Statistics Questions

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

Evaluate the following linear equation for the given values X 4 1 L 3 y 4x 5

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

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

Use the quadratic formula to solve the equation Be sure to simplify your answers Enter both answers separated by a comma 16x 4 0

2x 5 x 1 r

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

Consider the following probability model associated with the number of raffle tickets purchased by each customer a 0 15 b 0 25 c 0 35 d 0 20 OC OD O A

Suppose 70 of all adults drink coffee If you were to conduct a simulation involving coffee drinkers and non coffee drinkers which of the following is a valid assignment of digits to represent coffee drinkers a 0 1 2 coffee drinker 3 4 5 6 7 8 9 not a coffee drinker b 0 1 2 3 coffee drinker 4 5 6 7 8 9 not a coffee drinker c 0 1 2 3 4 coffee drinker 5 6 7 8 9 not a coffee drinker d 0 1 2 3 4 5 6 coffee drinker 7 8 9 not a coffee drinker OC OB

You play tennis regularly with a friend and from past experience you believe that the outcome of each match is independent For any given match you have a probability of 0 6 of winning The probability that you lose the next two matches is a 0 16 b 0 40 c 0 64 d 0 36 OB OA C

A statistics teacher states the probability of a surprise quiz on any given day is 0 30 If quizzes are given independently each day what is the probability there will be a surprise quiz on the next two consecutive days a 0 09 b 0 21 c 0 42 d 0 60 O A OB

A statistics teacher states the probability of a surprise quiz on any given day is 0 30 If quizzes are given independently each day what is the probability there will be a surprise quiz on the next two consecutive days a 0 09 b 0 21 c 0 42 d 0 60 O A OB

Which of the following statements is alse a All possible outcomes together must have probabilities that add up to 1 b An event is random if individual outcomes are uncertain c The probability of any outcome must be a number between 0 and 1 d A probability can be a number greater than 1 OA OD

Which of the following statements is alse a All possible outcomes together must have probabilities that add up to 1 b An event is random if individual outcomes are uncertain c The probability of any outcome must be a number between 0 and 1 d A probability can be a number greater than 1 OA OD

Select the correct answer for each question s The test pages are attached below for your review All questions may not be listed Chapter 4 Test first 2 pages pdf D Question 1 2 A statistics teacher states the probability of a surprise quiz on any given day is 0 30 If quizzes are gir Independently of the day what is the probability there will be a surprise quiz on the next two consecutive days a 0 09 b 0 21 c 0 42 d 0 60 OA OD

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 for g 14g 2 280 20 20 Og Og Og 20 20

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 the inequality and write your answer in interval notation 20x3 17 2x

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

A student was asked to find a 95 confidence interval for widget width using data from a random sample of size n 29 Which of the following is a correct interpretation of the interval 10 5 p 23 7 Check all that are correct There is a 95 chance that the mean of a sample of 29 widgets will be between 10 5 and 23 7 There is a 95 chance that the mean of the population is between 10 5 and 23 7 With 95 confidence the mean width of all widgets is between 10 5 and 23 7 With 95 confidence the mean width of a randomly selected widget will be between 10 5 and 23 7 The mean width of all widgets is between 10 5 and 23 7 95 of the time We know this is true because the mean of our sample is between 10 5 and 23 7

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