Statistics Questions

Determine the following probabilities a For n 3 and 0 15 what is P X 0 b For n 11 and 0 30 what is P X 10 c For n 11 and 0 50 what is P X 9 d For n 5 and 1 0 87 what is P X 4 a When n 3 and 0 15 P X 0 Round to four decimal places as needed b When n 11 and 0 30 P X 10 Round to four decimal places as needed c When n 11 and 0 50 P X 9 Round to four decimal places as needed d When n 5 and 1 0 87 P X 4 Round to four decimal places as needed

Researchers collect continuous data with values ranging from 0 100 In the analysis phase of their research they decide to categorize the values in different ways Given the way the researchers are examining the data determine if the data would be considered nominal ordinal or ratio you may use choices more than once Two categories low vs high frequency count of values between 0 49 and frequency of values between 50 100 Three categories low medum high frequency count of values between 0 25 26 74 75 100 Analyze each number in the set individually Choose Ordinal Ratio Nominal Choose

What level of measurement is household income O Ordinal O Nominal O Ratio O Interval

Which of the following measures of central tendency can be used for nominal level data choose one or more Variance Standard deviation Mean Mode

Which of the following descriptive statistics can be used for ratio data choose one or more Variance Standard deviation Mode Mean

Based on this correlation matrix which of the following statements is not accurate Number of Group Infant Birthweight in grams Visits Attended Fructosamine Number of Group Visits Attended Infant Birthweight in grams Fructosamine 1 0 83825039 0 843276728 1 0 67319823 1 As more group visits are attended fructosamine levels increase As fructosamine levels increase birthweight increases As more group visits are attended infant birthweight decreases

Per cent very happy or quite happy 80 60 40 Nom Me and Gingis Aban Americ Zimbabw P Mekdows Salvad Cate China Man Turkey Ukraine Bil Macedania Uregaty Kassian Federation chie Nilgaria Dom Republ Romania 10000 Croatia Arges Lama Poland Lis Wiki Tato Malis Pomagal Svei Hungary Keres Ciech Republic 20000 wZealande Offe As happiness goes up so does income This scatterplot shows an indirect relationship This scatterplot shows a direct relationship As happiness goes up income goes down luac Carany traly 30000 plaid National income per person S Figure 1 2 Happiness and average incomes data for UK unavailable In this scatterplot the x axis national income per person y axis scale of happiness Which of the following statement s is are TRUE choose one or more Wrest 40000

What is the standard deviation s of the following set of scores 12 25 6 9 16 13 11 10 8 7 6 14 16 12 05 5 49 07

Which of the following are nominal data choose one or more three categories low medium high of heart rate ranges five categories of race four categories of satisfaction low somewhat satisfied satisfied very satisfied two categories of exposure to a treatment exposed and unexposed

Given the following data what is the correlation between age and length of sentence O 87 79 HU O 65 O 58 Respondent 1 2 3 4 Average Age x 14 15 15 20 16 Length of Sentence months 80 65 155 192 123

Which of the correlations is the weakest 0 25 O 0 78 0 88 O 0 52

evaluations by students from the past few years A matter of concern to her is how she is viewed by students of different majors She s decided to look at Question 17 on the teacher evaluation form which reads Would you recommend this professor to another student Each of Prof Bryant s students can be placed into one of three categories according to the student s major school as shown in the contingency table below Students who have majors from more than one school are not included This table contains a summary of the data that Prof Bryant has collected for 500 of her students Each of the 500 students is classified according to two variables major school School of Social Science School of Engineering or School of Physical Sciences and response to Question 17 No Maybe or Yes In the cells of the table are written the respective observed frequencies In addition three of the cells have blanks beneath the observed frequencies Fill in these blanks with the frequencies expected if the two variables response to Question 17 and student s major school are independent Round your answers to two or more decimal places Send data to Excel Response to Question 17 No Maybe Yes School of Social Sciences 49 57 146 Student s major school School of Engineering 21 32 74 School of Physical Sciences 35 0 15 71 Total 105 104 291 X S

Which of the following correlations would be interpreted as a moderate relationship O 45 0 3

Which of the correlations is the weakest O 0 25 O 0 78 O 0 88 O0 52

Calculate a correlation matrix for the following data Which two variables have a strong positive relationship Number of Group Visits Fructosamine Attended 152 173 174 175 176 183 188 192 202 205 210 215 220 258 6 LO 5 4 4 3 2 3 3 2 2 1 Infant Birthweight in grams 2 2 1 160 3175 3225 3350 3400 3530 3540 3525 3650 3600 3550 3950 3325 4500 4800 Infant birthweight and number of group visits attended Number of group visits attended and fructosamine O Infant birthweight and fructosamine

When using the SUM function in Excel which of the following are you calculating

Consider the following data 0 0 0 0 1 1 1 3 3 3 4 5 20 30 Which of the following statements are true choose one or more mean is affected by outliers most values are under 5 median is best estimation of central tendency mean is best estimation of central tendency Omode represents the low end of the distribution O mode is best estimation of central tendency

A scientist has read that the mean birth weight of babies born at full term is 7 3 pounds The scientist has good reason to believe that the mean birth weight of babies born at full term is greater than this value and plans to perform a statistical test She selects a random sample of birth weights of babies born at full term and finds the mean of the sample to be 7 5 pounds and the standard deviation to be 1 8 pounds Based on this information complete the parts below a What are the null hypothesis Ho and the alternative hypothesis H that should be used for the test Ho H 0 b Suppose that the scientist decides not to reject the null hypothesis What sort of error might she be making Choose one c Suppose the true mean birth weight of babies born at full term is 7 3 pounds Fill in the blanks to describe a Type I error A Type I error would be Choose one Choose one Choose one V Choose one the hypothesis that u is when in fact u is 0 X X OSO O 0 0 0 0 S

Which measure s of central tendency is are affected by outliers Choose one or more Median Mean Mode

Where are functions found in Excel O under the Insert tab

What is a function in Excel Mathematical operations O Statistical analysis O A predefined formula OA shorthand notation

When you create a formula that goes beyond a simple one you need to remember which of the following The order in which the operations appear The order in which the answers appear The order in which operations are carried out The order in which the cells appear

According to our class lecture which of the following ARE ways that statistics may be misleading chose one or more O Implied connections Skewed curves Detached statistics Suspicious samples

Among the literature on quitting smoking are data detalling the relative successfulness of people of different ages in quitting smoking A study of 400 adults who began various smoking cessation programs produced the data in the table below In the table each participant is classified according to two variables length of their smoking cessation period Less than two weeks Between two weeks and one year or At least one year and age 21 34 or 35 and over In the table less than two weeks means that the individual returned to smoking within two weeks of beginning the program between two weeks and one year means that the individual lasted the first two weeks without smoking but retuned to smoking within a year and at least one year means that the individual has not smoked for at least a year since beginning the program The table is a contingency table whose cells contain the respective observed frequencies of classifications of the 400 smokers In addition three of the cells have blanks beneath the observed frequencies Fill in these blanks with the frequencies expected if the two variables age and length of the smoking cessation period are independent Round your answers to two or more decimal places Send data to Excel Age 21 34 35 and over Total Length of smoking cessation period Less than two weeks 69 32 101 Between two weeks and one year 113 79 192 At least one year 66 41 0 107 Total 248 152 400 X

Find the final monthly payment required to pay off a loan with 900 remaining principal and a 12 annual interest rate A 912 00 B 891 00 C 909 00

Westminster Financial has released a summary of investor and investment package information from the past fiscal year During this time Westminster provided a choice among several pre designed investment packages The investment packages were classified according to two variables riskiness of investment package chosen Risky Moderate mixed and Conservative and age of investor Under 35 35 49 or 50 Suppose that we re interested in the possible relationship between the age of the investor and the riskiness of the investment package the investor chose The following contingency table gives a summary of the information released by Westminster regarding age and riskiness of investment package for 150 investors In the cells of the table are the respective observed frequencies and three of the cells also have blanks Fill in these blanks with the frequencies expected if the two variables riskiness of investment package chosen and age of investor are independent Round your answers to two or more decimal places Send data to Excel Age of investor in years Under 35 35 49 50 Total Riskiness of investment package chosen Moderate mixed 13 Risky 14 10 22 12 48 30 28 0 71 Conservative Total 7 7 0 17 31 34 59 57 150 S

summarized in the accompanying table Assume that the two samples are independent simple random samples selected from normally distributed populations Do not assume that the population standard deviations are equal Complete parts a to c OA Ho H1 H H H H a Use a 0 01 significance level to test the claim that the mean IQ score of people with low blood lead levels is higher than the mean IQ score of people with high blood lead levels What are the null and alternative hypotheses Assume that population 1 consists of subjects with low lead levels and population 2 consists of subjects with high lead levels OC Ho H H H H H Round to two decimal places as needed The P value is Round to three decimal places as needed State the conclusion for the test Low Lead Level High Lead Level 2 The test statistic is OB Ho H1 H H H H O D Ho H1 92 93 76793 15 17928 21 87 86218 9 80529 H2 H H H O A Fail to reject the null hypothesis There is sufficient evidence to support the claim that subjects with low lead levels have higher IQ scores OB Reject the null hypothesis There is not sufficient evidence to support the claim that subjects with low lead levels have higher IQ scores OC Reject the null hypothesis There is sufficient evidence to support the claim that subjects with low lead levels have higher IQ scores OD Fail to reject the null hypothesis There is not sufficient evidence to support the claim that subjects with low lead levels have higher IQ scores b Construct a confidence interval appropriate for the hypothesis test in part a Duuc

dom sample of subjects with high lead levels in their blood were collected The statistics are summarized in the accompanying table Assume that the two samples are independent simple random samples selected from normally distributed populations Do not assume that the population standard deviations are equal Complete parts a to c a Use a 0 01 significance level to test the claim that the mean IQ score of people with low blood lead levels is higher than the mean IQ score of people with high blood lead levels What are the null and alternative hypotheses Assume that population 1 consists of subjects with low lead levels and population 2 consists of subjects with high lead levels OA Ho H1 H H H H O C Hoi Hq U2 H H H Round to two decimal places as needed The P value is Round to three decimal places as needed The test statistic is State the conclusion for the test Low Lead Level 92 93 76793 15 17928 High Lead Level 2 21 87 86218 9 80529 1 Round to one decimal place as needed OB Ho H1 H H H H OD Ho H1 H2 H H H2 OA Fail to reject the null hypothesis There is sufficient evidence to support the claim that subjects with low lead levels have higher IQ scores OB Reject the null hypothesis There is not sufficient evidence to support the claim that subjects with low lead levels have higher IQ scores OC Reject the null hypothesis There is sufficient evidence to support the claim that subjects with low lead levels have higher IQ scores OD Fail to reject the null hypothesis There is not sufficient evidence to support the claim that subjects with low lead levels have higher IQ scores b Construct a confidence interval appropriate for the hypothesis test in part a

Researchers conducted a study to determine whether magnets are effective in treating back pain Pain was measured using the visual analog scale and the results shown below are among the results obtained in the study Higher scores correspond to greater pain levels Assume that the two samples are independent simple random samples selected from normally distributed populations and do not assume that the population standard deviations are equal Complete parts a to c below Reduction in Pain Level After Magnet Treatment n 29 x 0 55 s 0 89 Reduction in Pain Level After Sham Treatment n 29 x 0 49 s 1 46 a Use a 0 01 significance level to test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment similar to a placebo What are the null and alternative hypotheses OA Ho H1 H H H H OC Ho H H H H H The test statistic t is Round to two decimal places as needed The P value is Round to three decimal places as needed State the conclusion for the test the null hypothesis There b Construct a confidence interval appropriate for the hypothesis test in part a 044 20 OB Ho H H H H H OD Ho H1 H H H 2H sufficient evidence to support the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment

gency for 500 NASDAQ stocks from last Monday Tuesday and Wednesday Each of the 500 stocks are classified according to two variables closing price movement from Monday to Tuesday Closing price up on Tuesday or Closing price not up on Tuesday and closing price movement from Tuesday to Wednesday Closing price up on Wednesday or Closing price not up on Wednesday In the cells of the table are the respective observed frequencies in addition three of the cells also have blanks Fill in these blanks with the frequencies expected if the two variables closing price movement from Monday to Tuesday and closing price movement from Tuesday to Wednesday are independent Round your answers to two or more decimal places Send data to Excel Closing price up on Tuesday Closing price movement from Monday not up on to Tuesday Tuesday Closing price Total Closing price movement from Tuesday to Wednesday Closing price up on Wednesday 147 0 91 0 238 Closing price not up on Wednesday 141 121 0 262 Total 288 212 500 X

In an experimental study researchers had each of their participants bet on each game of a professional football season In the contingency table below is some information from a random sample of 100 bets from this study placed on the Columbus Crush picking them to win during the last 14 games of the season the Crush had 7 wins and 7 losses over that period The table indicates for each bet placed on the Crush whether or not the team won and how the participant who placed the bet wagered the following week Each bet is classified according to two variables result of picking the Crush Crush won or Crush lost and bet placed the following week Picked Crush to win or Picked Crush to lose In the cells of the table are the respective observed frequencies and three of the cells also have blanks Fill in these blanks with the frequencies expected if the two variables result of picking the Crush and bet placed the following week are independent Round your answers to two or more decimal places Send data to Excel Result of picking the Crush Crush won Crush lost Total Bet placed the following week Picked Crush Picked Crush to win to lose 34 36 70 21 9 30 Total 55 45 100 X

The fundamental attribution error FAE in psychology is the tendency of a person to overemphasize dispositional factors and to underemphasize situational factors when attributing reasons for other people s behavior We re interested in seeing if there s a difference in tendency to commit the FAE among groups that differ in level of psychology training We show each participant a video on which a scenario is enacted and we ask the participant questions about why the characters in the enactment behaved as they did Suppose that our data are summarized in the contingency table below Each of the 150 participants is classified according to two variables type s of attributions emphasized Mostly situational Mixed or Mostly dispositional and level of psychology training No psych training Psych degree but not a psychologist or Psychologist Fill in these blanks with the frequencies expected if the two variables level of psychology training and type s of attributions emphasized are independent Round your answers to two or more decimal places Send data to Excel No psych training Psych degree but not a Level of psychology psychologist training Psychologist Total Type s of attributions emphasized Mostly situational 8 12 29 Mixed 18 0 16 15 49 Mostly dispositional 34 33 5 72 Total 61 57 32 150 X

1 What percentage of the data are male 2 What is the mean mode median mid range maximum and minimum IQ level 3 What is the range standard deviation variance coefficient of variation for IQ level 4 What is the first quartile IQR 10th percentile third quartile for IQ level 5 What is the skewness kurtosis IQ of data describe the shape of IQ distribution 6 Is there an outlier for IQ data if yes what are the outlier s 7 Draw a box plot for IQ data

Using the following data sets try to create the following tables either with Excel Chocolate Preference xlsx Table 1 Frequency Distribution of Gender Table 2 Frequency distribution of Chocolate Preference Table 3 Frequency distribution of Intention Buying intention 1 definitely not buying 5 definitely buying Table 4 Age Group Frequency Distribution 16 20 21 25 26 30 a file upload Table 5 Gender and Chocolate Preference Contingency table

Listed in the accompanying data table are student evaluation ratings of courses and professors where a rating of 5 is for excellent Assume that each sample is a simple random sample obtained from a population with a normal distribution a Use the 93 course evaluations to construct a 99 confidence interval estimate of the standard deviation of the population from which the sample was obtained b Repeat part a using the 93 professor evaluations c Compare the results from part a and part b Click the icon to view the data table XX

Include an appropriately labeled and shaded Normal curve for each part There should be three separate curves a What is the probability that a baby will have a length of 20 4 inches or more b What is the probability that a baby will have a length of 21 4 inches or more c What is the probability that a baby will be between 18 and 21 inches in length 6 30 White Blood Cells The distribution of white blood cell count per cubic millimeter of whole blood is approximately Normal with mean 7500 and standard deviation 1750 for healthy patients Include an appropriately labeled and shaded Normal curve for each part There should be three separate curves a What is the probability that a randomly selected person will have a white blood cell count of between 7000 and 10 000 b What is the probability that a randomly selected person will have a white blood cell count of between 5000 and 12 000 c What is the probability that a randomly selected person will have a white blood cell count of more than 10 000 d Are the answers to parts b and c the same or different Explain Height Inches 59 5 5 2 5 4 5 6 5 8 5 10 6 60 61 62 63 64 65 66 67 68 69 70 71 72 Frequency 2 5 7 10 16 23 19 15 9 6 6 3 1 1 TRY 6 39 Probability or Measurement Inverse Example 7 The Normal modal 500 100 describes the distri percentage SAI takers ween Suu and 600 6 37 New York City Weather New York City s mean mini mum daily temperature in February is 27 F http www ny com Suppose the standard deviation of the minimum temperature is 6 F and the distribution of minimum temperatures in February is approximately Normal What percentage of days in February has minimum temperatures below freezing 32 F score 6 38 Women s Heights Assume for this question that college women s heights are approximately Normally distributed with a mean of 64 6 inches and a standard deviation of 2 6 inches Draw a well labeled Normal curve for each part a Find the percentage of women who should have heights of 63 5 inches or less b In a sample of 123 women according to the probability obtained in part a how many should have heights of 63 5 inches or less c The table shows the frequencies of heights for a sample of women collected by statistician Brian Joiner in his statistics class Count the women who appear to have heights of 63 inches or less by looking at the table They are in the oval SECTION EXERCISES CHAPTER 6 29 6 43 Inverse Normal Standard Assume a standard Normal di tribution Draw a separate well labeled Normal curve for each part a Find the z score that gives a left area of 0 7123 b Find the z score that gives a left area of 0 1587 6 44 Inverse Normal Standard Assume a standard Normal di tribution Draw a separate well labeled Normal curve for each part a Find an approximate z score that gives a left area of 0 7000 b Find an approximate z score that gives a left area of 0 9500 TRY 6 45 Females SAT Scores Example 8 According to the College Board the mean quantitative SAT score for female college bound high school seniors in 2012 was 500 SAT scores are approximately Normally distributed with a population standard deviation of 100 A scholarship committee wants to give awards to college bound women who score at the 96th percentile or above or the SAT What score does an applicant need Include a well labele Normal curve as part of your answer See page 299 for guidance 6 46 Males SAT Scores According to the College Board the mean quantitative SAT score for male college bound high school seniors in 2012 was 530 SAT scores are approximately Normally distributed with a population standard deviation of 100 What is th SAT score at the 96th percentile for male college bound seniors 6 47 Tall Club Women Suppose there is a club for tall people that requires that women be at or above the 98th percentile in height Assume that women s heights are distributed as N 64 2 5 Find wha

A certain big company classifies its employees according to gender age group 6 categories and employment type 10 categories How many classifications are there Select one O a 120 O b 40 O c 30 d 60

In a professional division of a Hockey league there are 9 total teams How many different rankings are possible at the end of the year Hint there are no ties Select one O a 181 440 O b 40 320 O c 362 880 d 3 628 750

An experiment is conducted with numbers Let S be the sample space of experiment S 1 2 3 4 5 6 7 8 9 10 11 12 with events E 1 2 3 4 5 6 F 5 6 7 8 9 G 7 8 9 10 11 12 H 2 3 4 Assume each outcome is equally likely On your paper list the outcomes in F and G F and G are P F or G 4

Many everyday decisions like who will drive to lunch or who will pay for the coffee are made by the toss of a presumably fair coin and using the criterion heads you will tails I will This criterion is not quite fair however if the coin is biased perhaps due to slightly irregular construction or wear John von Neumann suggested a way to make perfectly fair decisions even with a possibly biased coin If a coin biased so that P h 0 5400 and P t 0 4600 is tossed twice find the probability P th The probability P th Type an integer or decimal rounded to four decimal places as needed

At a Phil s Cafe a dinner meal is made up of an appetizer a main course a dessert and a drink The choices for the appetizer are soup or salad for the main course are chicken fish steak or lobster for the dessert are ice cream pie sorbet or a pastry the drinks are coffee tea or milk How many different dinner meals are possible Select one O a 96 O b 52 OC 48 O d 16

6 44 Inverse Normal Standard Assume a standard Normal dis tribution Draw a separate well labeled Normal curve for each part a Find an approximate z score that gives a left area of 0 7000 b Find an approximate z score that gives a left area of 0 9500

Find the total number of different 4 digit numbers using all the digits in the number 4129 Hint you can t repeat digits Select one O a 24 O b 18 O c 12 O d 6

In an economics class with 30 students the teacher wants 2 different students to answer problems 4 and 9 in front of the class In how many ways can the teacher pick students for the problems Select one O a 435 O b 560 O c 870 O d 660

With the toss of a coin what is the probabilty of getting tails Select one O a 1 2 O b 1 OC 0 O d 2

Listed below are speeds mi h measured from traffic on a busy highway This simple random sample was obtained at 3 30 P M on a weekday Use the sample data to construct a 99 confidence interval estimate of the population standard deviation 61 65 65 57 65 53 59 58 59 70 58 67 Click the icon to view the table of Chi Square critical values The confidence interval estimate is mi h o Round to one decimal place as needed mi h

A knitting club has 14 members It has to send a team of 5 knitters to a knitting competition in the neighboring town Find the number of different knitting teams that can be sent Select one O a 240 240 O b 4 004 OC 2 200 d 2 002

Time left If there are 5 finalists at a singing competition in how many ways can they be ordered if they each take turns singing Select one a 60 b 120 OC 30 O d 40

2 2 cr tical values Use the given information to find the number of degrees of freedom the and R and the confidence interval estimate of o It is XR reasonable to assume that a simple random sample has been selected from a population with a normal distribution Nicotine in menthol cigarettes 90 confidence n 27 s 0 26 mg Click the icon to view the table of Chi Square critical values df 26 Type a whole number XL Round to three decimal places as needed

A statistician wants to analyze the time spent commuting to work in the morning To do so the statistician records the time in minutes it takes to get to work each morning for 10 mornings The data are reproduced in the table below Calculate the mean median and mode using a TI 83 TI 83 plus or TI 84 graphing calculator round your answers to one decimal place Duration of Commute 17 21 23 20 15 29 19 26 10 21 4 Ih