Statistics Questions

Determine the decision criterion for rejecting the null hypothesis in the given hypothesis test i e describe the values of the test statistic that would result in rejection of the null hypothesis A store manager claims that the mean amount of time customers spend waiting in line is less than 3 7 minutes You wish to test this claim at the 0 05 level of significance The mean waiting time for a random sample of 56 customers is 3 5 minutes with a standard deviation of s 1 2 minutes What criterion would be used for rejecting the null hypothesis that 3 7 Reject Ho if test statistic 1 645 O Reject Ho if test statistic 1 96 or 1 96 O Reject Ho if test statistic 1 96 Reject Ho if test statistic 1 673

Test the given claim using the traditional method A public bus company official claims that the mean waiting time for bus number 14 during peak hours is less than 10 minutes Karen took bus number 14 during peak hours on 18 different occasions Her mean waiting time was 7 5 minutes with a standard deviation of 1 6 minutes At the 0 01 significance level test the claim that the mean is less than 10 minutes O There is not sufficient evidence to support the claim that the mean is less than 10 minutes O There is sufficient evidence to warrant rejection of the claim that the mean is less than 10 minutes O There is not sufficient evidence to warrant rejection of the claim that the mean is less than 10 minutes O There is sufficient evidence to support the claim that the mean is less than 10 minutes

Should the statistician use a t distribution a normal distribution or neither to test the nul hypothesis The sample mean x bar for a data set is 3 36 s 0 376 and n 55 The data is approximately normal and ois unknown Ho M 3 326 H 3 326 O Neither O Normal distribution

Find the critical t value or values for the given hypothesis sample size and significance level H 2 3 n 6 a 0 01 O 3 707 O 3 365 O 3 143 000

Use the P value method to test the given hypothesis The National Weather Service says that the mean daily high temperature for October in a large midwestern city is 56 F A local weather service wants to test the claim of 56 F because it believes it is lower A sample of mean daily high temperatures for October over the past 42 days yields x 54 F and s 5 6 F Test the claim at the a 0 01 significance level O There s sufficient evidence to reject the claim that the mean is less than 56 degrees Fahrenheit O There s not sufficient evidence to support the claim that the mean is less than 56 degrees Fahrenheit There s not sufficient evidence to reject the claim that the mean is less than 56 degrees Fahrenheit O There is sufficient evidence to support the claim that the mean is less than 56 degrees Fahrenheit

Determine the decision criterion for rejecting the null hypothesis in the given hypothesis test i e describe the values of the test statistic that would result in rejection of the null hypothesis Ho o 37 4 H 0 37 4 n 28 a 0 05 O Reject Ho if test statistic 14 573 O Reject Ho if test statistic 16 151 O Reject Ho if test statistic 16 928 fach

1 2 3 4 5 SUM 2 3 7 8 8 28 Y 23 19 18 14 13 87 xy x 46 57 126 112 104 446 4 9 XC 49 64 64 190 y 529 361 324 196 104 The correlation coefficient is round to three decimal places r Find the slope intercept and correlation coefficient and report them accurately to three decimal places The regression equation is y 1 514

Fill out the table below 1 2 3 4 5 SUM x 2 2 4 6 Y 25 23 19 17 11 xy x

2 3 4 5 SUM 2 1 4 5 7 14 9 12 18 23 00000 Find the correlation coefficient and report it accurately to three decimal places 000000

1 2 3 5 SUM 1 7 7 8 9 23 19 19 19 12 The correlation coefficient is round to three decimal places r Find the slope intercept and correlation coefficient and report them accurately to three decimal places

1 2 3 4 5 5 4 10 7 12 15 11 12 12 SUM Find the correlation coefficient and report it accurately to three decimal places

2 3 4 5 SUM 5 8 00 8 9 23 14 10 10

Yessica thought that there was a correlation between the amount of time students slept the evening before their final exam and their final exam grade She took an SRS of 5 students in her class and recorded the sleep time the evening before their final exam and their final exam score Let the sleep time the evening before the final exam represents the explanatory variable and the fina exam score be the response variable Below is a sample data set 1 2 3 r 3 8 7 Calculate the sample correlation coefficient r to three decimal places x hour 4 9 4 5 Why would we expect the correlation coefficient to be positive As the sleep time decreases exam score increases As the sleep time increases exam score decreases There is no change in exam score to sleep time As the sleep time increases exam score increases y score 56 96 54 91 86

3 A warehouse employs 22 workers on first shift and 16 workers on second shift Eight workers are chosen at random to be interviewed about the work environment Complete parts a through d a Find the probability of choosing all first shift workers Round to four decimal places as needed b Find the probability of choosing all second shift workers Round to four decimal places as needed c Find the probability of choosing exactly six first shift workers Round to four decimal places as needed d Find the probability of choosing exactly four second shift workers Round to four decimal places as needed

5 Book Hint Print rences Health Cooperative is an outpatient surgical clinic It budgets 647 500 of overhead cost for the year The two main surgical units and their data follow Service General surgery Orthopedic surgery Budgeted Surgeries 450 250 1 Compute a single plantwide rate assuming the company allocates overhead cost based on 700 budgeted surgeries 2 In May of this year the company performed 25 general surgeries and 19 orthopedic surgeries Allocate overhead to each of the two types of surgeries for May using the single plantwide overhead rate Complete this question by entering your answers in the tabs below Required 1 Required 2 In May of this year the company performed 25 general surgeries and 19 orthopedic surgeries Allocate overhead to each of the two types of surgeries for May using the single plantwide overhead rate General surgery Orthopedic surgery Plantwide Overhead Rate Check my work Number of Surgeries Allocated Cost

For the given data set find the a mean b median c mode or state that there is no mode and d midrange The ages of teachers in the mathematics department of a certain high school are shown below 26 52 33 56 26 52 26 50 50 44 A a 41 5 b 47 c 26 d 41 O B a 41 5 b 47 c 50 d 41 O C a 31 1 b 47 c 26 d 41 O D a 26 1 b 47 c 26 d 41

Find the standard deviation for the group of data items Round to the nearest hundredth 4 4 4 7 10 10 10 A 3 00 B 2 85 OC 9 00 D 8 14 WEN

A questionnaire was given to students The first question asked was How stressed have you been in the last week on a scale of 0 to 10 with 0 being not stressed at all and 10 being as stressed as possible The responses are shown in the table a Which stress rating describes the greatest number of students out of 10 Type a whole number b How many students responded with this rating students Type a whole number Stress Rating 0 1 2 3 4 56 7 68 10 Frequency 5 3 4 20 18 15 13 28 33 10 12

Determine whether the statement makes sense or does not make sense and explain your reasoning The death rate from this new strain of flu is catastrophic because 25 of the people hospitalized with the disease have died Choose the correct answer below A This does not make sense because it is not clear whether the facts are derived from a sample of patients which is representative of the entire population of the patients suffering from the disease OB This does not make sense because the percentage of the hospitalized people is less than 50 C This makes sense because the percentage of the hospitalized people is less than 50 OD This makes sense because the sample of patients is representative of the entire population of patients suffering from the disease

The pie chart to the right shows how adults rate their financial shape Suppose 18 people are chosen at random from one of the 18 people would rate their financial shape as fair Make the assumption that the 500 people are represented by the pie chart group of 500 What is the probability that 4 Excellent 4 Good 42 Fair 38 Poor 14 Other 2

Describe what is misleading in the visual display of data below World Population in Billions 23 4 1960 7 5 6 1974 1987 1999 2012 2043 Choose the correct answer below OA Part of the time frame on the horizontal axis of the graph has been cut off OB Time intervals on the horizontal axis do not represent equal amounts of time OC OD The title does not explain what is being displayed The bars on the vertical axis curve around the globe instead of being on a straight line

In one common system for finding a grade point average or GPA A 4 B 3 C 2 D 1 F 0 The GPA is calculated by multiplying the number of credit hours for a course and the number assigned to each grade and then adding these products Then divide this sum by the total number of credit hours Because each course grade is weighted according to the number of credits of the course GPA is called a weighted mean Calculate the GPA for this transcript The grade point average is Round to the nearest hundredth as needed Grades of cre B B B C

For the given data set find the a mean b median c mode or state that there is no mode and d midrange The ages of teachers in the mathematics department of a certain high school are shown below 26 54 38 57 26 54 26 50 50 41 OA a 31 6 b 45 5 c 26 d 41 5 B a 26 6 b 45 5 c 26 d 41 5 IN OC a 42 2 b 45 5 c 50 d 41 5 OD a 42 2 b 45 5 c 26 d 41 5

7 A company that has 200 employees chooses a committee of 13 to represent employee retirement issues When the committee is formed none of the 56 minority employees are selected a Use technology to find the number of ways 13 employees can be chosen from 200 b Use technology to find the number of ways 13 employees can be chosen from 144 nonminorities c What is the probability that the committee contains no minorities when the committee is chosen randomly without bias d Does your answer to c indicate that the committee selection is biased Explain your reasoning a There are ways to choose 13 employees from 200 employees Use scientific notation Round to two decimal places as needed Use the multiplication symbol in the math palette as needed b There are ways to choose 13 employees from 144 nonminorities Use scientific notation Round to two decimal places as needed Use the multiplication symbol in the math palette as needed c The probability is Do not round until the final answer Then round to three decimal places as needed d 1 1 Yes O No 2 the committee selection is most likely 2 O biased 3 O large O unbiased small because the probability that was found in part c is 3

A professor had students keep track of their social interactions for a week The number of social interactions over the week is shown in the following grouped frequency distribution How many students had at least 60 social interactions for the week The number of students was Type a whole number www Number of Social Interactions 30 34 35 39 40 44 45 49 50 54 55 59 60 64 65 69 70 74 75 79 Frequency 5 17 16 18 18 10 6 6 1 1

The dataset below represents a sample of text messages sent during math class in a week by middle school students 74 64 97 82 56 76 56 57 94 87 Round your answers to three decimals where appropriate unless stated otherwise 1 Calculate the sample mean and the sample standard deviation of the sample Sample Mean 74 300 Sample Standard Deviation s 15 642 2 From the original sample data take a bootstrap sample and record the values below 57 76 57 76 57 76 3 Calculate the mean of your bootstrap sample Bootstrap sample mean 74 248 64 94 64 97 Instead of resampling manually as above we ll use StatKey to automate the process for us 4 Enter the data in Statkey first and generate a bootstrap distribution of about 10 000 bootstrap samples Use the distribution to construct 95 confidence interval to estimate the average number of texts sent during math class in a week by middle school students Give results for both Percentile and Standard Error Plug inmethods After generating 10 000 bootstrap samples take a screenshot of your entire StatKey window and upload it below Choose File eenshot 2023 11 06 at 8 09 14M png How take a screenshot Please upload the screenshot everytime you resubmit your work when attempting this question multiple times Percentile Method

The dataset below represents a sample of text messages sent during math class in a week by middle school students 96 65 76 92 59 66 96 94 65 77 90 56 Round your answers to three decimals where appropriate unless stated otherwise 1 Calculate the sample mean and the sample standard deviation of the sample Sample Mean 77 667 Sample Standard Deviation s 15 299 2 From the original sample data take a bootstrap sample and record the values below 56 92 65 92 66 94 3 Calculate the mean of your bootstrap sample 66 96 76 96 77 96

Current Attempt in Progress 1 0 0 5 Median a Use the cumulative distribution function in the figure above to estimate the median Enter your answer to the nearest integer 8 16 24 32 40 48 56 b Describe the density function For what values is it positive Increasing Decreasing Identify all local maximum and values Enter your answers to the nearest integer The density function is positive for i RAHAS P t FIFFE 28 The density function is increasing for i There is a local t The density function is decreasing for i value att AM I I I My THE i 52 i

The National Institute on Alcohol Abuse and Alcoholism has indicated that 52 percent of 18 22 year old college students have had an alcoholic drink in the past month Suppose Western Carolina University s Division of Student Affairs takes a sample of 170 students between the ages of 18 and 22 NOTE For the following problems you should use a standard deviation o rounded to THREE decimal places A What is the probability that the proportion of WCU students from the sample p who drank in the past month is greater than 0 63 Probability B What is the probability that the proportion of WCU students from the sample p who drank in the past month is between 0 43 and 0 76 Probability C 20 percent of the sample proportions p are less than this value C C

A report says that 79 of British Columbians over the age of 25 are high school graduates A survey of randomly selected residents of a certain city included 1260 who were over the age of 25 and 955 of them were high school graduates a What are the mean and standard deviation of the sample proportion of 1260 British Columnbians over the age of 25 that are high school graduates The mean of the sampling distribution for p is The standard deviation of the sampling distribution for p is rounded to four decimal places b What is the z score assocated with the sample proportion 955 1260 2 c You wonder if the city s result of 955 unusually low thus you want to know the probability that a sample proportion is less than 955 1260 What is this probability P 9556560 1260 diel prodit on this problem

A study claims that 30 of children under the age of 13 in British Columbia have not been vaccinated from the chicken pox A survey of randomly selected residents of a certain city included 650 children who were under the age of 13 and 215 of them were not vaccinated Part a What is the approximated probability that sample proportion of non vaccinated children in a sample of 650 children is more than 215 650 Please carry answers to at least six decimal places in intermediate steps Give your final answer to the nearest four decimal places Part b Is the number of non vaccinated children in this city sample unusually high low or neither Answer High

Provide a real world example in which the Z score would be a useful number to have

If we know that the mean of a given data set is 20 and its standard deviation is 3 What is the Z score for a data point with value 15 What of the data is smaller than that given data point

If a given data point has a Z score of 0 5 what of the data is smaller than that given data point

Z image png Z x u standard deviation

ecorded at the end of the experiment Z Y 4 5 Plant Height cm To start the class discussion about the results of the experiment the teacher randomly chooses two of the plants Preview Questions How many plants are there The total number of plants is 9 What do we know about each plant X 8 4 W 12 1 V 11 U 9 A B T 3 8 S 5 2 R 6 GED Test Question What is the probability of drawing two plants that ar taller than 10 cm

Number of cars sold 0 1 2 3 4 5 Total Number of days 54 117 72 42 12 3 300 what is the probability that more than 4 cars were sold on a given day

In your own words define what it means for two events to be Mutually Exclusive

In your own words what is the difference between a discrete and continuous variable

Promoted Not Promoted Total Men 288 672 960 Women 36 204 240 Total 324 876 1200 Based on the table above what is the probability that someone randomly selected from a group of men was not promoted

4 A local news agency conducted a survey about unemployment by randomly dialing phone numbers until it had gathered responses from 1000 adults in its state In the survey 19 of those who responded said they were not currently employed Explain why this study might result in bias and give the likely direction of the bias

Suppose Abby tracks her travel time to work for 60 days and determines that her mean travel time in minutes is 35 6 Assume the travel times are normally distributed with a standard deviation of 10 3 min Determine the travel time x such that 17 36 of the 60 days have a travel time that is greater than x Give your answer rounded to two decimal places X 35 6 min

Use the given data to find the 95 confidence interval estimate of the population mean Assume that the population has a normal distribution IQ scores of professional athletes Sample size n 15 Mean 104 Standard deviation s 14

The following random sample was selected from a normal distribution 10 13 14 8 8 9 14 4 12 6 a Construct a 90 confidence interval for the population mean OSASO b Construct a 95 confidence interval for the population mean MEM

For a given binomial distribution use normalization to approximate the binomial 7 6 a Use the normal approximation of the binomial distribution to approximate the probability of rolling exactly 10 odd values in 20 rolls of a fair six sided die b Use the normal approximation of the binomial distribution to approximate the probability of rolling less than 5 odd values in 20 rolls of a fair six sided die c Use the normal approximation of the binomial distribution to approximate the probability of rolling values less than 3 for 9 or more rolls out of 20 rolls of a fair six sided die

A random sample of 11 size AA batteries for toys yield a mean of 3 75 hours with standard deviation 1 24 hours a Find the critical value t for a 99 Cl t b Find the margin of error for a 99 Cl Note You can earn partial credit on this problem

A poll is taken in which 334 out of 575 randomly selected voters indicated their preference for a certain candidate a Find a 98 confidence interval for p P 0 b Find the margin of error for this 98 confidence interval for p c Without doing any calculations indicate whether the margin of error is larger or smaller or the same for an 80 confidence interval A larger B smaller C same

A random sample of 1700 home owners in a particular city found 459 home owners who had a swimming pool in their backyard Find a 95 confidence interval for the true percent of home owners in this city who have a swimming pool in their backyard Express your results to the nearest hundredth of a percent Answer to

Based on a random sample of 50 a 95 confidence interval for the population proportion was computed Holding everything else constant which of the following will reduce the length of the confidence interval by half CHECK ALL THAT APPLY OA Decrease the sample proportion by half B Change the confidence level to 68 C Change the confidence level to 99 7 D Double the sample size E Quadruple the sample size

Assume that population proportion is to be estimated from the sample described Use the sample results to approximate the margin of error and 95 confidence interval Sample size n 535 sample proportion p 0 8 The margin of error is Round to four decimal places as needed