Statistics Questions

Use the following scenario for questions 1 4 Suppose it is estimated that 14 of American women are currently on a diet A researcher would like to test this claim so he sets up a simple random survey He asks 200 women if they are on a diet and 39 said yes Conduct a one proportion test to determine if the percent of women on diets is not 14

7 When Liam commutes to work the amount of time it takes him to arrive is normally distributed with a mean of 55 minutes and a standard deviation of 4 5 minutes a What percentage of times does it take him LESS THAN 60 minutes to get to work 60 55 86 43 2 4 5 578 8643 1 11 b What percentage of times does it take him BETWEEN 46 and 46 55 4 5 2 86 43 2 28 84 15 d What times mark the middle 80 of the commute times e 505 55 59 5 64 68 5 02 28 c Out of the 207 days that Liam commutes to work per year how many times would his commute be between 46 and 60 minutes to the nearest whole number 0 5 207 8415 174 times 10 1 29 x 5S 4 5 4 5 4 5 49 15 60 805 0 5 TOO 80 20 2 10 100 10 90 2 9 5565 1 55 10 5 805 FSS 5 60 805 40 29 x 55 4 5 49 195 4 5 5

Question 4 The diameters of screws in a batch are normally distributed with mean equal to 2 10 cm and standard deviation equal to 0 15 cm I a What proportion of screws are expected to have diameters greater than 2 50 cm 10 P b A specification calls for screw diameters between 1 75 cm and 2 50 cm What proportion of screws will meet the specification 15 P

Question 3 In a plant manufacturing light bulb 3 of the production is known to be defective under normal conditions A sample of 100 bulbs is drawn at random Assume defective bulbs occur randomly and independently a Find the probability that the sample contains no defective bulbs both using the binomial distribution and using the Poisson distribution 15 P b Find the probability that the sample contains more than 1 defective bulbs both using the binomial distribution and using the normal distribution Compare the results 10 P

Question 1 Scraps of iron were selected based on their densities x and their iron contents y were measured The results were as follows Xi Yi 2 8 2 9 27 23 3 3 1 3 2 30 28 30 3 2 3 2 3 3 3 4 34 33 30 32 a Find the regression line of y on x 10 P b Plot the scatter diagram of the data pair and regression line 10 P c Find the R values 5 P You need to do research on this question

a Define the hypergeometric random variable and explain briefly 10 P b The components of a 6 component system are to be randomly chosen from a thousand of 20 used components The resulting system will be functional if at least 4 of its 6 components are in working condition If 15 of the 20 components in the bin are in working condition what is the probability that the resulting system will be functional Use the hypergeometric random variable 15 P

The table below shows the scores of a group of students on a 10 point quiz Test Score Frequency 3 4 5 6 7 8 9 10 2 3 1 1 4 4 2 5 The mean score on this test is The median score on this toct is

The Real Estate Group NY reports that the mean monthly rent for a one bedroom apartment without a doorman in Manhattan is 2597 Assume the standard deviation is 513 A real estate firm samples 96 apartments What is the probability that the sample mean rent is less than 2 650 41

Give the mode for following GFDT Recall there is a definition for the mode appropriate for GFDTS Data Frequency 50 54 10 55 59 19 60 64 10 65 69 9 70 74 5 75 79 4 80 84 4 85 89 1 90 94 mode 1

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 2 6x3 10 44 AND 1x 4 3x 14 4x

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

Solve the inequality and write your answer in interval notatio 12x 15 24 5x

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 x 24x 432 Ox 18 0x 18 0x 18 Ox 18

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

Choose the most appropriate completion of the sentence In order to indicate a strong correlation between variables the correlation coefficient will be O near 10 O near 1 near 1 2 O near 0 O near 1 or 1 O near 1

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

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

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

The p value for a hypothesis test turns out to be 0 021868 At a 7 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 You find out that np is less than five What must you do to be able to perform a valid hypothesis test O Decrease the sample size so that np is less than five O Increase the sample size so that np is greater than five O Decrease the sample size so that np is greater than five O Increase the sample size so that np is less than five

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