Statistics Questions and Answers

A commonly cited standard for one way length duration of school bus rides for elementary school children is 28 minutes A local government office in a rural area randomly samples 100 elementary school children in their district and find an average one way commute time of 40 minutes with a standard deviation of 12 minutes Which of the following is the correct set of hypotheses for testing if the average commute time of elementary school students in this district is different than the commonly cited standard of 28 minutes OHA H 28 Ho x 28 O Ho x 40 HA 28 O Ho 28 HA x 40 O Ho H 28 HA 28 O Ho H 28 HA 28

Suppose the results indicate that the null hypothesis should be rejected thus it is possible that a type I error has been committed Given the type of error made in this situation what could researchers do to reduce the risk of this error O Instead of a 05 significance level choose a 01 significance level O Increase the sample size

Less than 33 of workers got their job through internet resume sites Express the null and alternative hypotheses in symbolic form for this claim Ho p HA P

Solve the inequality State the solution in interval notation 4 x 3 14 4 5x 5 2x

In an hypothesis test the decision was made to reject the null hypothesis The null hypothesis was later determined to be true What kind of error if any was committed O Type I error O Type II error O No error

A commonly cited standard for one way length duration of commute for an employee is 29 minutes A company samples 200 employees and find an average one way commute time of 38 minutes with a standard deviation of 9 minutes Which of the following is the correct set of hypotheses for testing if the average commute time of an employee of this company is different than the commonly cited standard of 29 minutes O Ho H 29 HA 29 O Ho H 29 HA H 29 O Ho H 29 HA x 38 O Ho x 38 HA 29 29 OHA H 29 Ho x

Solve for z 25z 500 Oz 20 Oz 20 Oz 20 7 20

Solve for y 4 Oy Oy 10 11 160 11 160 40 11

Solve the inequality and write your answer in interval notation 18x 102 1 14x

Use the quadratic formula to solve the equation Be sure to simplify your answers Enter both answers separated by a comma 49x 25 0

Solve 2 3 x 10 8 for x

Solve the proportion 31 11 16 x Round to two decimal places if necessary

8 FRQ A manufacturer makes and packages pencils The mean weight of an individual pencil is 16 g with a standard deviation of 1 g The weights of pencils are approximately Normally distributed a If one pencil is randomly selected what is the probability that it weighs less than 15 4 grams 1 5 pt b Pencils are grouped in to sets of 8 for later packaging What is the mean and standard deviation of the weight o one set of 8 pencils Assume that the weights of pencils are independent 2 pt 2 poncile will b 2 2 points

You measure 46 turtles weights and find they have a mean weight of 41 ounces Assume the population standard deviation is 10 7 ounces Based on this construct a 99 confidence interval for the true population mean turtle weight Note you will use the z distribution for your critical value since the population standard deviation is given Write your answer in the form of point estimate margin of error Give your answers as decimals to two places 1 ounces Write your answer using inequality notation

The city wishes to estimate the average commute distance for all city employees They collect a random sample of 79 employees and find a sample mean of 7 3 miles They also assume a population standard deviation of o 1 8 miles Calculate the z interval to estimate u the average commute distance for all city employees with 95 confidence Round your answers to 2 decimal places Find the Critical Value z Point Estimate Margin of Error Write the interval as lower bound upper bound

Solve the compound inequality and give your answer in interval notation 8x123 AND 2x 8 2

Express the confidence interval 34 6 7 8 in interval form

Solve the compound inequality and give your answer in interval nota 1x 6 2x9 AND 2 4x4 2 8x 86

Solve the inequality and write your answer in interval notation 20x4 1 11x

Solve for z 12z 216 18 18 Oz Oz O z 18

What changes the width of a confidence interval A marketing director wants a 95 confidence interval for the mean cost of running shoes She randomly samples 40 pairs of shoes and finds that the sample mean was 122 with a sample standard deviation s of 27 The marketing director concluded with 95 confidence that between 113 36 and 130 64 contains the mean cost of all running shoes What would change for a wider confidence interval Select all answers that will make the width wider If the point estimate was larger If the sample size decreased to 30 pairs of shoes If the point estimate was smaller If she increased the confidence level to a 99 confidence level If the sample standard deviation was smaller If she decreased the confidence level to a 90 confidence interval If the sample standard deviation was larger If the sample size increased to 50 pairs of shoes

A confidence interval for the population mean number of jobs a person has before the age of forty was found to be 8 1 to 10 5 Find the midpoint of this confidence interval

All else equal an increase in sample size will cause a n decrease increase O in the size of a confidence interval

Which of the following would result in the widest confidence interval OA sample size of 100 with 95 confidence OA sample size of 30 with 95 confidence OA sample size of 30 with 99 confidence OA sample size of 100 with 99 confidence

In a survey funded by the UW school of medicine 750 of 1000 adult Seattle residents said they did not believe they could come down with a sexually transmitted infection STI Construct a 95 confidence interval estimage of the proportion of adult Seattle residents who don t believe they can contract an STI Use a z score of 1 96 for your computations O 728 772 O 723 777 O 718 782 O 713 878 O 665 835

We wish to estimate what percent of adult residents in a certain county are parents Out of 200 adult residents sampled 130 had kids Based on this construct a 99 confidence interval for the proportion p of adult residents who are parents in this county Give your answers as decimals to three places

A random sample of 75 students at the University of Minnesota spend an average of 614 per month in rent with a standard deviation of 219 The distribution is moderately skewed to the high end Which of the following statements are true i 95 of students at the university spend 564 to 664 on rent ii We are 95 confident that the average rent for students at the university is between 564 and 664 iii Because we cannot examine other characteristics of the students in the random sample it is not advisable to construct a confidence interval Oi only O ii only O iii only Oi and ii O i ii and iii

Express the confidence interval 81 4 in interval form Express the answer in decimal format do not enter as percents Question Help Video Post to forum

Calculate x bar for the data shown to two decimal places X 17 2 2 2 7 4 27 1 9 1 14 9 25 5

Express the confidence interval 83 6 6 3 in interval form Express the answer in decimal format do not enter as percents

A student took six exams in a course last semester The scores are shown below 71 87 94 74 94 74 Calculate the mean variance and standard deviation Round to 4 decimal places when needed and use rounded answers for future calculations The mean is The variance is The standard deviation is o

Calculate x bar for the data shown to two decimal places X 18 1 15 1 6 4 10 2 26 6 9 16 7

Determine whether the value 74 4 is a parameter or statistic In a weight loss research study a sample of 130 adults 74 4 lost an average of 10 or more pounds O Parameter O Statistic

Find the width between the interval 5 3

Determine whether the value 41 is a parameter or statistic 41 of a State College A s students are from that state O Parameter O Statistic

Find the width between the interval 10 5

Find the midpoint between the interval 14 16

Run a regression analysis on the following bivariate set of data with y as the response variable X y 45 4 28 3 38 7 30 4 51 3 26 1 48 2 28 9 47 3 29 2 50 7 28 4 41 7 29 6 51 1 28 9 47 2 28 1 44 2 29 40 9 29 3 42 29 3 Find the correlation coefficient and report it accurate to three decimal places r What proportion of the variation in y can be explained by the variation in the values of x Report answer as a percentage accurate to one decimal place If the answer is 0 84471 then it would be 84 5 you would enter 84 5 without the percent symbol Based on the data calculate the regression line each value to three decimal places y X Predict what value on average for the response variable will be obtained from a value of 39 5 as the explanatory variable Use a significance level of a 0 05 to assess the strength of the linear correlation predicted response value Report answer accurate to one decimal place

1 During his NBA career Larry Bird made approximately 89 of all free throws Suppose Larry makes 10 free throws in a row What is the probability he will make the next free throw a 0 11 b 0 50 c 0 01 d 0 89

Brightness Level x Hours y 10 9 8 7 6 Hours 54 3 2 7 10 20 30 37 39 5 3 30 42 4 1 6 3 6 8 5 9 43 85 55 b Interpret the slope in context 4 5 hours 89 3 2 40 50 60 70 80 90 100 11 Brightness Level 1 a Find the equation for the line of best fit Keep at least 4 decimals for each parameter in the equation I Ashton should expect 0 0439 hours per brightness level Ashton should expect 0 0439 brightness level per hour 92 2 4 c What does the equation predict for the number of hours the phone will last at a brightness lev of 42

Which of the following is false If the correlation between two variables is close to 0 01 then there is a very weak linear relation between them If the correlation coefficient is 1 then the slope must be 1 as well O Correlation coefficient and the slope always have the same sign positive or negative Correlation measures the strength of linear association between two numerical variables

Mountain climbers use a general rule of thumb which estimates that the temperature will drop 3 degrees Fahrenheit for every 1000 ft of elevation The varible T is the temperature and E is the elevation in feet Which of the following best describes the dependent variable in this model Select an answer Which of the following best describes the independent variable in this model Select an answer

A researcher wishes to examine the relationship between years of schooling completed and the number of pregnancies in young women Her research discovers a linear relationship and the least squares line is y 3 2x where x is the number of years of schooling completed and y is the number of pregnancies The slope of the regression line can be interpreted in the following way When amount of schooling increases by one year the number of pregnancies increases by 3 When amount of schooling increases by one year the number of pregnancies decreases by 3 When amount of schooling increases by one year the number of pregnancies decreases by 2 When amount of schooling increases by one year the number of pregnancies increases by 2

Here is a scatter plot for a set of bivariate data What would you estimate the correlation coefficient to be 0 9 0 6 0 0 6 0 9

Please round all answers to 2 decimal places Given the table below use your calculator to find the Line of Best Fit x Y 8 9 1 23 6 7 1 4 7 13 7 1 5 5 7 1 1 8 7 1 15 18 8 7 7

Which of the following lines would be the best fit for the data points plotted in the scatter plot below Oy 0 7x 7 2 Oy 7 2x 0 7 Oy 7 2x 0 7 Oy 0 7x 7 2

Use linear regression to find the equation for the line that best fits this data Round both numbers to tw mx b decimal places Write your final answer in a form of an equation y X y 1 2 3 68 83 94 4 112 5 124 6 138

researcher wishes to examine the relationship between years of schooling completed and the number of regnancies in young women Her research discovers a linear relationship and the least squares line is 3 2x where x is the number of years of schooling completed and y is the number of pregnancies The slope of the regression line can be interpreted in the following way When amount of schooling increases by one year the number of pregnancies increases by 3 When amount of schooling increases by one year the number of pregnancies decreases by 3 When amount of schooling increases by one year the number of pregnancies decreases by 2 When amount of schooling increases by one year the number of pregnancies increases by 2

Mountain climbers use a general rule of thumb which estimates that the temperature will drop 3 5 degre Fahrenheit for every 1000 ft of elevation The varible T is the temperature and E is the elevation in feet Which of the following best describes the dependent variable in this model Select an answer Which of the following best describes the independent variable in this model

This bar graph shows the stopping distance in feet for a car traveling at different speeds 800 700 600 500 400 300 200 Distance ft 100 0 40 50 60 70 80 90 100 ft sec ft sec ft sec ft sec ft sec ft sec ft sec Speed Approximately how many feet would it take a car traveling at 60 ft sec to stop feet