Statistics Questions and Answers

Based on past experience a bank believes that 9 of the people who receive loans will not make payments on time The bank has recently approved 200 loans What are the mean and standard deviation of this model mean standard deviation accurate to 3 decimal places What is the probability that over 10 of these clients will not make timely payments

83 of phone numbers in a certain city are unlisted Express the null and alternative hypotheses in symbolic form for this claim Ho p HA P

In a mid size company the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell shaped and has a mean of 53 and a standard deviation of 11 Using the empirical rule as presented in the book what is the approximate percentage of daily phone calls numbering between 20 and 86 Do not enter the percent symbol ans

GPAS at CCSU are normally distributed with a mean of 2 32 and a standard deviation of 0 53 Find the z score for a GPA of 3 28 00 7170 O 1 340 O 0 5849 O 0 3962 O 0 3019

Solve the compound inequality and give your answer in interval notation 5x2 8 OR 3x 4 5

A manufacturer knows that their items have a lengths that are skewed right with a mean of 12 5 inches and standard deviation of 2 1 inches If 32 items are chosen at random what is the probability that their mean length is greater than 12 6 inches Round answer to four decimal places

Engineers must consider the breadths of human heads when designing helmets The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 6 9 in and a standard deviation of 0 8 in Using the Empirical Rule in what range would you expect to find the middle 98 of most head breadths Between and If you were to draw samples of size 45 from this population in what range would you expect to find the middle 98 of most averages for the breadths of human heads in the sample Between and Enter your answers as numbers Your answers ch L

A certain component is critical to the operation of an electrical system and must be replaced immediately upon failure If the mean life of this type of component is 80 hours and its standard deviation is 28 hours find the minimum number of these components to stock so that the probability that the system is in continual operation for the next 2000 hours is at least 0 95

A manufacturer knows that their items have a normally distributed lifespan with a mean of 13 5 years and standard deviation of 2 4 years If 11 items are picked at random 8 of the time their mean life will be less than how many years Give your answer to one decimal place

Solve the inequality and write your answer in interval notation 10 6x 17x 12

Solve for c 12c 240 Oc 20 Oc 20 Oc 20 Oc 20

Match each scatterplot shown below with one of the four specified correlation coefficients O O O O CO 08 O O O O O a 0 08 b 0 95 c 0 06 d 0 76

If the correlation coefficient is negative this means O there is a strong correlation between the variables Othere is no correlation between the variables O the test statistic t can not be calculated O the slope of the regression line is negative O the regression line can be used for prediction O the calculation was done wrong

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 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 O When amount of schooling increases by one year the number of pregnancies decreases by 3 O When amount of schooling increases by one year the number of pregnancies increases by 3 O When amount of schooling increases by one year the number of pregnancies decreases by 2 O When amount of schooling increases by one year the number of pregnancies increases by 2

The time spent studying for a test and the test scores are graphed below along with the best fit line 100 90 Exam score e points 80 70 60 50 10 e 1 04 t 38 4 20 30 40 Study Time t minutes 50 60 What score does the equation e 1 04t 38 4 predict for a student who studies for 20 minutes Round your answer to the nearest whole number score Select an answer Using subtraction find the vertical distance error between the point 25 59 and the line

Using your favorite statistics software package you generate a scatter plot with a regression equation and correlation coefficient The regression equation is reported as y 26 59x 70 48 and the r 0 325 What proportion of the variation in y can be explained by the variation in the values of x 7 96 Report answer as a percentage accurate to one decimal place

Here is a bivariate data set in which you believe y to be the response variable y X 24 8 75 28 3 42 7 29 9 57 17 40 5 41 7 80 2 17 3 44 6 29 8 75 9 19 2 57 4 33 7 48 8 23 6 42 9 18 3 39 3 43 7 94 3 24 4 38 3 30 7 40 7 Make a scatter plot of this data Which point appears to be an outlier

Suppose that you run a correlation and find the correlation coefficient is 0 281 and the 22 22 The centroid of your data was 6 6 15 5 regression equation is 5 7x If the critical value is 396 use the appropriate method to predict the y value when x is 8 4

ariable X y 49 4 15 6 22 5 53 3 58 2 70 3 49 9 1 9 48 7 31 74 6 83 2 36 6 47 8 41 7 42 2 82 4 88 7 68 9 55 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 sponse 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 56 7 as the explanatory variable Use a significance level of a 0 05 to assess the strength of the linear correlation What is the predicted response value Report answer accurate to one decimal place y

What type of model is the best choice for the data in the scatterplot below O Linear O Non linear

Let represent the profit or loss for a certain company years after 1965 Based on the data shown below a statistician calculates a linear model 2 12x 6 84 X Y 13 83 3 4 14 84 5 15 65 6 20 66 7 22 37 8 24 08 9 26 49 27 1 10 Use the model to estimate the profit in 1969 Round to the nearest cent

You are researching the growth of a species of fish You gather a sample of fish and record the age in weeks of each fish and its mass in grams The data is displayed on the grid below with the blue points Age of fish weeks Mass of fish g 4 100 150 550 12 8 16 550 20 32 36 40 550 1100 750 1050 You construct a linear model for the data and your equation is y 24 69x 81 6 where y is the mass in grams of the fish and is the age in weeks a Use the equation to identify the slope of the linear model Use the units for y and a along with the concept of rise over run to interpret the slope in this context b Use the equation to identify the y intercept of the linear model Use the units for y along with the concept that x 0 at the y intercept to interpret the y intercept in this context

The weight of a newborn animal is given by the formula W in grams and d is the number of days since hatching Which variable causes the other variable to change Select an answer 4d 5 where W is the weight 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 The number of days d is the input or independent variable since it causes the weight to change The weight W is the input or independent variable since it depends on the value of d The number of days d is the input or independent variable since it depends on the the weight W The weight W is the input or independent variable since it causes the value o

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

The weight of a newborn animal is given by the formula W 4d 5 where W is the weight in grams and d is the number of days since hatching Which variable causes the other variable to change Select an answer Which of the following best describes the dependent variable in this model Select an answer We say W is the output or dependent variable since it depends on the value of d We say d is the output or dependent variable since it depends on the weight W We say W is the output or dependent variable since it causes the value of d to change We say d is the output or dependent variable since it causes the height h to change

The following table gives the total number of live Christmas trees sold in millions in the United States from 2004 to 2011 Source Statista com 2 0 27 1 28 6 4 6 7 t number of years since 2004 C total number of Christmas trees sold in the U S in millions 1 Use the TABLE to determine the number of live Christmas trees sold in the year 2008 In 2008 there were approximately million live Christmas trees sold in the U S 2 Determine the linear regression equation that models the set of data above Use the indicated variables and proper function notation Round to the nearest hundredth as needed C 28 2 27 30 8 3 Interpret the meaning of the slope of your rounded regression model From 2004 to 2011 the number of Christmas trees sold in the U S increased by approximately million trees each year 4 Use the REGRESSION EQUATION to determine the number of live Christmas trees sold in the year 2008 In 2008 there were approximately million live Christmas trees sold in the U S 5 Your answers to parts 1 and 4 should be different Why is this the case O The data are linear The regression equation gives a more precise answer than the value from the table O The data are not perfectly linear The regression equation gives a more precise answer than the value from the table O The data are linear The regression equation gives only an approximation of the actual value not the exact value O The data are not perfectly linear The regression equation gives only an approximation of the actual

Please round all answers to 2 decimal places Given the table below use your calculator to find the Line of Best Fit X Y 3 8 4 4 1 2 2 7 12 2 14 1 8 3 9 9 5 6 16 7 8 4 5 2 16 4 22 3

A regression was run to determine if there is a relationship between hours of TV watched per day x and number of situps a person can do y The results of the regression were y ax b a 1 332 b 38 736 Use this to predict the number of situps a person who watches 7 5 hours of TV can do round to one decimal place

In 1991 the moose population in a park was measured to be 4750 By 1996 the population was measured again to be 5150 If the population continues to change linearly Find a formula for the moose population P in terms of t the years since 1990 P t

You are performing a right tailed test with test statistic z 1 344 find the p value accurate to 4 decimal places p value

The weight of a newborn animal is given by the formula W 4d 5 where W is the weight in grams and d is the number of days since hatching Which variable causes the other variable to change Select an answer The weight causes the number of days to change The number of days causes the weight to change

A well known brokerage firm executive claimed that 30 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 500 people 23 of them said they are confident of meeting their goals Test the claim that the proportion of people who are confident is smaller than 30 at the 0 10 significance level The null and alternative hypothesis would be Ho p 0 3 Ho p 0 3 Ho p 0 3 Ho 0 3 Ho p 0 3 Ho 0 3 H p 0 3 H p 0 3 H 0 3 H 0 3 H p 0 3 H 0 3 O O O O O The test is right tailed left tailed two tailed 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

Write an equation for the graph below in terms of a 5 4 3 2 3 2 1 y 1 2 3 A 54 2 ton

Part 1 Evaluate the following linear equation for the given values x 4 3 0 5 y 4x 2 Part 2 Graph the linear equation on the coordinate plane below 5 4 3 2 7 6 5 4 3 2 1 1 2 3 4 S Clear All Draw 1 2 3 4 5 1 6

The Food and Drug Administration FDA is a U S government agency that regulates food and Brugs for consumer safety One thing the FDA regulates is the allowable insect parts in arious foods When wheat is ground into flour insects that were in the wheat are ground up as well The mean number of insect parts allowed in 100 grams about 3 ounces of wheat flour is 75 If the FDA finds more than this number they conduct further tests to determine if the flour is too contaminated by insect parts to be fit for human consumption The FDA takes a random sample of 35 bags of flour for evaluation and finds that they contain an average of 80 insect parts per 100 grams with a standard deviation of 6 3 Which hypothesis test should be used to determine whether the sample contains more than the allowed 75 insect parts per 100 grams Oz test for the population mean O t test for the population mean Oz test for the population proportion Ot test for the population proportion Note First decide if it is a MEAN or a PROPORTION problem We do not use t tests on proportion problems If you decide MEANS remember the Z tests are ONLY USED if they give you a POPULATION STANDARD DEVIATION It may or may not also contain a sample standard deviation as well A If you decide MEANS remember the T Tests are ONLY USED if you ONLY have the SAMPLE STANDARD DEVIATION You will not have prior information deviation

Suppose that a recent article stated that the mean time spent in jail by a first time convicted burglar is 3 2 years A study was then done to see if the mean time has decreased in recent years A random sample of 38 first time convicted burglars was recently selected The mean length of time in jail from the survey was 2 2 years Suppose that it is somehow known that the population standard deviation is 3 years Conduct a hypothesis test at the a significance level to determine if the mean length of jail time has decreased Assume the 0 05 distribution of the jail times is approximately normal Ho Ha Select an answer a P value years years Enter the correct symbol and value round your answer to 4 place values Based on the above we choose to Select an answer Question Help Post to forum Reject the null hypothesis Faill

68 of workers indicate that they are satisfied with their job Express the null and alternative hypotheses in symbolic form for this claim enter as a percentage Ho P H P Use the following codes to enter the following symbols 2enter

the following True or False Suppose a sample size of 87 was used to conduct a right tailed hypothesis test for a single population mean The null hypothesis was Ho 45 and the sample mean was 50 and the p value was 0 03 Then there is a 3 chance that 87 randomly selected individuals from a population with a mean of 45 and the same standard deviation would have a sample mean greater than 50 O false O true

Evaluate the following linear equation for the given values y 3x 4 x 2 1 1

You are performing a right tailed test with test statistic z 0 44 find the p value to 4 decimal places

The p value for a hypothesis test turns out to be 0 06012 At a 4 level of significance what is the proper decision O Reject Ho O Fail to reject Ho

You are performing a hypothesis test of a single population proportion What must be true about the value of the products np and nq O Both np and nq must be less than five O Both np and nq must be greater than five O Only np must be greater than five O There are no restrictions on these products

The IQ test is constructed so that Full Scale IQ scores follow a normal dis mean of 100 and a standard deviation of 15 The dean of a school believes their students are smarter than the national average and wants to use it the intelligence of the students as a marketing tool to bring students to the school A researcher is hired to conduct a study to determine whether the schools students have on average higher Full Scale IQs than the population A random sample of 100 people from the school were given the IQ test and were found to have an average Full Scale IQ of 105 Which hypothesis test should be used to determine whether the mean Full Scale IQ score of the schools students is higher than the national average Oz test for the population proportion O t test for the population mean Ot test for the population proportion Otest for the population mot

The shape of the distribution of the time required to get an oil change at a 10 minute oil change facility is unknown However records indicate that the mean time is 10 5 minutes and the standard deviation is 4 minutes a To compute probabilities regarding the sample mean using the normal model what size sample would be required O Any sample size could be used O The sample size needs to be greater than 30 O The normal model cannot be used if the shape of the distribution is unknown O The sample size needs to be less than 30 b The probability that a random sample of n 46 oil changes results in a sample mean time less than 10 minutes is approximately Round to 4 decimal places c Suppose the manager agrees to pay each employee a 50 bonus if they meet a certain goal On a typical Saturday the oil change facility will perform 45 oil changes between 10 A M and 12 P M Treating this as a random sample at what mean oil change time would there be a 11 chance of being at or below This will be the goal established by the manager There would be a 11 chance of being at or below to the nearest 1 decimal place minutes Round

Food inspectors inspect samples of food products to see if they are safe This can be thought of as a hypothesis test with the following hypotheses Ho the food is safe Ha the food is not safe The following is an example of what type of error The sample suggests that the food is safe but it actually is not safe O type II O type I O not an error

A manufacturer of cell phone batteries markets its batteries as having on average 500 charges A consumer group decides to test this claim by assessing the number of times 30 of their cell phone batteries can be recharged and finds the average is 497 with a standard deviation of 10 The resulting p value is 1111 thus the null hypothesis is not rejected The consumer group concludes that the manufacturer s claim that its cell phone batteries can be recharged on average 500 times is accurate What type of error is possible in this situation O type I O type II O neither O both

An ice cream inspector inspects samples of ice cream to see if they are safe This can be thought of as a hypothesis test with the following hypotheses Ho the ice cream is safe Ha the ice cream is not safe The following is an example of what type of error The sample suggests that the ice cream is safe but it actually is not safe O type I O type II not an error

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