Statistics Questions and Answers

Last year s freshman class at Big State University totaled 5 310 students Of those 1 258 received a merit scholarship to help offset tuition costs their freshman year although the amount varied per student The amount a student received was M 3 457 477 If the cost of full tuition was 4 450 last year what percentage of students who received a merit scholarship did not receive enough to cover full tuition Round your answer to the nearest whole percent Percentage of students

9 Pam is comparing the prices of two different brands of peanut butter Each brand comes in different sizes and is sold at different prices She wants to determine which brand is a better deal She has recorded her data for Brand A in the graph below and her data for Brand B in the table below Cost Dollars 10 5 0 0 5 Brand A 10 Size Ounces I 15 20 25 Size Cost Ounces Dollars 5 3 75 7 50 10 Brand B 16 12 00

10 pts A Gallup poll asked 1050 randomly chosen adults if they are familiar with the 2015 VW emissions scandal Of this sample 73 said that they were familiar with the scandal a Construct and interpret a 95 confidence interval for the proportion of all US adults that are familiar with the VW emissions scandal Show work for checking the necessary conditions constructing the interval and an interpretation

8 pts The average speed of vehicles traveling of Interstate 5 Freeway 1 5 in California is 73 miles hour and the standard deviation is 4 8 miles hour Assume the speeds are normally distributed Write each answer in a complete sentence a What is the probability that a vehicle is traveling between 71 miles hour and 85 miles hour

The numbers of items that customers purchased using a self checkout lane ar shown 8 4 6 5 4 3 15 4 4 1 10 3 4 12 7 2 4 6 21 18 4 10 13 4 Which measure or measures of central tendency best reflect the data Select EACH correct answer Omean mode median

The total points scored by two youth soccer teams are shown Rockets 3 0 3 4 2 6 1 0 3 Jets 2 3 2 1 0 0 0 2 1 Match the correct values statements The median score for the Jets is The Rockets typical score is the Jets typical score The m dian score for the Rockets is 1 2 4 2 3 3 9 4 1 5 1 2 6 2 7 less than 8 greater than

wenty one percent of U S employees who are late for work blame oversleeping You randomly select four U S employees who are late for work and ask them wheth hey blame oversleeping The random variable represents the number of U S employees who are late for work and blame oversleeping Find the mean of the binomial distribution Round to the nearest hundredth as needed

Christy received a loan of 1800 effective January 20 2021 with an interest rate of 7 5 and maturity da of August 29 2021 Christy made two partial payments 600 on February 5 2021 and 500 on May 15 2021 Use the United States Rule to determine the balance due on the loan at the date of maturity Amount due at maturity Round your answer to the nearest cent

Percentage of Students Scoring 85 or Better Mathematics x 27 12 13 10 30 45 20 English y 46 28 45 34 56 67 42 Write the linear regression equation for these data rounding all values to the nearest hundredth State the correlation coefficient of the linear regression equation to the nearest hundredth Explain the meaning of this value in the context of these data

2 At the local veterinarian school the number of animals treated each day over a period of 20 days was recorded 28 34 23 35 16 17 47 05 60 26 39 35 47 35 38 35 55 47 54 48 a Construct a stem plot for the data b Describe the distribution thoroughly Remember your S O C C S

Based on the following calculator output determine the range of the dataset 1 Var Stats x 114 285714286 Ex 800 Ex 92018 Sx 9 91151326681 ox 9 17627820157 n 7 minX 102 Q 104 Med 115 Q3 122 maxX 128

The gas mileages in miles per gallon for 29 cars are shown in the frequency distribution Approximate the mean of the frequency distribution The approximate mean of the frequency distribution is Round to one decimal place as needed Gas Mileage in miles per gallon 27 31 32 36 37 41 42 46 Frequency 13 9 3 4

Select the correct answer from each drop down menu Elwood invested 5 000 in a money market account and has been tracking its progress He found that after 3 years the account held 7 100 and after 8 years the account held 10 350 Use this information to complete the statements Over the first 3 years the value of the account increased at the value of the account increased at an average rate of approximately over the last 5 years Over the entire 8 years annually

Frequency 15 10 5 0 2 Histogram of Quality Defects 6 8 Defects per hour 10 12 n 80 X axis is giving midpoints so the first interval on left side bar shown is going from 1 5 defe 2 5 defects for its interval so based off that understanding answer the following Estimate the interval that contains the median The interval that contains the median is from to

Tasneem has a sample of 12 bags of candy She recorded the mass in grams of each bag Her data is shown 46 6 46 7 46 7 46 8 46 8 47 1 47 2 47 3 47 5 47 9 48 48 1 Aalia has a different sample of 12 bags of candy She recorded the mass in grams of each bag The median mass for Aalia s sample is greater than the median mass of Tasneem s sample Which dot plot could represent Aalia s data OA 46 8 OB 46 8 00 00015 47 47 O 47 2 474 47 6 47 8 Mass grams 47 2 474 47 6 47 8 Mass grams 48 48 OC O D 00 46 8 46 8 47 47 2 474 47 6 47 8 Mass grams 000 47 48 472 474 47 6 47 8 48 Mass grams

22 In a recent survey 65 of those surveyed were in favor of a local school levy The margin of error was 2 How many people were surveyed Hint Use the Margin of error formula in the previous question Let ME 0 02 and p 0 65 Solve for n

48 Suppose you are comparing two populations and get the following statistics from random sampling n y SD population 1 population 2 35 100 11 9 5 0 4 0 5 Which sentence best describes this data a Strong evidence that the populations have differ ent means b The data is consistent with equal population

Watching TV In 2012 the General Social Survey asked a sample of 1314 people how much time they spent watching TV each day The mean number of hours was 2 85 with a standard deviation of 2 62 A sociologist claims that people watch a mean of 3 hours of TV per day Do the data provide sufficient evidence to conclude that the mean hours of TV watched per day is less than the claim Use the a 0 05 level of significance and the P value method with the TI 84 Plus calculator Part 0 4 Part 1 of 4 a State the appropriate null and alternate hypotheses Ho H This hypothesis test is a Choose one test O O D O O O H O O

Amazon claims that if you are a prime member 85 of your packages will arrive within two business days You have decided that you want to know if this claim is true You take a simple random sample of 25 students at your school and 19 of the students claim that their packages arrived within two business days of ordering

Which of the following chi square tests is appropriate for analysis of one categorical variable from a single popula O chi square test of homogeneity O chi square test for independence chi square goodness of fit test

How would you interpret a statistical significance level of 0 48 This means that the probability for the null hypothesis to be false is 0 48 O This means that the probability for the null hypothesis to be true is 0 48 O This means that the probability for the alternate hypothesis to be true is 1 0 48 This means that the probability for the alternate hypothesis to be false is 1 0 48

Which one of these statements is NOT an example of a straw man null hypotheses O Families with cars have the same access to healthcare providers as families without cars O Cats and dogs differ in their interest in human relationships O Students who do their homework regularly get better grades or the same grades as students who do not O There is no difference in the number of doctor visits per year for people who wash their hands more than three times a c compared to those who wash their hands three times or less a day

Select one answer 10 points In a fictional study suppose that a psychologist is studying the effect of daily meditation on resting heart rate The psychologist believes the patients who not meditate have a higher resting heart rate For a random sample of 45 pairs of identical twins the psychologist randomly assigns one twin to one of two treatments One twin in each pair meditates daily for one week while the other twin does not meditate At the end of the week the psychologist measures the resting heart rate of each twin Assume the mean resting heart rate is 80 heart beats per minute The psychologist conducts a T test for the mean of the differences in resting heart rate of patients who do not meditate minus resting heart rate of patients who do meditate Which of the following is the correct null and alternative hypothesis for the psychologist s study A OH u 80 H 80 B OH 0 H 0 C OH u 0 H 0

During a 5 day period a florist served a different number of customers at a flower shop each day The mean number of daily customers served during this period was 17 In the following month during another 5 day period the florist served 16 customers per day for four of the days but served 25 customers on the fifth day What is the difference between the mean number of customers the florist served during each of the two five day periods Adapted from Khan Academy 00 O 0 8 O 1 0

Stories in the World s Tallest Buildings The number of stories in each of a sample of the world s 24 tallest buildings follows Construct a grouped frequency distribution and a cumulative frequency distribution with 7 classes 88 70 88 69 85 78 88 55 65 70 77 80 Send data to Excel Part 0 5 Part 1 of 5 75 64 56 72 The class width is What is the class width for a frequency distribution with 7 classes 75 79 55 60 71 60 80 55 X C C E 0 E

The frequency table below summarizes a list of the number of words randomly selected students spelled correctly during a spelling bee Find the mean vide your answer below Value 10 12 13 14 15 16 17 Frequency 7 2 1 316 3 1

lan wants to figure out if there is a relationship between how much a piece of furniture weighs and how much it costs He samples some items and comes up with the following scatterplot Cost dollars 800 600 400 200 10 20 30 40 50 60 70 80 90 Weight kg Here s lan s description of the scatterplot There is a moderately strong positive linear association between how much a piece of furniture weighs and how much it costs There don t seem to be any obvious outliers What if anything is missing from this description Choose 1 answer Direction of the Points Possible Outliers

When considering different sampling methods cluster sampling includes the steps list the members of the population use simple random sampling to select a starting point in the population let k number of individuals in the population number of individuals needed in the sample choose every kth individual in the list starting with the one that was randomly selected divide the population into groups use simple random sampling to identify a proportionate number of individuals form each group O Identify individuals of the poulation that are easily accessible obtain data from these individuals use simple random sampling to select a set of groups every individual in the chosen groups is included in the sample

1 A city planning board wants to plan activities that would be fun for families So they sent a survey to 100 households to collect information One of the questions asked was how many children live in the household A clerk working in the city office made the following frequency table based on the responses they received for that question a of children of households reporting this number of children 8 12 18 11 b 0 1 2 3 4 5 6 7 8 69 64 4 2 0 2 1 2 points How many survey responses were used to generate the frequency table above answer 2 points Your friend wants to know how you came up with your answer in part a Please write an explanation that provides clear details about which numbers you used and how you got your

In a survey of 2035 workers 73 reported working out 3 or more days a week What is the margin of error What is the interval that is likely to contain the exact percent of all people who work out 3 or more days a week Show all work

Shift D Total Avg Head count 95 80 55 45 275 Total 16 14 8 4 42 Year to Date Turnover 90 Day 8 5 2 0 15 This Year 16 8 17 5 14 5 8 9 15 3 Last Year 16 2 11 1 9 8 10 3 14 3 Which shift will you focus your efforts on in order to reduce 90 day turnover during the second half of this year Shift A Shift B Shift C Shift D

Fastex Shoes claims that it has designed a new range of lightweight shoes that allow athletes to run faster than they can using any other shoes SportsPlus a rival shoe manufacturer then came up with a design that it claims performs even better than Fastex s design A sports magazine decided to test the claims It created two groups of 15 randomly selected athletes each Members of both groups were pretested and determined to have equal athletic ability Additionally they followed the same nutrition plan and training program during the study The athletes did a 1 mile run to test the shoes The magazine found that the athletes who used Fastex shoes had reduced their 1 mile run time by an average of 3 and athletes who used SportsPlus shoes had reduced their 1 mile run time by an average of 2 Given the magazine s data collection method and findings what conclusion can be made The data collection method used was fair since both shoe designs were tested on identical parameters The data collection method used was unfair since the athletes given Fastex shoes may have been better runners than the athletes given SportsPlus shoes O C The data collection method used was nonrandom since the athletes using Fastex shoes may have trained better The data collection method used was random since the athletes in the two groups used two different shoe designs O A O B D

The parallel dotplots below display the number of cars parked for several days in each of two parking lots Parked Cars by Lot Lots A B N 21 2 22 23 24 25 26 27 28 29 Number of Cars Which of the following statements is true O The range for the distribution of the number of cars is larger in lot A The range for the distribution of the number of cars is larger in lot B O There is a smaller standard deviation in the distribution of the number of cars in lot B The standard deviation in the distribution of the number of cars is the same for both lots

Transforming random A restaurant sells three sizes of shakes The small medium and large sizes each cost 2 00 3 00 and 3 50 respectively Let X represent the restaurant s income on a randomly selected shake purchase Based on previous data here s the probability distribution of X along with summary statistics X income P X Small 2 00 0 28 Medium Large 3 00 3 50 0 40 0 32 Mean x 2 88 Standard deviation x 0 59 During the last hour of business the restaurant offers a special that gives customers 1 off any size shake Assume that the special doesn t change the probability that corresponds to each size Let Y represent their income on a randomly selected shake purchase with this special pricing What are the mean and standard deviation of Y dollars

2 The data in the table shows the times for Men s 500 m Speed Skating event at the Winter Olympics Let x be the number of years since 1980 Year 1984 Time sec 38 19 36 45 37 14 1988 1992 1994 36 33 1998 35 59 2002 34 42 2006 34 84 Source www infoplease com a Find a quadratic model for the data set b Find a cubic model for the data set c Find a quartic model for the data set d Compare the models and determine which one is more appropriate Explain your choice

X 1 900 2 35 3 500 4 300 EX X X deviation Remember to use commas and round numbers to the nearest tenth X X X X 466 2 398 8 66 2 2 133 8 159 041 4 10 X X 398 668 6 The mean is The variance is 99 667 2 The standard deviation is n

1 The following table represents the Statisti test scores from your class Find the value for all measures of center Round your answer to the nearest tenth if necessary 100 100 Statistics Unit Test Scores 100 96 Mean Median Mode CO

Determine the 95 confidence interval for the difference of the sample means Then complete the statements The 95 confidence interval is The value of the sample mean difference is 1 74 which falls interval to the 95 confidence

What is wrong the following conclusion All students in North Carolina should take an online SAT course in order to help improve their score This conclusion came from students at Mathville High school All students at Mathville High school in North Carolina took an online SAT prep course Their average increase in test scores after the course was 200 points The conclusion cannot be trusted since offical scientists did not administer the online course The conclusion should have been made for the entire United States not just the students in North Carolina Their scores did not improve enough to say there was a difference The sample was not a simple random sample

Use the given minimum and maximum data entries and the number of classes to find the class width the lower class limits and the upper class limit minimum 20 maximum 131 8 classes The class width is Type a whole number

A table below displays the mathematics achievement test scores for a random sample of n 10 college freshmen along with their final calculus grades And we assume there exists a linear relationship betwe he mathematics achievement test scores and calculus grades Please find the least squares prediction lin For the calculus grade data and interpret your result x 65 39 1521 78 43 1849 52 21 441 82 64 4096 92 57 3249 89 2209 784 5625 1156 2704 Yi 73 98 X 72535 47 28 56 75 Sum 760 460 23 634 34 y 4225 6084 2704 6724 5244 8464 4183 7921 2044 5329 7350 9604 Xiyi 2535 3354 1092 5248 1904 3136 3900 5625 36 854 59 816

Matt and Linda each start the year with 15 vacation days The table below shows how many vacation days each of them had left at the end of each quarter Jan Mar Apr June July Sept Oct Dec 13 11 7 4 11 7 0 Matt Linda 12 Which statement is true OA The mean number of vacation days Matt has remaining is greater than the mean number of vacation days Linda has remaining OB The median number of vacation days Matt has remaining is less than the median number of vacation days Linda has remaining OC Both the mean and the median number of vacation days Matt has remaining are greater than the mean and the median number of vacation days Linda has remaining The median number of uncation da Inde OD

You want to obtain a sample to estimac population mean. Based on previous evidence, you believe the population standard deviation is approximately o = 29.4. You would like to be 90% confident that your estimate is within 3 of the true population mean. How large of a sample size is required? n = Do not round mid-calculation. However, you are encouraged to use a critical value accurate to three decimal places - this is important for the system to be able to give hints for incorrect answers.

Adelaide wants to buy a new generator. The generator costs $2750. Adelaide decides to finance the generator for 36 months at an APR of 11.5%. Determine Adelaide's monthly payment. Round your answer to the nearest cent, if necessary.

The intelligence of the clones of Jango Fett are deteriorating at a rate that has a standard distribution. If the average I.Q of a clone is 90 with a standard diviation of 2.6, what percent of the clones are smarter than a clone with an I.Q of 85? (round to the nearest hundredth.) % are smarter than a clone with an I.Q of 85.

The power of Darth Vader using the force can lift a speeder 14m off the ground with a thought. The average Sith can lift a speeder 10 meters with a standard deviation of 1.2. This data fits a standard distribution. What is Vader's z-score? (Round to the nearest 10th.) Z= type your answer...

Suppose the supply and demand for a certain DVD are given by p=1/6 q2 and p = -1/6q2+44, respectively, where p is price and q is quantity. Find the equilibrium price. A. $26 B. The supply and demand curves do not intersect. C. $24 D. $21 E. $22

Find the mean of the following data set. Assume the data set is a sample. Round your answer to the nearest hundredth, if necessary. 22, 29, 30, 35, 18, 30, 31, 24, 28, 25, 25

Each voter in a county is given a number that uniquely identifies them. A computer is used to select 500 of these numbers at random. The 500 voters identified by the computer are interviewed for a study. Which type of sampling was used? systematic random cluster convenience

One year Alex had the lowest ERA (earned-run average, mean number of runs yielded per nine innings pitched) of any male pitcher at his school, with an ERA of 3.29. Also, Sally had the lowest ERA of any female pitcher at the school with an ERA of 2.68. For the males, the mean ERA was 4.047 and the standard deviation was 0.993. For the females, the mean ERA was 4.397 and the standard deviation was 0.626. Find their respective z-scores. Which player had the better year relative to their peers, Alex or Sally? (Note: In general, the lower the ERA, the better the pitcher.)