Statistics Questions

A strain of bacteria is placed into a petri dish at 30 C and allowed to grow The following data are collected Theory states that the number of bacteria in the petri dish will initially grow according to the law of uninhibited growth The population is measured using an optical device in which the amount of light that passes through the petri dish is measured Complete parts a e Time hours x 0 2 5 3 5 4 5 6 Population y 0 15 0 31 0 46 0 62 0 89 4 a Treating time x as the predictor variable a graphing utility to fit an exponential function the data y ab Round to four decimal places as needed

10 16 A random sample of 250 observations is taken from population A which has 30 of its population living in poverty A 3 A second random sample of size 350 is taken indepen dently taken from population B which has 15 of its population living in poverty TB 15 a What are the mean and standard deviation of the difference in the sample propor tions A B b Describe the shape of the sampling distribution of the difference in the sample proportions A B c Is it appropriate to use the normal approximation to the sampling distribution of the difference in the sample proportions A B 10 17 Refer to Exercise 10 16 Assuming that equal sample sizes will be taken from the two popu lations how large a sample should be taken from each of the populations to obtain a 99 confi dence interval for TA TB with a width of at most 02 Hint Use A 3 and B 15 from Exercise 10 16

H R R Refer to Exercise 10 40 Suppose the recruitment director is preparing a presentation for upper management to recommend new hiring practices of the firm a Provide a graph of the data in Exercise 10 40 b Comment on the results from Exercise 10 40 in terms of do whether hiring practices over the past 1 2 years appear to be successful If not suggest some changes 10 40 The recruitment director for a large engineering firm categorizes universities based on their rankings by U S News as most desirable desirable adequate or undesirable for purposes of hiring the engineering graduates from the universities The director reviews the performance records of 156 engineers employed by the firm for 1 2 years The following table cross classifies the annual performance ratings of the engineers with the universities from which they earned their BS degrees University Type Most desirable Desirable Adequate Undesirable Performance Rating of Employee Outstanding 21 4 13 10 Average 20 26 7 7 Poor 4 36 2 6 a What is the population of interest represented by the data in the above table b Can the director conclude that there is a relationship between the university type and the performance rating of the employee c Are the conditions for applying your test in part b satisfied

ov 10 43 Refer to Exercise 10 42 Suppose that the initial analysis of the age discrimination had included only two levels of age as contained in the following table Promotion Decision Promoted Not promoted Gov Age at Promotion Decision 39 or younger 40 or Older 38 80 a Is the age of the fireman related to whether or not the fireman is promoted Use 05 b Is your conclusion concerning age discrimination different from your conclusion using the data in Exercise 10 42 see powe your upp 10 42 The fire department in a large city is examining its promotion policy to assess if there is the potential for an age discrimination lawsuit A random sample of 248 promotion decisions over the past 5 years yields the following information Promotion Decision Under 30 Promoted Not promoted 9 41 46 84 Age at Promotion Decision 30 39 29 39 40 49 34 46 50 or Older 12 38 a Provide a graph of the promotion information b Is the promotion decision for the fireman related to the age of the fireman Use a 05 c What is the population to which your conclusion in part b is applicable d What are some other variables besides age that needed to be addressed in an age discrimination analysis

1 10 20 Biofeedback is a treatment technique in which people are trained to improve their health by using signals from their own bodies Specialists in many different fields use biofeedback to help their patients cope with pain A study was conducted to compare a biofeedback treatment for chronic pain with an NSAID medical treatment A group of 2 000 newly diagnosed chronic pain patients were randomly assigned to receive to one of the two treatments After 6 weeks of treatments the pain levels of the patients were assessed with the following results Treatment Biofeedback NSAID Total Significant Reduction in Pain Yes No 560 680 1 240 440 320 760 Total 1 000 1 000 2 000 10 11 Exercises 537 a For both treatments place 95 confidence intervals on the proportions of patients who experienced a significant reduction in pain b Is there significant evidence a 05 of a difference in the two treatments relative to the proportions of patients who experienced a significant reduction in pain c Place a 95 confidence interval on the difference in the two proportions

R 10 40 The recruitment director for a large engineering firm categorizes universities based on their rankings by U S News as most desirable desirable adequate or undesirable for purposes of hiring the engineering graduates from the universities The director reviews the performance records of 156 engineers employed by the firm for 1 2 years The following table cross classifies the annual performance ratings of the engineers with the universities from which they earned their BS degrees University Type Most desirable Desirable Adequate Undesirable Performance Rating of Employee Outstanding 21 4 13 10 Average 20 26 7 7 Poor 4 36 2 6 a What is the population of interest represented by the data in the above table b Can the director conclude that there is a relationship between the university type and the performance rating of the employee c Are the conditions for applying your test in part b satisfied

Phi Delta Kappa PDK is an international professional organization for educators that in collaboration with Gallup has been conducting polls on the public s attitudes toward the public schools since 1969 The following was one of the questions on the most recent poll conducted June 4 13 2011 Most teachers in the nation now belong to unions or associations that bargain over salaries working conditions and the like Has unionization in your opinion helped hurt or made no difference in the quality of public school education in the United States The respondents answers broken down by party affiliation is shown below Helped Hurt Made no difference Don t know refused TOTAL Helped Hurt Republican Democrat 146 78 105 12 Made no difference Don t know refused TOTAL 290 35 197 52 6 341 1 Independent Calculate the conditional distribution of opinion on unions given political affiliation Round to 3 decimal places if necessary 341 1 Republican Democrat Independent 69 178 90 4 1 TOTAL 250 453 247 22 972 Gun Viol What is the percent of people who thought unions hurt given they were Republican Write as a percent rounded to 1 decimal place do not write the What is the percent of people who thought unions hurt given they were Democrat Write as a percent rounded to 1 decimal place do not write the What is the percent of people who thought unions hurt given they were Independent Write Activity

19 In recent study 76 of U S consumers age 18 and older said they spicy food when eating out A local restaurant owner believes that this proportion is higher The owner randomly surveyed 500 clients with the result that 387 clients reported they order hot and spicy food What type of hypothesis test would you recommend he should perform for this situation Hypothesis test for 2 proportions Hypothesis test for 1 proportion Hypothesis test for 2 means Hypothesis test for 1 mean

A CCBC professor claims that there is a difference between the mean class statistics day students on the Final Exam and statistics evening students on the Final Exam The professor takes random samples from each group of students The summary is shown in the table below Use a 0 05 significance level to test the professor s claim Day Students Evening Students A n 65 56 45 55 59 09 P value do not round Ho MD HE H HD HE HAMD HE HA HD HE First choose which hypothesis statements is correct B t stat round to 2 decimal places S 21 8 17 82 C ecision Type Retain Ho or Reject Ho Ho MD HE HA MD HE D H 55 H 55

Extracurricular activities are very school students have an average of 6 extracurricular activities A school administrator would like to find if the students at her school meet the average in extracurricular activities She takes a random sample of students in her school to determine if the mean number of extracurricular activities is significantly different than 6 What is a type 1 error in this situation The school administrator concludes the mean number of extracurricular activities the students have in her school is different than 6 when in fact it is actually 6 The school administrator concludes that the mean number of extracurricular activities the students have in her school is 6 when in fact it is different than 6 The mean number of extracurricular activities the students have in her school is different than 6 and the school administrator concludes the mean is different than 6 The mean number of extracurricular activities the students have in her school is 6 and the school administrator concludes the mean is 6

15 A If a they like the new ice cream while only 34 of 140 adults reported liking it Use the output below to ensumers A survey found that 56 of 180 children reported that test whether the proportion of children who like the new ice cream is greater than the proportion of adults who like it Hypothesis test results Difference Count Totall Count2 Total2 PC PA 56 180 34 140 H H ki Htc ki Ho or Retain First choose which hypothesis statements is correct A 0 10 what is your decision De Reject Ho or Retain Ho A B A Ho Pc PA H Pc PA 0 01 what is your decision C Sample Diff 0 068253968 Ho Pc PA HA PC PA Std Err 0 050665218 D Z Stat 1 3471563 Ho Pc PA HA Pc PA P value 0 089

The model below could be used in step 3 does the position B represent O sample mean Op value standard error T population mean 1 B

to 3 decimal places Confidence Limit A 3 decimal places points mary sentence for the confidence interval you calculated in the prior

Questio The average tip left by adult Americans at the restaurant is 20 of the total bill A restaurant owner believes that the mean percentage tip has decreased lately The owner recorded the percentage tip left by 25 randomly selected customers who dined at the restaurant in a given week Assume that the percentage tips are normally distributed At the level of significance 0 10 test whether the mean percentage tip is lower than 20 Click here to open the data in StatCrunch Which set of Hypothesis Statement are correct A Ho p 20 HA p 20 A A B t stat round to 2 decimal places P value do not round A H 20 H 20 Decision Type Retain Ho or Reject Ho C H 20 HA 20 D H 25 H 25

The US Energy Information Administration reported that 47 of homes are heated by natural gas A random sample of 150 homes in Maryland were selected and found that 65 were heated by natural gas At the level of significance 0 10 test if the proportion of homes that are heated by natural gas in Maryland is smaller than the national proportion Ho 4 at round to 2 decimal places e do not round A Type Retain Ho or Reject Ho 5 points A

Suppose researchers determined the 95 confidence interval for the average life expectancy of an Asian woman is 87 to 90 years What are they attempting to estimate OH

10 7 The test for screening donated blood for the presence of the AIDS virus was developed in the 1980s It is designed to detect antibodies substances produced in the body of donors carrying the virus however it is not 100 accurate The developer of the test claimed that the test would pro duce fewer than 5 false positives and fewer than 1 false negatives In order to evaluate the accuracy

10 2 For each of the following values for and n compute a 95 confidence interval for the population proportion using both the standard large sample procedure and the WAC adjusted procedure Comment on whether the WAC adjustment was needed a n 20 35 b n 35 80 C n 50 34 d n 100 12

Use the grid to draw the graph of each line 12 y 3x 1 13 y 2x 3 14 y x 122 C 1 15 y 1 5x 1430 d e f

You may need to use the appropriate appendix table or technology to answer this question The reliability of two types of machines used in the same manufacturing process is to be tested The first machine failed to operate correctly in 108 out of 360 trials while the second t operate correctly in 66 out of 300 trials Let d Machine 1 Machine 2 a Give a point estimate of the difference between the population proportions of these machines Round your answer to four decimal places b Calculate the pooled estimate of the population proportion Round your answer to four decimal places c Carry out a hypothesis test to check whether there is a statistically significant difference in the reliability for the two types of machines using a 0 10 level of significance O We do not reject Ho There is no significant difference O We do not reject Ho There is a significant difference We reject Ho There is no significant difference We reject Ho There is a significant difference

Tutorial Exercise Assume that the population proportion is 0 70 Compute the standard error of the proportion for sample sizes of 100 200 500 and 1 000 What can you say about the size of the standard error of the proportion as the sample size is increased Step 1 The standard error of a proportion is used to describe the standard deviation of a sample proportion p Recall the calculation for the standard error sample of size n from the population P p 1 n p op of a population proportion p for a Since n is included in the computation for the standard error the standard error will change depending on the sample size for a given population proportion Here the population proportion is given to be 0 70 so p

b What is the probability that a sample of 90 female graduates will provide a sample mean within 1 00 of the population mean 27 83 Let x represent the sample mean hourly wage for a group of 90 females To be within 1 00 of the population mean of 27 83 gives a range of hourly wages between 27 83 1 00 and 27 83 1 00 Therefore the desired probability that a sample mean of 90 females is within 1 00 of the population mean is P sxs

You may need to use the appropriate appendix table or technology to answer this question In 2017 a website reported that only 10 of surplus food is being recovered in the food service and restaurant sector leaving approximately 1 5 billion meals per year uneaten Assume this is t true population proportion and that you plan to take a sample survey of 535 companies in the food service and restaurant sector to further investigate their behavior a Show the sampling distribution of p the proportion of food recovered by your sample respondents 0 07 0 08 0 09 0 10 0 11 0 12 0 13 2 1 0 1 2 3 0 02 0 01 0 00 0 01 0 02 0 03 0 04 0 05 0 03 0 02 0 01 0 00 0 01 0 02 0 03 b What is the probability that your survey will provide a sample proportion within 0 03 of the population proportion Round your answer to four decimal places c What is the probability that your survey will provide a sample proportion within 0 015 of the population proportion Round your answer to four decimal places P G

6 2 Negative z scores 0 00 0 01 0 02 0 03 0 04 0 05 0 06 0 07 0 08 0 09 3 4 0 0003 0 0003 0 0003 0 0003 0 0003 0 0003 0 0003 0 0003 0 0003 0 0002 33 0 0005 0 0005 0 0005 0 0004 0 0004 0 0004 0 0004 0 0004 0 0004 0 0003 3 2 0 0007 0 0007 0 0006 0 0006 0 0006 0 0006 0 0006 0 0005 0 0005 0 0005 3 1 0 0010 0 0009 0 0009 0 0009 0 0008 0 0008 0 0008 0 0008 0 0007 0 0007 3 0 0 0013 0 0013 0 0013 0 0012 0 0012 0 0011 0 0011 0 0011 0 0010 0 0010 2 9 0 0019 0 0018 0 0018 0 0017 0 0016 0 0016 0 0015 0 0015 0 0014 0 0014 2 8 0 0026 0 0025 0 0024 0 0023 0 0023 0 0022 0 0021 0 0021 0 0020 0 0019 2 7 0 0035 0 0034 0 0033 0 0032 0 0031 0 0030 0 0029 0 0028 0 0027 0 0026 2 6 0 0047 0 0045 0 0044 0 0043 0 0041 0 0040 0 0039 0 0038 0 0037 0 0036 2 5 0 0062 0 0060 0 0059 0 0057 0 0055 0 0054 0 0052 0 0051 0 0049 0 0048 2 4 0 0082 0 0080 0 0078 0 0075 0 0073 0 0071 0 0069 0 0068 0 0066 0 0064 0 0107 0 0104 0 0102 0 0099 0 0096 0 0094 0 0091 0 0089 0 0087 0 0084 0 0139 0 0136 0 0132 0 0129 0 0125 0 0122 0 0119 0 0116 0 0113 0 0110 0 0179 0 0174 0 0170 0 0166 0 0162 0 0158 0 0154 0 0150 0 0146 0 0143 2 0 0 0228 0 0222 0 0217 0 0212 0 0207 0 0202 0 0197 0 0192 0 0188 0 0183 1 9 0 0287 0 0281 0 0274 0 0268 0 0262 0 0256 0 0250 0 0244 0 0239 0 0233 1 8 0 0359 0 0351 0 0344 0 0336 0 0329 0 0322 0 0314 0 0307 0 0301 0 0794 1 7 0 0446 0 0436 0 0427 0 0418 0 0409 0 0401 0 0392 0 0384 0 0375 0 0367 2 2 2 The area to the right of z 1 54 P z 1 54 under a standard normal distribution is closest to 0 938 0 062 0 067

10 5 A public opinion polling agency plans to conduct a national survey to determine the proportion of people who would be willing to pay a higher per kilowatt hour fee for their electricity provided the electricity was generated using ecologically friendly methods such as solar wind or nuclear How many people must be included in the poll to estimate the population proportion within 04 of the population value using a 95 confidence interval Consider two separate situations a Suppose the polling agency has no previous information about the population proportion b Suppose the polling agency is fairly certain that the population proportion is less than 30 c Why are the sample sizes so different for the two situations

0 4 A random sample of 1 200 units is randomly selected from a population If there are 732 uccesses in the 1 200 draws a Construct a 95 confidence interval for T b Construct a 99 confidence interval for 7 c Explain the difference in the interpretation of the two confidence intervals

Suppose you collect a dataset with mean 7 and standard deviation 2 Ifx represents each data value in the data set and new data values are created using the transformation y 2x 1 what will be the mean and standard deviation of y mean 15 standard deviation 2 mean 15 standard deviation 4 mean 14 standard deviation 4

You can convert temperatures in degrees Celsius to degrees Fahrenheit using the formula F 9 5 C 32 If a sample of temperatures in Celsius has a mean 30 and standard deviation 4 the mean and standard deviation in Fahrenheit will be mean 86 standard deviation 7 2 mean 54 standard deviation 7 2 mean 86 standard deviation 4

Converting P 36 39 x 38 39 to the standard normal random variable z gives P 2 06 z 2 06 This is the probability that a sample of 90 male graduates will provide a sample mean within 1 00 of the population mean 37 39 Recall that the standard normal table gives the area under the normal curve to the left of a given z value Z 0 00 0 01 0 02 0 03 0 04 0 05 0 06 0 07 0 08 2 1 0 0179 0 0174 0 0170 0 0166 0 0162 0 0158 0 0154 0 0150 0 0146 2 0 0 0228 0 0222 0 0217 0 0212 0 0207 0 0202 0 0197 0 0192 0 0188 1 9 0 0287 0 0281 0 0274 0 0268 0 0262 0 0256 0 0250 0 0244 0 0239 Z 0 00 0 01 0 02 0 03 0 04 0 05 0 06 1 9 0 9713 0 9719 0 9726 0 9732 0 9738 0 9744 0 9750 2 0 0 9772 0 9778 0 9783 0 9788 0 9793 0 9798 0 9803 2 1 0 9821 0 9826 0 9830 0 9834 0 9838 0 9842 0 9846 0 9850 0 07 0 08 0 9756 0 9761 0 9808 0 9812 0 9854 Use the above table to compute P 2 06 z 2 06 rounding the result to four decimal places P 2 06 z 2 06 P Z 2 06 P z 2 06 0 9803 0 09 0 0143 0 0183 0 0233 0 09 0 9767 0 9817 0 9857

ccesses Let a success be that someone from the Hawaii plant is in the sample of employees who fill out the questionnaire Previously we found the probabilities of exactly x 0 successes f 0 and exactly x 1 success f 1 To find the desired probability that 2 or more employees in this sample work in the Hawaii plant there will be x Select 2 5 Therefore the probability will be calculated as f 2 f 3 f 15 Submit Skip you cannot come back W WNN 2 15 3 4 15 3

A sample of size 110 is selected from a population with p 0 60 a What is the expected value of p b What is the standard error of p Round your answer to four decimal places c Show the sampling distribution of p 2 1 0 1 2 0 10 0 05 0 00 0 05 3 0 10 P P 0 05 0 00 0 05 0 10 0 15 P 0 50 0 55 0 60 0 65 0 70

Tutorial Exercise You may need to use the appropriate appendix table or technology to answer this question The Food Marketing Institute shows that 17 of households spend more than 100 per week on groceries Assume the population proportion is p 0 17 and a sample of 900 households will be selected from the population a Show the sampling distribution of p the sample proportion of households spending more than 100 per week on groceries b What is the probability that the sample proportion will be within 0 02 of the population proportion c Answer part b for a sample of 1 800 households Step 1 a Show the sampling distribution of p the sample proportion of households spending more than 100 per week on groceries Recall that a sampling distribution of p is a discrete probability distribution but can be approximated by a normal distribution when np 5 and n 1 p 5 where n is the sample size and p is the population proportion Here it is given that p 0 17 There is a sample of 900 households so n np n 1 p 0 17 nd n 1 1 0 17 0 5 the normal approximation Select be used Find the values of np and n 1 p

The sampling distribution of P P2 is approximated by a normal distribution Ot distribution with n n degrees of freedom O P P distribution Ot distribution with n n 1 degrees of freedom

The length of a rectangle is 6 meters greater than 4 times its width The perimeter of the rectangle is 36 meters What is the area of the rectangle in meters A 24 B 28 36 42

Solve by substitution or elimination by subtraction or addit 42 15y 17 42 20y 52

Solve by substitution or elimination by subtraction or addition 2z 3y 1 y z 1

Solve the following linear equation for k 2 Ak 2 B k 4 k 5 3k k 6 k 1 k 0

Solve 5 3 2x 3

Directions Write an equation of a line given the slope and y intercept y mx b 1 m 2 b 7 Equation

19 The perimeter of a rectangular yard is 120 meters What is the length if its width is twice its length 10 meters B 20 meters 16 meters 24 meters

4 Match the following given inequalities with their corresponding solutions 32 122 15 2z 539 52 853 3z 5216 DRAG DROP THE ANS z 14 27 9 25

In a stadium the ratio of home fans to visiting fans in a crowd is 4 5 Which of the following could be the total number of fans in the stadium A 10 326 B 9 198 31 812 D 23 566

John travels 56 miles in 3 hours before taking a break He then travels 38 miles in 2 5 hours Convert his average rate of miles per hour rounded to the nearest hundredth to meters per millisecond expressed in scientific notation rounded to the nearest hundredth 1 km 0 621371 mile A 7 64 10 3 2 95 10 3 m ms m ms 3 67 10 9 m ms

Johnny spends of his income on food To of his income on gas and of his income on rent What percentage of his income remains after he has paid for food gas and rent A 61 8 B 32 5 42 1 D 38 2

What is the value of x in the following equation 3 1 1 42 8 2 1 3 A B 2 D C 6 6

5 The ratio of boys and girls in a class is 4 8 If there are 72 students in the class how many more boys should be enrolled to make the ratio 1 1 12 B 36 D 24 18

In the diagram which one has a positive slope A AB B DB AC C 8

A football team had 30 000 to spend on supplies The team spent 24 000 on new balls New sport shoes cost 140 each Which of the following inequalities represent the number of new shoes the team can purchase A 24 000x 140 30 000 B 140x 24 000 30 000 24 000x 140 30 000 140x 24 000 30 000

c What is the probability that 2 or more of the employees in the sample work at the plant in Hawaii Let a success be that someone from the Hawaii plant is in the sample of employees who fill out the questionnaire Previously we found the probabilities of exactly x 0 successes f 0 and exactly x 1 success f 1 To find the desired probability that 2 or more employees in this sample work in the Hawaii plant there will be x Select successes Therefore the probability will be calculated as Select f 3 f 2 f 3 f 4 f 15 f 2 f 3 f 15 Submit Skip you cannot come back

Step 2 Now that the values of 3 and x 6 are on the same 5 minute time interval the formula for the Poisson distribution can be applied Find the probability of receiving 6 calls in a 5 min interval of time rounding the result to four decimal places f x X 36 e 3