Statistics Questions and Answers

You were running a trial and measured lots of supporting data in case something affected the results for the trial You find a couple of unexpected correlations in this supporting data What should you do with these correlations Select all that apply Ignore them they are probably just a side effect of measuring so many things Report them but make it clear that they are probably a side effect of measuring so many things Do more research on those correlations to confirm or deny them Report them as interesting but separately from your main results Report them as confirmed with your main results

Which acts are evidence of confirmation bias Select all that apply only recording evidence that confirms your expectations ignoring evidence that defies your expectations conducting experiments that you know will not contradict your expectations planning a study that might show statistical evidence of a relationship you think exists assigning subjects to study groups in such a way that your expectation is more likely to be confirmec

You want to study the migration patterns of Canadian geese so you radio tag some geese that you catch in your local marsh Which kind of selective reporting are you doing O not reporting data about all the subjects in the sample Obad sampling O not reporting all the variables measured comparing things that are not comparable

Which of the following would be done with the two sample t test O comparing how many hours men vs women sleep O comparing pass fail rates of men vs women O defining an interval describing how long men and women sleep O defining an interval for how long it takes to complete a task

Which of the following would be measured with parametric statistics Select all that apply human height number of fish in a lake whether students pass or fail depending on whether they studied more or less than two hours per day the proportion of people that use a self checkout without error how many radioactive particles are left after a certain time determined by half life gestation time for elephants

A sample of people who completed a 250 mile backpacking trip gives values of 20 0 21 3 22 5 22 2 23 1 24 7 and 12 5 days for the time required to complete the trip Which of the following is the most appropriate single value to represent the typical time needed to complete this trip 22 2 20 9 20 5 22 3

Which of the following would be measured with non parametric statistics Select all that apply weights of toddlers number of bears in a sector in Yellowstone customer satisfaction measured on a scale of 1 5 the proportion of people who score blue on a color personality profile life expectancy of fruit flies

Which of the following is the correct kind of point estimate for data of 1 2 2 3 9 and why Take the mean due to the small sample size and small spread Take the geometric mean due to the small sample size and large spread Take the median due to the small sample size and skewness O Take the mean due to the small sample size and large spread

When given a statistic like four out of five dentists recommend this toothpaste you should Take it as truth Read the fine print O Go buy the toothpaste right away Call your dentist to see if he recommends it

What are reasons a statistic could be misleading Select all that apply it came from a simple random sample all the information from the sample is given the survey had loaded questions it came from a convenience sample some data was left out of the calculation by accident

Why is the following graph misleading Select all that apply Number of singles sold 1995 1996 1997 1998 2018 Glynlyon Inc Ono labels on the y axis the slanted axes Oyears are skipped it is 3D it is a pictograph

Identify why this graph is misleading 7 2 6 9 6 6 6 3 6 Conversion Rate November December 2018 Gynon Inc O the y axis does not start at zero O the months are not in order O the graph is in 2D O it does not add up to 100 As January February

18 734 No high school diploma 27 915 High school diploma 51 206 Bachelor s degree 74 602 Advanced degree 2018 Glynyon Inc Othere are no labels Othere are no axes one dimensional data given in three dimensions

Examine the graph below and give reasons as to why it is misleading Select all that app BETWEEN 2007 AND 2014 MORE STUDENTS EARNED THEIR HIGH SCHOOL DIPLOMAS THAN EVER BEFORE HIGH SCHOOL GRADUATION RATE 75 2007 08 75 78 2018 Gynyon Inc the scale does not start at zero years are skipped each book equals 15 79 80 2008 09 2009 10 2010 11 2011 12 2012 13 Data Source U S Department of Education National Center for Education Statistics 81 each book value is not the same same this shows the drastic difference from 75 to 82 this makes it seem like a drastic difference from 75 to 82 82 2013 14

What is misleading about this graph Number of hurricanes 2109 11 9886 5 4 3 2 TO 1 0 Misleading Bar Graph Hurricanes Increasing in the 1990s 2 1992 1994 1995 1997 1999 2000 2018 Glynyon Inc O The y axis does not start at zero O The graph is skewed left The bars are not the same color Years

The stem and leaf display below gives sample air fares from St Louis to two cities Salt Lake City and Cincinnati There were 20 air fares recorded for the Salt Lake City route and 19 recorded for the Cincinnati route Use the display to answer the questions that follow Air fares dollars from St Louis Salt Lake City 97 20 4 8 8 210 21 01158 985110 22 3 4 5 7 87651 23 022 378 8 610 24 1 Key 207 7 20 4 204 Cincinnati a What were the ranges of air fares for the two routes Salt Lake City Cincinnati 0 0 b Which route had the higher median air fare OSalt Lake City OCincinnati The medians were the same c Which route had more air fares from 240 to 249 Cincinnati OEach had the same OSalt Lake City X

Eye color is determined by your genes You took two random samples of people in your town In one sample 15 out of 30 had brown eyes In your second sample 12 out of 30 had brown eyes Find the calculated z score used to compare proportions and interpret it Use a confidence level of 95 For your convenience the formula is z P1 P p 1 P Confidence Level 90 95 99 5 2 5 0 5 Critical z score 1 645 1 96 2 576 The calculated z score is 0 78 which is not greater than the critical value of 1 645 so we fail to reject the null hypothesis The calculated z score is 0 78 which is not greater than the critical value of 1 645 so we reject the null hypothesis The calculated z score is 0 78 which is not greater than the critical value of 1 96 so we fail to reject the null hypothesis The calculated z score is 0 78 which is not greater than the critical value of 1 96 so we reject the null hypothesis

The color of your eyes is determined by your genes Eight percent of the world s people have blue eyes This inspires you to do your own sampling You find that 10 of the 30 people in your English class have blue eyes while 8 out of the 32 people in your math class have blue eyes Which statement below is correct Select all that apply You cannot use a z test to compare proportions since your samples are not random The two classes do have a statistically significant difference in their proportions at the 99 confidence level The two classes do not have a statistically significant difference in their proportions at the 99 confidence level The students have a greater proportion of blue eyes than the general population The students have a lower proportion of blue eyes than the general population You can use a z test to compare proportions since your samples are random

Select the terms that best complete the statement All the students in a school district take the same standardized test in Grade 11 The average score is 79 4 with a standard deviation of 14 3 If 55 students from the district are sampled the mean of the sampling distribution is and the standard deviation of the sampling distribution is

A tutoring center advertised it could raise a student s college entrance exam score by 10 points A random sample of 50 students had a mean increase of 8 points with a standard deviation of 5 points Using the table below find the 99 confidence interval O 6 18 to 9 82 O 6 84 to 9 16 6 614 to 9 39 6 20 to 9 84 Confidence Level as a percent 90 95 99 z value 1 645 1 960 2 576

A state s public health department randomly contacted 30 hospitals in the state to find the number of cases of flu reported in the previous week The mean was 83 and the standard deviation was 24 They then randomly contacted 60 hospitals in the state and found the same mean and standard deviation The 90 confidence interval for the sample size of 30 is The 90 confidence interval for a sample size of 60 is m When n Confidence Level as a percent 90 95 99 When n 30 75 79 to 90 21 When n 60 77 90 to 88 10 When n 30 74 41 to 91 59 When n 60 73 93 to 89 07 30 77 90 to 88 10 When n 60 75 79 to 90 21 When n 30 73 93 to 89 07 When n 60 74 41 to 91 59 z value 1 645 1 960 2 576

The sandwich chain was embarrassed to find out that the mean length of a foot long sandwich is less than a foot They made some changes and asked you to repeat your study with a random sample of 40 sandwiches The mean for this The 99 new random sample is 12 08 with a standard deviation of 0 2 The 95 confidence interval is confidence interval is Confidence Level as a percent 95 interval is 12 02 to 12 14 99 interval is 12 00 to 12 16 O95 interval is 12 00 to 12 16 99 interval is 12 02 to 12 14 O95 interval is 12 03 to 12 13 99 interval is 12 00 to 12 16 95 interval is 12 02 to 12 14 99 interval is 12 03 to 12 13 90 95 99 z value 1 645 1 960 2 576

A grocery sold hamburger in one pound packages An inspector weighed thirty five packages and found a mean of 1 84 pounds with a standard deviation of 0 03 pounds Using the table below find the 90 confidence interval 01 032 to 1 048 O 1 030 to 1 050 O 1 027 to 1 053 1 350 to 1 052 Confidence Level as a percent 90 95 99 z value 1 645 1 960 2 576

An inspector tested the weights of one pound packages of hamburger twice Each time 40 random packages were tested The mean was 1 08 for both samples but the first sample had a standard deviation of 0 2 and the second sample had a standard deviation of 0 5 The inspector found the 95 confidence level for both samples The first sample with a standard deviation of 0 2 had a confidence interval of The second sample with a standard deviation of 0 5 had a confidence interval of Confidence Level as a percent C First sample 1 03 to 1 13 Second sample 0 95 to 1 21 O First sample 0 95 to 1 21 Second sample 1 03 to 1 13 O First sample 1 018 to 1 14 Second sample 0 925 to 1 24 O First sample 0 925 to 1 23 Second sample 1 018 to 1 14 90 95 99 z value 1 645 1 960 2 576

A sandwich chain advertises that it has foot long sandwiches Wanting to know if this advertisement is accurate you measured a random sample of forty sandwiches and found the mean length as 11 9 inches and the standard deviation is 0 4 inches Using the table below find the 95 confidence interval 11 78 to 12 02 11 80 to 12 00 11 74 to 12 06 E Confidence Level as a percent 90 95 99 valuez 1 645 1 960 2 576

When you increase the confidence level from 90 to 95 the width of the margin of error increases O decreases O remains the same might increase or decrease

When you increase the sample size the confidence interval increases decreases O remains the same Omight increase or decrease

Your parents bought you a used car for your seventeenth birthday and you want to know how many miles to a gallon the car gets You kept records for the miles you drove each time you filled up the tank with gas For the first forty tanks of gas you had a mean of 29 5 miles per gallon with a standard deviation of 4 9 Using the table below find the 90 confidence interval 28 23 to 30 77 O27 981 to 31 02 O27 50 to 31 50 Confidence Level as a percent G 90 95 99 z value 1 645 1 960 2 576

A confidence interval of 90 means that 90 of the time the true value is in the interval O you can be confident that 90 of sample data is within this interval of an infinite number of samples taken with the same n 90 will have means that fall within the inte there is a 90 chance that the mean is in the interval

If you want to reduce the size of a 95 confidence interval found from a sample of one hundred pieces by a factor of five how many pieces need to be in the new sample 500 2 500 1 000 20

Under which circumstances should you report a confidence interval Select all that apply how much grain was harvested from a farm field a student newspaper poll with a sample of ten students a student council election measuring the length of every fish you catch testing the battery life of a sample of a certain kind of smartphone

What does it mean if a confidence interval is nearly as large as the range of possible values for a measurement The sample size is too small and needs to be increased You are always going to be right You need new measuring equipment The sample size is too large and needs to be decreased

A fish farmer selects a sample of fish from one of the ponds in which all of the tilapia were spawned at the same time If the sample mean length is 6 2 inches with a population standard deviation of 0 91 inches what are the 90 confidence intervals for the true mean with sample sizes of 16 and 64 Confidence Interval 80 O 5 8 6 6 and 6 0 6 4 O 5 7 6 7 and 6 1 6 3 O 5 9 6 5 and 5 9 6 5 5 75 6 65 and 5 95 6 45 85 90 95 1 282 1 440 1 645 1 960 z value 95 4 2 99 99 5 99 7 99 9 3 2 576 2 807 3 291

If you want to reduce a confidence interval to half of its former size how much larger does the sample need to be Otwice as large O four times as large O ten times as large O one hundred times as large

Which of the following are situations where you need to be confident that your sample represents the whole population the results from election day Opolling prior to an election when a recipient selects a part at random from every pallet they receive to check that it meets specifications when you measure every part that comes off of an assembly line when a recipient selects a a pallet at random out of every one hundred received and measures all of the parts on it measuring a fish after you caught it W

Which of the following are good uses of statistical methods Select all that apply understanding measurements better communicating your results precisely confusing your audience Omanipulating your data understanding what your measurements do not mean

A report from a drug company states that the confidence interval of the amount in milligrams of active ingredient in one of their pills is 59 934 60 046 that they tested a sample of ten thousand pills and that the mean and standard deviation of the active ingredient were found to be 59 99 mg and 1 997 mg respectively The report did not mention the confidence level What is it W O 99 5 O 99 O 99 7 99 9 85 90 95 1 282 1 440 1 645 1 960 Confidence Interval 80 z value 99 5 99 7 99 9 2 576 2 807 3 3 291 95 4 99 2

What is the 90 confidence interval for the weight of house cats if a sample of one hundred house cats had an averag weight of eleven pounds and the population standard deviation is two pounds O 0 2 lb O 0 329 lb O 10 8 lb 11 2 lb Confidence Interval 80 10 671 lb 11 329 lb z value 90 85 1 282 1 440 1 645 1 960 95 95 4 99 99 5 99 7 99 9 2 2 576 2 807 3 3 291

500 000 pie chart represents how Harriet spent her Lottery winnings of Examine this graph and then answer the questions on the next page Gifts 10 Savings 20 Unused 30 a In dollars how much did Harriet spend on a new home Harriet s Big Win New Home 40 ii Unused Answer New Home Savings Answer Gifts b How much more in dollars was her unused amount compared to the amount saved 5 marks Unused c Use your protractor to determine as accurately as possible the number of degrees of the pie that are used to represent i Savings laulote the number of degrees each slice of the pie

A company has many salespersons working in many sales regions The volume of sales generated by each person was calculated for the first day in September The standard deviation of the western sales staff was 83 The standard deviation for the eastern sales staff was 64 A sample of 25 eastern staff had a mean of 550 A sample of 30 western was 590 What is the probability of observing these sample means if the population means are the same O 0 0488 O 0 0244 0 1970

A company offers all its employees a physical each year The blood cholesterol level for men aged 30 to 39 has a standard deviation of 12 mg dL For women in the same age group the standard deviation is 24 mg dL A sample of 20 men aged 30 to 39 had a mean cholesterol level of 204 mg dL A sample of 28 women aged 30 to 39 had a mean cholesterol level of 210 mg dL What is the probability of observing these sample means if the population means are the same O 0 2542 00 1271 01 14 0114

7 Jim spends his weekly income as follows food 200 outstanding loan payments 10 transportation 50 rent 125 and miscellaneous items 25 You are asked to construct a circle graph that reflects this data a Please calculate then list the number of degrees of the circle that will be used to represent each item Food Loan Payments Transportation Rent Miscellaneous items 5 marks b Construct a circle granh that clearly demonstrates this data

A company offers its employees a free physical each year The blood cholesterol level for women aged 30 to 39 has a standard deviation is 38 mg dL The blood cholesterol level for men aged 30 to 39 has a standard deviation of 29 mg dL Before the samples were taken the company chose an alpha of 0 05 A sample of 45 women aged 30 to 39 had a mean cholesterol level of 224 mg dL A sample of 32 men aged 30 to 39 had a mean cholesterol level of 210 mg dL Find the probability of observing these sample means if the population means are the same If your alpha is 0 05 wha will you conclude O Fail to reject the null hypothesis which states that the population means are equal O Reject the null hypothesis which states that the population means are equal O You do not know enough to accept or reject the null hypothesis In this situation an ethical researcher will change the alpha so that the null hypothesis can be rejected

When testing for a difference between two population means using a z test you obtain a z score of 2 15 What is the total area under the two tails on a normal curve 0 0316 O2 1500 0 0158

The following data give the total rebounds per game x and points per game y for a random sample of 11 professional basketball players 9 8 7 Create a scatterplot for the data 11 10 y 6 5 4 3 2 1 Clear All Draw x y 10 1 4 2 T 0 2 X 1 2 3 4 5 6 7 8 9 10 11 8 5 79 Determine the least squares regression line for the data Round values to four decimal places if necessary 3 9 6 3 4 7 6 8 3 5 29 Determine the correlation coefficent Round the solution to four decimal places if necessary Use the model to predict the points scored in a game by a professional basketball player who achieves 3 rebounds in a game Round the solution to the nearest whole number

You have two samples Sample 1 has 200 African American people and Sample 2 has 300 Hispanic people Sample 1 has 104 individuals with type O and Sample 2 has 180 individuals with type O Find the calculated z score used to compare proportions and interpret it Use a confidence level of 95 PP For your convenience the formula is z p 1 P Confidence Level Critical z score 90 95 99 5 2 5 0 5 1 645 1 96 2 576 The calculated z score is 1 77 which is not less than the critical value of 1 96 so we fail to reject the null hypothesis The calculated z score is 1 77 which is not less than the critical value of 1 96 so we reject the null hypothesis The calculated z score is 1 77 which is not greater than the critical value of 1 96 so we fail to reject the null hypothesis The calculated z score is 1 77 which is not greater than the critical value of 1 96 so we reject the null hypothesis

You performed a simulation to examine mutation proportions You put fifty candies in each of two bags You hit both bags with a book to simulate a genetic mutation occurring The first bag had five broken candies and the second bag had ten broken candies Which statement is correct O Your sample size was too small to use the z test to compare proportions The proportions of candies in the bags were not statistically significantly different at the 90 confidence level O The proportions of candies in the bags were statistically significantly different at the 90 confidence level The proportions of candies in the bag could not be determined

Let z represent the calculated z score If your critical z score is 1 96 when do you reject the null hypothesis for a two tailed test When z 1 96 When z 1 96 O When z 1 96 or z 1 96 When z 1 96 or z 1 96

What critical value would you use when you want a 95 confidence level on a two tailed test Confidence Level 2 a Critical z score 5 1 645 1 96 O2 576 2 354 90 95 99 2 5 0 5 45 1 645 1 96 2 576

The data shown below is collected from a sample 8 5 8 9 8 8 9 1 8 2 8 0 9 0 8 6 8 4 8 3 8 2 To determine how much the sample mean differs from the population mean of 8 5 a student calculates the t value The student incorrectly calculates the t value using the steps shown below Step 1 7 8 5 8 9 8 8 9 1 8 2 8 0 9 0 8 6 8 4 8 3 8 2 11 Step 2 S2 1 327273 0 1327273 Step 3 t 8 5455 8 5 1 08 0 1327273 Step 3 t In which step did the student make the first error and what is the correct expression for it O Step 2 S 1 327273 0 12067 O Step 2 S 1 327273 0 1327273 Step 3 t 8 5455 85 0 41 0 137722 11 8 5455 8 5 0 1327273 F 8 5455 1 14