Statistics Questions and Answers

Last year it was recorded that among the 2 896 students in the school district 1 325 have visited the school nurse You believe that the proportion of students who visited the school nurse this year has changed and decide to test this using a 0 1 level of significance Of a sample of 300 students in a school district 153 have visited the school nurse Match the variable to its value 1 p 2 Po 3 n 0 458 0 51 300

Sam feels that he scored better in math than he did in English So he averages all the scores in math and English separately to compare them He uses the method of hypothesis testing to compare the scores of two subjects Frame the correct null hypothesis for his research O Null hypothesis Mean score in math is more than mean score in English O Null hypothesis Mean score in math is less than mean score in English O Null hypothesis Mean score in math is equal to mean score in English Null hypothesis Mean score in English is less than mean score in math

Type I error occurs when Onull hypothesis is not correct but we accept it O null hypothesis is not correct and we reject it null hypothesis is correct and we accept it O null hypothesis is correct but we reject it

The trainer believes that in the age group of 13 to 18 boys are taller than girls To test his claim he compared the average heights of boys to the average heights of girls He got a p value of 0 04 Draw the conclusion at significance level 0 01 and 0 05 Conclusion At a 0 01 he concludes that the average height of boys is larger than that of girls at a 0 05 concludes that the average height of boys and girls is same Conclusion At a 0 01 and 0 05 average height of boys is larger than that of girls Conclusion At a 0 01 and 0 05 he concludes that average height of boys and girls is same Conclusion At a 0 01 he concludes that the average height of boys and girls is same and at a 0 05 concludes that the average height of boys is larger than that of girls

If the critical value for a right tailed test is 1 96 and the test statistic is 1 64 what would you conclude O fail to reject the null hypothesis fail to reject the alternate hypothesis reject the alternate hypothesis reject the null hypothesis

For a fishing trip Latoya is going to choose lures to put in her tackle box She has 6 lures that are crankbaits and 7 that are jigs In how man ways can she choose 5 lures if 4 or more must be jigs If necessary consult a list of formulas S

Henry is investigating how long his phone s battery lasts in hours for various brightness levels on a scale of 0 100 His data is displayed in the table and graph below 8 7 6 5 Hours WA C H Brightness Level x 20 56 58 61 63 64 72 83 Hours y 4 5 5 1 3 9 4 5 3 4 3 9 3 7 2 10 20 30 40 50 60 70 80 90 100 110 Brightness Level a Find the equation for the line of best fit Keep at least 3 decimals for each parameter in the equation b Interpret the slope in context Henry should expect 0 0327 brightness level per hour Henry should expect 0 0327 hours per brightness level

Assume that a country s economy is currently in recession a Draw a correctly labeled graph of the long run and short run Phillips curves Label the current equilibrium as point Z b Assume the banking system has limited reserves banks in the country hold no excess reserves and the public s holding of currency is constant The required reserve ratio is 25 The central bank of the country buys 100 billion in bonds from the nonbank public 1 By how much will the monetary base of the country change 1 Calculate the change in the amount of loans in the banking system in the country Show your work I Calculate the change in the money supply in the country Show your work c Draw a correctly labeled graph of the money market and show the effect of the change in the money supply identified in part b iii on the nominal interest rate D d Assume there is no change in inflationary expectations On your graph in part a label a point W that is consistent with the effect of the change in the nominal interest rate identified in part c

Fill in the table below last row is for sums x Sums X 6 4 8 Y 5 4 9 18 18 OF Regression Equation Submit All Parts 36 25 0 X 16 0 64 3 116 0 16 OF 81 B 08 X Enter an integer or decimal number more 122 09 xy 30 OF 16 08 Calculate the following by hand Round values to four decimal places if necessary 72 0 118

3 What does the shape of the histogram for the second sample tell you about the data Count 12 10 8 6 4 2 n 30 85 89 90 94 Mean weight is 97 7 grams Median weight is 90 grams 95 99 100 104 105 109 Bagel Weight g 110 114 115 119

2 Find the following a Find the critical t

how all work including any calculator functions used Clearly indicate answers Round to 3 decimals 1 Determine the critical value Za 2 that corresponds to the given level of confidence a 94

The chart below depicts revenues and costs for a fim in perfect competition Quantity Mkt PMR MC TR TC G 14 1 2 3 4 5 6 7 8 9 10 14 14 14 14 14 14 14 14 14 6 4 14 20 27 41 66 87 115 170 Profi Fill in the chart Also what is your favorite fruit and what is your favorite vegetable b In what two ways can the firm in perfect competition behave so as to maximize it profit c Draw these two ideas as two separate graphs property and fully labeling your work Demonstrate the optimal quantity in both graphs

A vertical photo has an air base of 265 ft Stereoscopic measurements of parallax at a point representing the top of a 200 ft tower are 0 275 in The camera focal length is 6 5 in Photos were taken at an elevation of 7 700 ft Determine the elevation of the base of the tower in ft

The stem and leaf display below gives the number of minutes that customers waited for their orders at two different restaurants There were 22 wait times recorded for the first restaurant and 17 recorded for the second Use the display to answer the questions that follow Number of minutes customers waited First restaurant Second restaurant 8877 067889 773 21 1568 532111 2 2 3 3 68899 541 10 3 7 10 4 Key 7 7 0 6 6 a What were the ranges of wait times for the two restaurants First restaurant Second restaurant b Which restaurant had the greater median wait time OFirst restaurant Second restaurant The medians were the same c Which restaurant had more wait times from 40 to 49 minutes O First restaurant Second restaurant OEach had the same

Digitalis is a technology company that makes high end computer processors Their newest processor the luteA is going to be sold directly to the public The processor is to be sold for 3300 making Digitalis a profit of 429 Unfortunately there was a manufacturing flaw and some of these luteA processors are defective and cannot be repaired On these defective processors Digitalis is going to give the customer a full refund Suppose that for each luteA there is a 13 chance that it is defective and an 87 chance that it is not defective If necessary consult a list of formulas If Digitalis knows it will sell many of these processors should it expect to make or lose money from selling them How much To answer take into account the profit earned on each processor and the expected value of the amount refunded due to the processor being defective O Digitalis can expect to make money from selling these processors In the long run they should expect to make dollars on each processor sold O Digitalis can expect to lose money from selling these processors O Digitalis should expect to neither make nor lose money from selling these processors

Find the mean median and mode s of the data in the following stem and leaf plot The leaf represents the ones digit 0 6 1 45 2 2338 34 Part 1 of 3 Find the mean Round your answer to one decimal place if necessary Mean 598 2 Part 2 of 3 X Part 3 of 3 Find the median Round your answer to one decimal place if necessary Median 25 5 S X Find the mode s If there is more than one separate them with commas There is no mode O There is at least one mode Mode s 23 10

3 A social psychologist is testing the effect of type of speaker in a commercial on attitude She recruited 25 people Every person watched three commercials each for a different consumer product One featured a celebrity speaker one had a common person speaker and one had an expert speaker She assessed attitude toward the product after each commercial What are a The factor s b The levels c Between or within groups

2 The test statistic of z 1 77 is obtained when testing the claim that p This is a left tailed test Using a 0 10 significance level complete parts a and b Click here to view the standard normal distribution table for negative z scores Click here to view the standard normal distribution table for positive z scores a Find the critical value s Select the correct choice below and fill in the answer box es within your choice Round to two decimal places as needed A There is one critical value the critical value is OB There are two critical values the lower critical value is GLIDE and the upper critical value is

but often they must be addressed as preliminary analyses to questions about the two means For this latter reason the variance test is presented prior to tests of two means EXAMPLE 7 1 Among the few reptilian lineages to emerge from the Mesozoic ex tinction are today s reptiles One of these the tuatara Sphenodon punctatus of New Zealand is the sole survivor of a group that otherwise disappeared 100 million years ago The mass in g of random samples of adult male tuatara from two islets in the Cook Strait are given below Is the variability in mass of adult males different on the two islets CHAPTER 7 Tests of Hypothesis Involving Two Samples Location A Location B 510 790 773 440 836 435 505 815 765 460 650 600 600 575 452

pts See Details f tion below ct value from the

last try 5 of 6 pts See Details for more retry this question below ts of newborn babies are normally distributed with a mean of 8 5 pounds and a standard of 2 pounds A random sample of 25 newborns are selected Central Limit Theorem be applied because the standard deviation is too low because the sample size is more than 20 because even though the sample size is less than 30 the original distribution is normally ributed because the sample size is less than 30 e standard deviation of the mean of the 25 newborn babies Round to 1 decimal place s the probability that the mean weight of this sample is less than 7 5 pounds Round to 4 decimal is the probability that the mean weight of the sample is between 7 5 and 8 pounds Round to 4 places

The average retirement age in America is 65 years old Do small business owners retire at a younger average age The data below shows the results of a survey of small business owners who have recently retired Assume that the distribution of the population is normal 60 56 70 70 72 71 72 60 59 62 56 What can be concluded at the the x 0 10 level of significance level of significance a For this study we should use t test for a population mean O b The null and alternative hypotheses would be H H B 65 65 c The test statistic t 0 321 please show your answer to 3 decimal places d The p value Please show your answer to 4 decimal places e The p value is a f Based on this we should Select an answer the null hypothesis g Thus the final conclusion is that The data suggest the population mean retirement age for small business owners is not significantly younger than 65 at a 0 10 so there is insufficient evidence to conclude that the population mean retirement age for small business owners is younger than 65 The data suggest the population mean is not significantly younger than 65 at a 0 10 so there is sufficient evidence to conclude that the population mean retirement age for small business owners is equal to 65 The data suggest the populaton mean is significantly younger than 65 at a 0 10 so there is sufficient evidence to conclude that the population mean retirement age for small business owners is younger than 65

Question 14 A half hour daytime ty show has an

Nationally patients who go to the emergency room wait an average of 4 hours to be admitted into the hospital Do patients at rural hospitals have a lower waiting time The 13 randomly selected patients who went to the emergency room at rural hospitals waited an average of 2 1 hours to be admitted into the hospital The standard deviation for these 13 patients was 2 3 hours What can be concluded at the the a 0 01 level of significance level of significance a For this study we should use Select an answer b The null and alternative hypotheses would be Ho Select an answer H Select an answer c The test statistic d The p value e The p value is a f Based on this we should g Thus the final conclusion is that please show your answer to 3 decimal places Please show your answer to 4 decimal places Select an answer the null hypothesis The data suggest the populaton mean is significantly lower than 4 at a 0 01 so there is statistically significant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is lower than 4 hours The data suggest that the population mean awaiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is not significantly lower than 4 hours at a 0 01 so there is statistically insignificant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is lower than 4 hours The data suggest the population mean is not significantly lower than 4 at a 0 01 so there is statistically insignificant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is equal to 4 hours

Assume that the amount of time it takes a five year old eat a PB J sandwich is uniformly distributed with a mean of 15 minutes and a standard deviation of 4 minutes A sample of 36 five year olds are randomly selected a Can the Central Limit Theorem be applied O No because the mean comes from a uniform distribution O Yes because the original population is normally distributed O No because the original population is not normally distributed Yes because the sample size is greater than 30 b What is the mean of all sample means for number of minutes it takes a five year old to eat a PB J sandwich c Find the standard deviation of all sample means for the number of minutes it takes a five year old to eat a PB J sandwich Round to 3 decimal places d Find the probability that the sample mean is more than 14 minutes Round to 3 decimal places e Find the 80th percentile for the mean number of minutes Round to 2 decimal places f Find the 70th percentile for the mean number of minutes Round to 2 decimal places g Find the 10th percentile for the mean number of minutes Round to 2 decimal places h Find the probability the mean time will be between 13 and 16 minutes Round to 3 decimal places

A half hour evening tv show has an average of 10 4 minutes of commercials Assume the number of minutes of commercials follows a normal distribution with standard deviation of 2 0 minutes a Find the probability a half hour soap opera has less than 11 minutes of commercials Use the exact value found in the z table b Find the probability a half hour soap opera has between 10 and 11 minutes of commercials Use the exact values found in the z table c Find the probability a half hour soap opera has more than 10 4 minutes of commercials Use the exact value found in the z table d Find the probability a half hour soap opera has more than 14 5 minutes of commercials Use the exact value found in the z table e The lowest 25 of minutes of commercials is at most how long In other words find the maximum minutes for the lowest 25 of number of minutes of commercials Use the nearest value in the z table f Find the upper number of minutes of commercials for the middle 80 of shows Use the nearest value in the z table g Find the lower number of minutes of commercials for the middle 80 of shows Use the nearest value in the z table

Inches 3 2 0 Jan Feb March April May June July Key City 1x Aug Sep Oct Nov Dec City 2 1 4in 1 What is the average rainfall in City 1 in August 2 What is the average rainfall in City 2 in February bin 3 How much more rainfall does City 1 get in November than City 2 4 4 1 3 4 1 about 4 4 in The information for February and March is missing for City 1 4 What is a reasonable prediction for the amount of rainfall In February 3 8 in 5 What is a reasonable prediction for the amount of rainfall in March 3 in 6 Other than the missing information there is at least one error made when creating t graph What component s of a good graph are missing What would you change or adc

Question 1 Consider a normal distribut a Find the z score for x 2

473 Send data to Excel Part 1 of 3 Assume the population standard deviation is a 91 Part 2 of 3 391 399 a Explain why it is necessary to check whether the population is approximately normal before constructing a confidence interval 350 28 23 11 24 PM It is necessary to check whether the population is approximately normal because the sample size is less than or equal to 30 310 Part 2 3 b Following is a dotplot of these data Is it reasonable to assume that the population is approximately normal Part 3 of 3 304 400 450 able to GALIO 608 500 550 www www aleka com alekscgi lal exa 10 igNalkasNWEDBAGPVRituSgTZa07521mBPJOWICOSCnXEZEVEDOXS 600 650 that the mandation in animali mal ALEKS Abimbola Abudu Section 8 1 Homework 700 40b52280

The length of human pregnancies is approximately normal with mean 266 days and standard deviation 16 days Complete parts a through f Click here to view the standard normal distribution table page 1 Click here to view the standard normal distribution table page 2 The probability that the mean of a random sample of 48 pregnancies is less than 260 days is 0 0047 Round to four decimal places as needed Interpret this probability Select the correct choice below and fill in the answer box within your choice Round to the nearest integer as needed OA If 100 independent random samples of size n 48 pregnancies were obtained from this population we would expect sample s to have a sample mean of exactly 260 days OB If 100 independent random samples of size n 48 pregnancies were obtained from this population we would expect sample s to have a sample mean of 260 days or less OC If 100 independent random samples of size n 48 pregnancies were obtained from this population we

After an oil spill in the ocean oil continues to leak into the water In the accompanying table x represents time in hours and y represents the diameter of the spill on the surface in meters Write a power regression equation for this set of data rounding all coefficients to the nearest hundredth Using this equation find how much time has passed to the nearest tenth of a an hour if the diameter of the spill is 679 meters Hours since Spill Diameter in Meters y 198 274 378 351 369 395 3 7 10 12 13 15

The following table gives the millions of metric tons of carbon dioxide CO emissions from biomass energy combustion in a certain country for selected years from 2010 and projected to 2032 CO CO emissions Year Year emissions 2010 336 5 2022 557 2 2012 362 5 2024 594 9 2014 395 1 2026 629 7 2016 421 8 2028 662 1 2018 452 1 2030 705 1 2020 496 4 2032 741 7 a Create a scatter plot of the data with x equal to the number of years past 2010 and y equal to the millions of metric tons of carbon dioxide 1000 800 600 400 200 15 20 1000 800 600 400 200 1000 800 600 400 200 no

Consider the following X 2 1 0 1 2 3 4 y 16 9 1 2 1 3 12

The developing economies share of the global gross domestic product GDP from 2003 to 2017 is shown in the following table Share Year of GDP 20 22 23 27 28 31 31 33 2003 2004 2005 2006 2007 2008 2009 2010 Share Year of GDP 2011 35 2012 38 39 40 41 42 43 2013 2014 2015 2016 2017 a Find the quadratic function that best models the developing economies share of the global GDP as a function of the number of years after 2000 Round all numerical values to fe places y x Capitalization of variable s is important Check that your upper and lower case match the question b Use technology to find the maximum share of GDP that the developing economies can achieve according to this model Round your answer to ono decimal place

A wheel has 8 equally sized slices numbered from 1 to 8 Some are grey and some are white The slices numbered 3 and 6 are grey The slices numbered 1 2 4 5 7 and 8 are white The wheel is spun and stops on a slice at random Let X be the event that the wheel stops on a white slice and let P X be the probability of X Event A not X b Subtract Let not X be the event that the wheel stops on a slice that is not white and let P not X be the probability of not X a For each event in the table check the outcome s that are contained in the event Then in the last column enter the probability of the event Outcomes 1 2 3 4 5 6 7 8 00 U 0 1 P not X 0 U 0 U 000 U U 8 Probability P not X X c Select the answer that makes the sentence true P X 00 7 6 X 81 54 2 3 Est

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7 Jupiter weighs 1 898 000 000 000 tons If 1 0 ton is equal to 2000 lbs and 2 5 lbs equals 1 0 Couric How much does Jupiter weigh in Couric

Arandom sample of 860 births included 426 boys Use a 0 01 significance level to test the claim that 50 6 of newborn babies are boys Do the results support the belief that 50 of newborn babies are boys Identity the null and alternative hypotheses for this test Choose the correct answer below OA H p0 506 H p 0 506 OB Hp 0 506 H p 0 506 OC H p 0 506 H p 0 506 OD H p 0 506 H 0506

Suppose that 45 of all babies born in a particular hospital are girls If 6 babies born in the hospital are randomly selected what is the probability that fewer than 2 of them are girls Carry your intermediate computations to at least four decimal places and round your answer to two decimal places If necessary consult a list of formulas 7

7 Timone and Pumba each invest 200 in a savings account Timone gains 4 13 compounded weekly while Pumba gains 3 88 compounded continuously Who will have more money in their account after 10 years of investing Formula 1 Formula 2 Formula 3

5 In the Hidden Flower Village a secret government agent was tasked to murder a clan of powerful ninjas After the massacre only 2 ninjas survived 2 5 of the original population Determine how many Ninjas were in the original population

Felipe is putting 11 colored light bulbs into a string of lights There are 3 yellow light bulbs 4 blue light bulbs and 4 white light bulbs How many distinct orders of light bulbs are there if two light bulbs of the same color are considered identical not distinct X

A troupe of 10 dancers is going to line up on stage Of these dancers 5 are wearing blue and s are wearing white A dancer wearing blue must be in the first position and they must alternate between colors In how many ways can the dancers line up X

A certain train has 9 cars that are being lined up on a track One of the cars is the engine and another is the caboose The engine will be the first car in line The caboose will be the last car in line In how many ways can the cars be lined up X

Which distribution has a mean of 5 Multiple Choice O O O hypergeometric with N 100 n 10 s 50 bernoulli with 3 binomial with n 200 05 poisson with 25

Agriculture Table 3 shows the yield in bushels per acre and the total production in millions of bushels for corn in the United States for selected years since 1950 Use 4 decimal places im answers Table 3 US Corn Production Year Yield bushels per acre Total Production million bushels 1950 37 6 1960 55 6 1970 81 4 1980 97 7 1990 2000 A Let x represent years since 1900 and find the logarithmic model for the yield YDX D What is the value for the equation in part C 115 6 139 6 8 What is the value for the equation in part A 2 C Let x represent years since 1900 and find the logarithmic model for the production P x 2 782 3 479 4 802 6 867 7 802 10 192

The following table gives the U S national debt for selected years from 1900 to 2013 U S Debt billions 3233 5225 5674 7933 11 957 13 529 15 476 U S Debt billions 1 1 24 16 43 259 273 314 Year 1900 1910 1920 1930 1940 1945 1955 1965 1975 533 1985 1823 a Using a function of the form y a b x with x 0 in 1900 and y equal to the national debt in billions model the data Round your coefficients to four decimal pla Year 1990 1996 2000 2005 2009 2010 2011 2012 2013 16 067 16 856 b Use the model to predict the debt in 2021 Round your answer to the nearest billion billion c Predict the year in which the debt will be 99 trillion 99 000 billion

The following table gives the value of an investment after intervals ranging from 0 to 7 years of 50 000 invested at 10 compounded annually Year y 50 000 00 55 000 00 60 500 00 66 550 00 73 205 00 5 80 525 50 6 88 578 05 97 435 86 7 a Develop an exponential model for these data accurate to four decimal places with x in years and y in dollars Amount Investment Grows to 0 1 2 3 b Use the model to find the amount to which 59 0 will grow in 20 years if it is inunched 1000

The amount of money that needs to be deposited into an account to reach some future goal is called the present value The following table gives the present value to the nearest dollar for an account that earns 10 compounded annually so that the account value will be 50 000 after intervals ranging from 1 to 7 years Present value 45 455 41 322 37 566 34 151 Years 1 2 3 4 5 6 7 31 046 28 224 26 658 a Using x as the years and y as the present value in dollars develop an exponential model for these data Round your numerical values to four decimal places b Use the model to find the present value to the nearest dollar of this account for its value to be 50 000 after 11 years