Statistics Questions

The Census Bureau reports the average commute time for citizens of Cleveland Ohio is 33 minutes To see if the commute time is different in the winter a random sample of 40 drivers were surveyed The average commute time for the month of January was calculated to be 34 2 minutes and the population standard deviation is assumed to be 7 5 minutes At the 0 05 level of significance can it be concluded that the commuting times are different in the winter a What are the null and alternative hypotheses O O Hoi u 33 H 33 Hoi A 33 H 33 Hoi H 33 H 33 b What is the test statistic Round to 2 decimal places c What is the p value Round to 4 decimal places d Which is the decision O Fail to reject the null hypothesis O Reject the null hypothesis e Which is the interpretation of the decision There IS NOT enough evidence to concluded that the mean commute times are different in the winter

A cat breeder suspects her kittens weigh more than the larger population of kittens A random sample of 31 of her kittens were weighed The sample weighed an average of 1 15 pounds The population weight of kittens follows a normal distribution with a standard deviation of 0 4 pounds Using a significance level of 0 05 test the claim that the mean weight of kittens is more than the larger population of 1 00 pounds a What are the null and alternative hypotheses Ho X 1 O H Xs l Ho 1 O H 1 Ho H 1 O H 1 Ho X 1 O H X 1 b What is the test statistic Round to 2 decimal places c What is the p value Round to 4 decimal places d Which is the decision to this test O Reject the null hypothesis Fail to reject the null hypothesis e What is the interpretation of the decision There IS enough evidence to support the claim that the average weight of her kittens is over 1 pound

A doctor speculates that the red blood cell count of adults over the age of 70 is less than the larger adult population The red blood cell count from a random sample of 42 of these older adults has a sample mean of 5 31 and a sample standard deviation of 0 54 The larger adult population has a mean of 5 4 Use a significance level of 0 01 to test whether the red blood cell count of adults over 70 is less than the larger population a What are the null and alternative hypotheses Ho 5 4 OH 5 4 Ho H 5 4 O H H 5 4 Hoi u 5 4 O H H 5 4 Ho 5 4 OH 5 4 b What is the test statistic Round to 2 decimal places c What is the p value Round to 4 decimal places d Which is the decision O Reject the null hypothesis O Fail to reject the null hypothesis e What is the interpretation of the decision There IS NOT enough evidence that the sample

A local road was designed to handle a daily mean of 200 cars The local city council is concerned that the road it getting more traffic than it was designed to handle A recent sample of 50 days found a sample mean of 207 cars per day and a sample standard deviation of 33 9 mph We will perfrom a hypothesis test to determine if this is strong evidence that the mean number of daily cars is more than the road was designed to handle Define your variable Let u be the mean number of cars that use the road on a daily basis Let p be the proprotion of cars in the sample that use the road Let p be the proportion of cars that use the road Let u be the mean number of of cars that use the road on the sampled days Write your hypotheses Ho HAH Find the P value Type your answer as a decimial rounded to three decimal places Do not type a percentage or a percent sign P value Using an a level of 5 you should Fail to Reject Ho Reject Ho and Accept HA

It is believed that 11 of all Americans are left handed A college needs to know how many left handed desks to place in the big lecture halls being constructed on its campus In a random sample of 150 students from that college whether or not a student was left handed was recorded for each student The college wants to know if the data provide enough evidence to show that students at this college have a lower percentage of left handers than the general American population State the random variable population parameter and hypotheses State the Type I and Type II errors in the context of this problem a The symbol for the sample variable involved in this problem is p The sampling distribution of this variable in context is as follows b The symbol for the parameter involved in this problem is p The wording for the parameter in context is as follows The percentage of all students from that college that are left handed c Fill in the correct null and alternative hypotheses Ho p Ha p The percentage of 150 randomly selected students from that college that are left handed 4

Compute the P value Round the answer to at least four decimal places P value 0 0146 Part 4 of 5 Determine whether to reject Ho At the a 0 01 level do not reject the null hypothesis Ho Part 4 5 Part 5 of 5 Using a 0 01 can you conclude that less than half of HIV positive smokers have used a nicotine patch At the a 0 01 level of significance there Choose one enough evidence to conclude that less than half of HIV positive smokers have

Compute the value of the test statistic Round the answer to at least two decimal places Z 2 33 Correct Answer z 2 18 Part 2 5 Part 3 of 5 Compute the P value Round the answer to at least four decimal places

Wire electrical discharge machining WEDM is a process used to manufacture conductive hard metal components It uses a continuously moving wire that serves as an electrode Coating on the wire electrode allows for cooling of the wire electrode core and provides an improved cutting performance An article gave the following sample observations on total coating layer thickness in m of eight wire electrodes used for WEDM 22 17 29 35 42 24 25 25 Calculate a 99 CI for the standard deviation of the coating layer thickness distribution Round your answers to two decimal places Is this interval valid whatever the nature of the distribution Explain Yes there are enough data points for this interval to be valid No validity of this interval requires that coating layer thickness be at least approximately normally distributed You may need to use the appropriate table in the Appendix of Tables to answer this question

ermine the t critical value s that will capture the desired t curve area in each of the following cases Assume that central areas are centered at t 0 Round your answers to three decimal places USE SALT a Central area 0 95 df 10 b Central area 0 95 df 20 c Central area 0 99 df 20 d Central area 0 99 df 60 e Upper tail area 0 01 df 30 f Lower tail area 0 025 df 5

At the a 0 05 level reject Part 4 5 Part 5 of 5 the null hypothesis Ho e State a conclusion At the a 0 01 level of significance there Choose one At the a 0 05 level of significance there Choose one enough evidence to conclude that less than 78 of emails are spam enough evidence to conclude that less than 78 of emails are spam

At the a 0 01 level do not reject the null hypothesis Ho Part 4 5 Part 5 of 5 State a conclusion At the a 0 01 level of significance there Choose one enough evidence to conclude that less than 59 of children aged 8 12 have phones is is not

Determine the values of the following quantities Round your answers to two decimal places USE SALT a x 0 05 5 b x 0 05 35 2 X c X 0 025 35 d x 0 005 35 2 e x 0 95 35 f X 0 995 35

Part 3 of 5 Compute the P value Round the answer to at least four decimal places P value 0 0384 Part 3 5 Part 4 of 5 Determine whether to reject Ho At the a 0 01 level Choose one the null hypothesis Ho X

sample of 13 joint specimens of a particular type gave a sample mean proportional limit stress of 8 41 MPa and a sample standard deviation of 0 73 MPa a Calculate and interpret a 95 lower confidence bound for the true average proportional limit stress of all such joints Round your answer to two decimal places MPa Interpret this bound With 95 confidence we can say that the value of the true mean proportional limit stress of all such joints is centered around this value With 95 confidence we can say that the value of the true mean proportional limit stress of all such joints is greater than this value With 95 confidence we can say that the value of the true mean proportional limit stress of all such joints is less than this value What if any assumptions did you make about the distribution of proportional limit stress O We must assume that the sample observations were taken from a chi square distributed population We must assume that the sample observations were taken from a uniformly distributed population We do not need to make any assumptions We must assume that the sample observations were taken from a normally distributed population b Calculate and interpret a 95 lower prediction bound for proportional limit stress of a single joint of this type Round your answer to two decimal places MPa Interpret this bound If this bound is calculated for sample after sample in the long run 95 of these bounds will provide a lower bound for the corresponding future values of the proportional limit stress of a single joint of this type If this bound is calculated for sample after sample in the long run 95 of these bounds will provide a higher bound for the corresponding future values of the proportional limit stress of a single joint of this type If this bound is calculated for sample after sample in the long run 95 of these bounds will be centered around this value for the corresponding future values of the proportional limit stress of a single joint of this type

Assume that the helium porosity in percentage of coal samples taken from any particular seam is normally distributed with true standard deviation 0 73 a Compute a 95 CI for the true average porosity of a certain seam if the average porosity for 24 specimens from the seam was 4 85 Round your answers to two decimal places b Compute a 98 CI for true average porosity of another seam based on 18 specimens with a sample average porosity of 4 56 Round your answers to two decimal places c How large a sample size is necessary if the width of the 95 interval is to be 0 3 Round your answer up to the nearest whole number specimens d What sample size is necessary to estimate true average porosity to within 0 24 with 99 confidence Round your answer up to the nearest whole number specimens

Part 2 of 5 b Compute the value of the test statistic Round the answer to at least two decimal places Z 2 16 Part 2 5 Part 3 of 5 c Compute the P value Round the answer to at least four decimal places P value X 5

An article reported that in a study of a particular wafer inspection process 356 dies were examined by an inspection probe and 202 of these passed the probe Assuming a stable process calculate 95 two sided confidence interval for the proportion of all dies that pass the probe Round your answers to three decimal places You may need to use the appropriate table in the Appendix of Tables to answer this question

Part 3 of 5 c Using the result from part b compute the P value Round the final answer to at least four decimal places P value 0 0036 Part 3 5 Part 4 of 5 d Determine whether to reject Ho Choose one the null hypothesis Reject Do not reject X

Part 2 of 5 b Compute the test statistic Do not round intermediate steps Round the answer to two decimal places 2 91 Part 2 5 Part 3 of 5 c Using the result from part b compute the P value Round the final answer to at least four decimal places P value X S

Kids with phones A marketing manager for a phone company claims that less than 59 of children aged 8 12 have phones In a survey of 822 children aged 8 12 by a national consumers group 460 of them had phones Can you conclude that the manager s claim is true Use the a 0 01 level of significance and the P value method with the TI 84 Plus calculator Part 0 5 Part 1 of 5 State the appropriate null and alternate hypotheses Ho H This hypothesis test is a Choose one test 0 0 00 X O O P 0 0

Curing diabetes Vertical banded gastroplasty is a surgical procedure that reduces the volume of the stomach in order to produce weight loss In a recent study 82 patients with Type 2 diabetes underwent this procedure and 59 of them experienced a recovery from diabetes Does this study provide convincing evidence that those with diabetes who undergo this surgery will recover from diabetes differs from 56 Use the a 0 01 level of significance with the P value method and Excel Part 0 5 Part 1 of 5 a State the appropriate null and alternate hypotheses Ho H This hypothesis test is a Choose one test 5 07 P X 8 0 B DI V d

Spam A researcher reported that 71 8 of all email sent in a recent month was spam A system manager at a large corporation believes that the percentage at his company may be 78 He examines a random sample of 500 emails received at an email server and finds that 370 of the messages are spam Can you conclude that the percentage of emails that are spam is less than 78 Use both a 0 01 and a 0 05 levels of significance and the P value method with the TI 84 Plus calculator Part 0 5 Part 1 of 5 a State the appropriate null and alternate hypotheses Ho H This hypotheses test is a Choose one test right tailed D X P S

Quit smoking In a survey of 444 HIV positive smokers 199 reported that they had used a nicotine patch to try to quit smoking Can you conclude that less than half of HIV positive smokers have used a nicotine patch Use the a 0 01 level of significance and the P value method with the TI 84 Plus calculator Part 0 5 Part 1 of 5 State the appropriate null and alternate hypotheses Ho H This hypothesis test is a Choose one test 0 0 X P 0 0

Part 0 5 LA Game consoles A poll surveyed 341 video gamers and 81 of them said that they prefer playing games on a console rather than a computer or hand held device An executive at a game console manufacturing company claims that less than 27 of gamers prefer consoles Does the poll provide convincing evidence that the claim is true Use the a 0 01 level of significance with the P value method and Excel Part 1 of 5 5 a State the appropriate null and alternate hypotheses Ho H This hypothesis test is a Choose one test 0 0 O O 0 0 p X 0 0

Itranscript Calculate the monthly mortgage payment Round to the nearest cent Answer 2 Points 220 000 is financed for 15 years at 4 APR

Find the standardized test statistic t for the hypothesis test defined by H 13 6 z 13 2 8 2 0 n 20 and a 0 05 Round your answer to three decilmall places 0894 1 233 0 872

Construct a 95 confidence intervall for the popallation mean Assume the population has a normal distribution A sample of 20 part time workers had mean annual earnings of 3120 with a standard deviation of 677 Round to the neare 2803 3437 2135 2567 2657 2891 1324 1567

Find the indicated probability Assume that the random variable Xs normally didt buted with mean p standard deviation 16 Compute the probability PX90 CO POSS

In a recent survey 67 of the community favored building a health center in the neighborhood If 14 citizens are chosen find the probability that exactly 9 of th favor the building of the health center 0670 0085

At a particular point in time the stock marken ook big wings up and down A survey of 999 adult investors and how often thang bracked their portfolio The table shows the investor responses What is the probability that an adult investor tracks his or her portfolio daily Express your answer as a simplified fraction and as a decimall rounded to three decimal places

transcript Brianna is buying a house for 220 000 She plans to make a 18 down payment Closing costs include 700 for 6 months of homeowners insurance 600 for 6 months of property tax 125 for the title fee and 350 in transaction fees Brianna also agreed to pay four points in exchange for a 1 reduction in interest rate Determine the amount of money Brianna needs to cover closing costs Round your answer to the nearest cent Answer 2 Points Key Keyboard Sho

the close of the stock markets on a day in 2017 there were 6100 companies listed with certain stock exchanges On this day the probabilities of advancing eclining and unchanged company stocks appears in the table for the two exchanges Find the probability that a stock was listed on Exchange 2 given that it dvanced Exchange Exchange 1 Exchange 2 Percentage of Probability of Probability of Stock Stock Companies Listed 0 5209 Advancing Declining 0 7224 0 2492 0 4791 0 6224 0 3255 Let F be Exchange 2 and E be an advance R E and P F Probability the Stocks Remain Unchanged 0 0284 0 0521

Given the following five number summary find the NOR 07 13 2

You wish to test the following claim H at a significance level of a 0 01 H 71 7 H 71 7 You believe the population is normally distributed but you do not know the standard deviation You obtain the following sample of data data 77 8 76 1 78 9 What is the test statistic for this sample Report answer accurate to three decimal places test statistic What is the p value for this sample Report answer accurate to four decimal places p value The p value is O less than or equal to a Ogreater than a This test statistic leads to a decision to reject the null accept the null fail to reject the null As such the final conclusion is that There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 71 7 There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 71 7 The sample data support the claim that the population mean

The heights of ten femalle students in inches in a college math class are listed below Find the mean 65 66 67 66 67 70 67 70 71 68 700 inches 71 1 inches 67 7 inches 65 5 inches

The commuting times in minutes of an employee for ten consecutive below Find the median commute 71 67 67 72 76 72 73 68 72 72 73 minutes 67 minutes 72 minutes

summarized in the table S 1 15 lb 1 lb 1 1 lb 1 05 lb 19 Find the class width

Which of the following is not true of statistics Statistics can be used to organize and analyze information Statistics is used to draw conclusions using data Statistics involves collecting and summarizing data Statistics is used to answer questions with 100 certainty

Provide an appropriate response Which branch of statistics deals with the organization and summarization of collected information Inferential statistics Computational statistics Descriptive statistics

A well known brokerage firm executive claimed that 20 of investors are currently confident of meeting their investment goals An XYZ Investor Optimism Survey conducted over a two week period found that in a sample of 600 people 29 of them said they are confident of meeting their goals Test the claim that the proportion of people who are confident is larger than 20 at the 0 10 significance level The null and alternative hypothesis would be Ho p2 0 2 Ho p 0 2 Ho 0 2 Ho p 0 2 Ho 0 2 Ho 0 2 H p 0 2 H p0 2 H 0 2 H p 0 2 H p0 2 H p 0 2 O O O O O The test is left tailed right tailed two tailed O The test statistic is The p value is Based on this we O Reject the null hypothesis O Fail to reject the null hypothesis to 3 decimals to 4 decimals

34 Hy p They find that p value 00025 and use an a 001 level of significance Do the environmental engineers have enough evidence to say the level of lead in the water is significantly higher than the standard Since the p value there is insufficient evidence that the level of lead is significantly higher than the standard theire is sufficient evidence that the level of lead is Since the p value significardly higher than the standard Since the p value significantly higher than the standard there is insufficient evidence that the level of lead is Since the p value o there is sufficient evidence that the level of head is significantly higher than the standard

d Determine whether to reject Ho Reject Part 4 5 Part 5 of 5 the null hypothesis Ho e State a conclusion There Choose one enough evidence to conclude that the mean commute time is greater than 25 minutes

2 3 4 5 6 7 What is the relationship between confidence intervals and hypothesis testing When testing Ho Ho versus H Ho if a 90 confidence interval does not contain Ho we Choose one H at the reject do not reject X S level 8 E B

This hypothesis test is a two tailed Alternate Answer Ho 35 000 H 35 000 This hypothesis test is a two tailed test Part 1 5 Part 2 of 5 b Compute the value of the test statistic Round the answer to two decimal places Skip Part Check test 3

ne table below contains pulse rates after running for 1 minute collected from a random sample of females who drink alcohol Find a 99 confidence interval for the mean itse rate after exercise of all women who do drink alcohol P Parameter What is the correct parameter symbol for this problem P o What is the wording the parameter in the context of this problem A Assumptions The mean pulse rate after running one minute of all women who drink Since quantitative pulse rate after running one minute in bpm 89 110 128 116 143 147 82 157 74 64 124 128 195 123 95 36 95 195 108 115 75 78 65 141 NZ 20m n2 30 or normal population n 1 P 2 10 np 2 10 n 1 P 2 10 a is known no outliers in the data a is unknown n p 2 10 outliers in the data OF O Information was collected from each object what conditions do we need to check Check all that apply

Ticon one way commute time was 20 minutes with a standard deviation or 15 minutes A transportation engineer Ciams that the meort commote time is greater than 25 minutes Do the data provide convincing evidence that the engineer s claim is true Use the a 0 05 level of significance and the P value method with the TI 84 Plus calculator Part 1 of 5 a State the appropriate null and alternate hypotheses Hoi 25 H 25 This hypothesis test is a right tailed Y test Part 1 5 Part 2 of 5 b Compute the value of the test statistic Round the answer to two decimal places Ella Espe OF B 42 P dlo E

1 2 3 4 5 6 Select the appropriate word or phrase to complete the sentence 7 If we decrease the value of the significance level a we Choose one the probability of a Type II error increase decrease do not affect X S

Only about 20 of people who try to quit smoking succeed Sellers of a motivational tape claim that listening to the recorded messages can help people quit Match the appropriate null and alternative hypotheses in this setting Ho Ha a P 20 b P 20 c P 20 d P 20 e P2 20 1 P 20 Match a type I and type II error in context Type II Error Type 1 Error a Thinking the motivational tapes helped people quit smoking when they actually didn t b Thinking the tapes didn t help people quit smoking when they actually did help Select an answer Which error the Type I or the Type Il do you consider a worse mistake Select an answer How would you limit the probability of making this error A M Doing this would increase the probability of making a

1 Part 0 5 3 Part 1 of 5 4 5 Commuting to work A community survey sampled 1923 people in Colorado and asked them how long it took them to commute to work each day The sample mean one way commute time was 25 7 minutes with a standard deviation of 13 minutes A transportation engineer claims that the mean commute time is greater than 25 minutes Do the data provide convincing evidence that the engineer s claim is true Use the a 0 05 level of significance and the P value method with the TI 84 Plus calculator a State the appropriate null and alternate hypotheses Ho H This hypothesis test is a Choose one test 6 X O 0 0 P 3 E d

The US Department of Energy reported that 45 of homes were heated by natural gas A random sample of 346 homes in Oregon found that 146 were heated by natural gas Test the claim that proportion of homes in Oregon that were heated by natural gas is different than what was reported Use a 5 significance level Give answer to at least 4 decimal places a What are the correct hypotheses Select the correct symbols and use decimal values not percentages Ho Select an answer H Select an answer Based on the hypotheses compute the following b Test Statistic c p value V d Based on the above we choose to Select an answer e The correct summary would be Select an answer that the proportion of homes in Oregon that were heated by natural gas is different than what the DOE reported value of 45