 100%, 100%, 93%) Homework Grade (89%)

a) 78.85% b) Yes, it is possible to get a B. No, an A is impossible.

The following data, obtained from the Sullivan Statistics Survey, represents the number of speeding tickets individuals received in the past 12 months: Tickets-Frequency 0-169 1-21 2-4 3-4 For a-c calculate and round to the nearest tenth if necessary: a. The mean b. The variance c. The standard deviation

a. 0.2 tickets b. 0.3 tickets2 c. 0.6 tickets

As part of a semester project in a statistics course, Carlos surveyed a sample of 15 high-school students and asked "How many days in the past week have you consumed an alcoholic beverage?" and recorded the results: 0, 0, 1, 4, 1, 1, 1, 5, 1, 3, 0, 1, 0, 1, 0 For #7-12 calculate and round to the nearest tenth if necessary: a. The mean b. The median c. The mode d. The variance e. The standard deviation f. The range

a. 1.3 days b. 1 day c. 1 day d. 2.4 days2 e. 1.5 days f. 5 days

Researcher Katherine Tucker and associates wanted to determine whether consumption of cola is associated with lower bone density. They looked at 1125 men and 413 women Framingham, Massachusetts, beginning in 1971. The first examination in this study began between 1971 and 1975, with participants returning for an examination every 4 years. Based on results of questionnaires, the researchers were able to determine cola consumption on a weekly basis. Analysis of the results indicated that women who consume at least one cola per day (on average) had a bone mineral density that was significantly lower at the femoral neck than those who consumed less than one cola per day. The researchers did not find this relation in men. a. Identify the research objective.

a. Determine whether consumption of cola is associated with lower bone density.

Researcher Katherine Tucker and associates wanted to determine whether consumption of cola is associated with lower bone density. They looked at 1125 men and 413 women Framingham, Massachusetts, beginning in 1971. The first examination in this study began between 1971 and 1975, with participants returning for an examination every 4 years. Based on results of questionnaires, the researchers were able to determine cola consumption on a weekly basis. Analysis of the results indicated that women who consume at least one cola per day (on average) had a bone mineral density that was significantly lower at the femoral neck than those who consumed less than one cola per day. The researchers did not find this relation in men. b. What is the response variable?

b. Bone mineral density at the femoral neck

Researcher Katherine Tucker and associates wanted to determine whether consumption of cola is associated with lower bone density. They looked at 1125 men and 413 women Framingham, Massachusetts, beginning in 1971. The first examination in this study began between 1971 and 1975, with participants returning for an examination every 4 years. Based on results of questionnaires, the researchers were able to determine cola consumption on a weekly basis. Analysis of the results indicated that women who consume at least one cola per day (on average) had a bone mineral density that was significantly lower at the femoral neck than those who consumed less than one cola per day. The researchers did not find this relation in men. c. What is the explanatory variable?

c. Amount of cola consumption

Using the information from your frequency distribution on Problem #18, construct a histogram and a frequency polygon.

check answer key question 21

Researcher Katherine Tucker and associates wanted to determine whether consumption of cola is associated with lower bone density. They looked at 1125 men and 413 women Framingham, Massachusetts, beginning in 1971. The first examination in this study began between 1971 and 1975, with participants returning for an examination every 4 years. Based on results of questionnaires, the researchers were able to determine cola consumption on a weekly basis. Analysis of the results indicated that women who consume at least one cola per day (on average) had a bone mineral density that was significantly lower at the femoral neck than those who consumed less than one cola per day. The researchers did not find this relation in men. d. Is this an observational study or a designed experiment? Why?

d. Observational study because no variables are manipulated intentionally

Researcher Katherine Tucker and associates wanted to determine whether consumption of cola is associated with lower bone density. They looked at 1125 men and 413 women Framingham, Massachusetts, beginning in 1971. The first examination in this study began between 1971 and 1975, with participants returning for an examination every 4 years. Based on results of questionnaires, the researchers were able to determine cola consumption on a weekly basis. Analysis of the results indicated that women who consume at least one cola per day (on average) had a bone mineral density that was significantly lower at the femoral neck than those who consumed less than one cola per day. The researchers did not find this relation in men. e. What is the conclusion of the study?

e. Women who consume at least one cola per day (on average) had a bone mineral density that was significantly lower at the femoral neck than those who consumed less than one cola per day. The researchers did not find this relation in men.