UNIT 3

Based on the histograms, what is the most likely value of the population mean?

3.0

in june 2015, gallop conducted a poll of a random sample of 15000 adults to determine the well being of people in the United states

56.3% and 43.7% are both statistics

Which of the following is the best approximation for the std dev of our 10,000 sample means? std 7.2 best approx for mean 97

7.2/sqrt(97)

Based on the histograms, what is the most likely value of the population mean? (grey)

8

Suppose that battery life is a normal random variable with mean 8 and std of 12, battery lasts longer than 10.4 hours

8 34% 10.4 13.5% 11.6 2.5% 12.8 .15% answ: 16%

What is the minimum surgery length that would be considered unusually risky. mean 132.4 std 15.7 top 4%

=NORM.INV(.96,132.4,15.7)

Suppose that the top 4% of the exams will be given an A+. In order to be given an a, an exam must earn atleast what. mean 75 std 8

=NORM.INV(.96,75,8)

Jeronica is a social worker with an hourly wage of 31.60. What is her z score. mean 28.08 and std 1.97

=STANDARDIZE(31.60, 28.08,1.97)

Which of the following is the primary reason they increase the sample size?

A larger sample size gives a narrower confidence interval.

When the population is not normally distributed, the sampling distribution of the mean approximates which of the following?

A normal distribution given a large enough sample

Which of the following statements about the sampling distribution of the sample mean, x-bar, is true? Check all that apply

all is true

Suppose that we now compute a 90% confidence interval. As confidence level decreases, the interval width

decrease

What is the probability that the average thickness of the 100 sheets is less than 3.91 mm? mean 4 std 1.1

std = 1.1/sqrt/100) =norm.dist(3.9,4, std,1)

a social scientist wishes to conduct a surver.

the sample proportion from the sample 900 is more likely to be close...

The bottle of Maria's favorite sports drink says that it holds 20 fluid ounces. Maria suspects that the sports drink actually holds a different amount...unlikely

true

True or false? The researcher could produce a narrower confidence interval by increasing the sample size to 150.

true

True or false? The students could produce a narrower confidence interval by increasing the sample size to 100.

true

Two bottling plants package a certain type of sports drink. Suppose the mean volume of all of this type of sports drinks is 18 fluid ounces.

Bottling plant B (with 176929 sports drinks per day), because the daily mean will be closer to 18 fluid ounces with more sports drinks in the sample.

If the study were conducted repeatedly which one of the following would be true regarding the resulting proportions of yes responses

Different sample proportions, p, would result each time but for either sample size they would be centered have their mean at the true population proportion

On a particular day, which hospital is less likely to record an average birth weight of 3437g or more?

Hospital A (with 53 births a day), because the mean will typically be closer to 3137 g with more births.

Suppose we take repeated random samples of size 20 from a population with a mean of 60 and a standard deviation of 8. Which of the following statements is true about the sampling distribution of the sample mean (x̄)

The distribution will be normal as long as the population distribution is normal The distribution's mean is the same as the population mean 60.

Suppose the american national studies agency wishes to conduct a survey. ...the sample proportion of p of yes response

The sample proportion from sample 1600 is more likely to be close to the true population

A doctor is measuring the mean systolic blood pressure of female students at a large college. Systolic blood pressure is known to have a skewed distribution. The doctor collects systolic blood pressure measurements from random sample of 28 female students. The resulting 90% confidence interval is (100.4, 159.6). Units of systolic blood pressure are mmHg.

The sampling distribution of means will probably not follow a normal distribution, so we cannot draw a conclusion.

acid rain

The sampling distribution of the proportion of trees is approx. normal

Which do you expect to have less variability (spread): a sampling distribution with sample size n = 112 or a sampling distribution with sample size n = 18?

The sampling distribution with sample size n = 112 will have less variability.

Which one of the following is true regarding the standard deviation of the sampling distribution of the sample proportion, ^p, of "yes" responses?

The standard deviation of the sampling distribution will be 3 times larger with sample size 100.

Suppose that 20% of the residents in a certain state support an increase in the property tax. An opinion....How likely is the resulting sample proportion, ^p, to be within 0.04 of the true proportion, p (i.e., between 0.16 and 0.24)?

There is roughly a 95% chance that the resulting sample proportion will be within 0.04 of the true proportion. mean .20 std sqrt(.2*(1-.2)/400 Norm.dist(.24,.2.std,1)- norm.dist(16,.20,std,1)

The run times of a marathon runner... -2 which of the following statements is correct int..

This week his time was 2 std lower than his average time

Race relations: A New York Times/CBS poll surveyed 1,027 adults nationwide about race relations in the United States. Of the sample, 61% responded that race relations in this country are generally bad. The 95% confidence interval is (0.58, 0.64). Which of the following is an appropriate interpretation of the 95% confidence interval?

We are 95% confident that the proportion of all Americans who say that race relations in this country are generally bad is between 58% and 64%.

Next, the students calculate a 95% confidence interval. As the confidence level increases, which of the following will happen to the interval width?

increase

Suppose that 88% of all dialysis patients will survive for at least 5 years...In a simple random sample of 100 new dialysis patients, what is the probability that the proportion surviving for at least five years will exceed 80%, rounded to 5 decimal places?

mean .88 stp = sqrt (.88(1-.88)/100) =1-norm.dist(.80,.88,std,1)

What us the exam score for an exam whose a score is 1.25 mean=75 std=8

z=(x-mean)/SD X= z*SD+ mean

In june 2017, a survey conducted..Roe v wade

30%, 67%, and 3% are all statistics

Suppose we randomly sample 99 values from this population and compute the mean, then repeat this sampling process 5,000 times and record all the means we get. Which of the following is the best approximation for the standard deviation of the 5,000 sample means?

=3.7/sqrt(99)

If each intern conducted the study repeatedly (selecting different samples of people each time ... but using the same sample size), which one of the following would be true regarding the resulting sample proportion, ^p, of "yes" responses for each intern?

Different sample proportions, ^p, could result for each intern, but for either sample size, they would be centered (have their mean) at the true population proportion, p.

The following displayed two normal distributions which of the following is true

I and II only

What do you expect for the variability (spread) of a sampling distribution with sample size n = 7?

Less variability than the population (a narrower distribution).

The percentage of cockroaches weighing between 77 grams and 83 grams us about mean 80 std 4

NORM.DIST(83,80,4,1) - NORM.DIST(77,80,4,1) *100

A researcher is estimating the mean income of residents in a large city. The income variable is usually skewed to the right. She collects a random sample of 25 people. The resulting 95% confidence interval is ($26700, $35400).

No conclusion can be drawn.

Find the probability that her score is atleast 74. Mean 73 and std 3

P(×>74) = 1 -NORM.DIST(74,73,3,1) .3694

A survey asks a random sample of 1500 adults in Ohio if they support an increase in the state sales tax from 5% to 6%, with the additional revenue going to education..93% of all adults in Ohio support the increase. The standard deviation of the sampling distribution is

Sqrt (.93*(1-.93)/1500)

we construct a 95% confidence interval for each sample to estimate the population mean. Which confidence interval will have greater precision (smaller width) for estimating the population mean?

The confidence interval based on the sample of 64 data values will be more precise.

The margin of error for this sample was 5.7%. What does this margin of error tell you about the results of the survey?

The population proportion is most likely within 5.7% of the sample proportion from a randomly selected sample.

They used the information from the survey to calculate the 95% confidence interval: (0.53, 0.72). To which population does the confidence interval apply?

The results do not apply to any population because this was a convenience sample.

He also conducted a hypothesis test. He found very strong evidence that more than half of voters would consider voting for Herman Cain.

The results do not apply to any population because this was a voluntary response sample.

Smoking habits: A group of statistics students conducted a survey about smoking habits on campus to determine the proportion of students who believe that smoking hookah (a wa

The sample needs to be random but we don't know if it is. The actual count of students who do not believe that smoking hookah is less harmful than smoking cigarettes is too small n(1−^p) is not greater than 10.

Which of the following is a reason the administration should not calculate a confidence interval for the proportion of all students who drive to campus?

The sample needs to be random but we don't know if it is. n(1−^p) is not greater than 10. The actual count of those who do not drive to campus is too small.

The probability is .997 what a bill will be received between which if the following number of days mean 31 std 6

Upper: 31+3*6 (.997 3 std dev) lower 31-3*6

Marijuana legalization: In a Public Policy Institute of California (PPIC) poll, 53% of 1,706 California adult residents surveyed say that marijuana should be legal. Based on the results, the 95% confidence interval is (0.506, 0.554). Which of the following is an appropriate interpretation of this confidence interval?

We are 95% confident that between 50.6% and 55.4% of California residents say that marijuana should be legal.

Genetically modified foods: In a Pew Research Center report from January 2015, 37% of American adults say that genetically modified (GM) foods are generally safe to eat. The margin of error for the 95% confidence interval is 3.1%.

We are 95% confident that the population proportion is within 3.1% of the sample proportion of 37%.

In April and May of 2011, the Pew Research Center surveyed cell phone users about voice calls and text messaging. They surveyed a random sample of 1914 cell phone users. 75% of the sample use text messaging. The 95% confidence interval is (73.1%, 76.9%). Which of the following is an appropriate interpretation of the 95% confidence interval?

We can be 95% confident that the proportion of all cell phone users who use text messaging is between 73.1% and 76.9%.

Confidence interval precision: We know that narrower confidence intervals give us a more precise estimate of the true population proportion. Which of the following could we do to produce higher precision in our estimates of the population proportion?

We can select a lower confidence level and increase the sample size.

In which of the following scenarios would the distribution of the sample mean x-bar be normally distributed? Check all that apply.

We take repeated random samples of size 15 from a population that is normally distributed. We take repeated random samples of size 50 from a population of unknown shape.

DO NOT apply the standard deviation rule 22 mean 2 std

What proportion of the students scored at least 27 points in this test 1-NORM.DIST(27,22,2,1) what is the 63 percentile if the distribution of test scores NORM.INV(.63, 22,2)

True or false? The researcher could produce a narrower confidence interval by increasing the confidence level to 99%.

false

True or false? The students could produce a narrower confidence interval by increasing the confidence level to 95%.

false

If the company sells the candy bars in packs of 4 bars, what can we say about the likelihood that the average weight of the bars in a randomly selected pack is 4 or more grams lighter than advertised?

mean 30 std =2/sqrt(4) Norm.dist(36,30,std,1)

If the company sells the jelly beans in packs of 9 bags, what can we say about the likelihood that the average weight of the bags in a randomly selected pack is 2 or more grams lighter than advertised? std 3

mean 30 std =3/sqrt(9) =Norm.dist(28,30,std,1) There is about a 2.5% chance of this occurring.

Left handedness occurs in about 12%...slightly more likely...random variables X and Y

np>10 n(1-p)>=10 males n 100 p .13 females n 80 p .11 Only X can be well approximated by a random variable

The number of hours a light bulb burns before failing varies from bulb to bulb. The distribution of burnout times is strongly skewed to the right. The Central Limit Theorem says that

the average burnout time of a large number of bulbs has a distribution that is close to Normal.

female college soccer players in the United States is μ = 68 inches and the standard deviation is σ =3.2 inches. Suppose we randomly sample 96 values from this population and compute the mean, then repeat this sampling process 5000 times and record all the means we get. Which of the following is the best approximation for the mean of our 5000 sample means?

u = 68 answer 68

The epa requires that the exhaust of each model

what is the 66th percentile for NOX NORM.INV(.66,1.45,.40) Find the interquartile range for the distribution of NOX levels IQR = Q3-Q1 q3. =NORM.INV( .75,1.45,.40) q1= NORM.INV (.25,1.45,.40)

A study was made of seat belt use among children who were involved in car crashes that caused them to be hospitalized....

what is the probability that their hospital stay is from 5 to 6 days =NORM.DIST(6,7.37,1.50,1)- NORM.DIST(6 5,7.37,1.50,1) what is the probability that their hospital stay is greater than 6 days 1-NORM.DIST(6,7.37,1.50,1)

Students in a statistics class are conducting a survey to estimate the mean number of units students at their college are enrolled in. The students collect a random sample of 47 students. The mean of the sample is 12.3 units. The sample has a standard deviation of 1.9 units. What is the 95% confidence interval for the average number of units that students in their college are enrolled in? Assume that the distribution of individual student enrollment units at this college is approximately normal.

xbar 12.3 n 47 std 1.9 st error = 1.9/sqrt(n) t= T.INV.2T( 1-.95,47-1) moe = t* st error lower = xbar - moe upper = xbar + moe

The SAT is the most widely used college admission exam. (Most community colleges do not require students to take this exam.) The mean SAT math score varies by state and by year, so the value of µ depends on the state and the year. But let's assume that the shape and spread of the distribution of individual SAT math scores in each state is the same each year. More specifically, assume that individual SAT math scores consistently have a normal distribution with a standard deviation of 100. An educational researcher wants to estimate the mean SAT math score (μ) for his state this year. The researcher chooses a random sample of 663 exams in his state. The sample mean for the test is 484. Find the 95% confidence interval to estimate the mean SAT math score in this state for this year. (Note: The critical z-value to use, zc, is: 1.960.)

xbar 484 n 663 sigma 100 st error = sigma/sqrt(n) z: 1.960 moe: st error * z lwr: xbar - moe upper: xbar + moe

In a study of the effects of acid rain, a random sample of 100 trees from a particular forest is examined. Forty percent of these show some signs of damage. Which of the following statements is correct?

40% is a statistic

Which of the following best describes the sampling distribution of a statistic?

A distribution of a single statistic from repeated random samples of the same size, from the same population.

Which of the following is a reason the administration should not calculate a confidence interval to estimate the proportion of all students who ride a bike to campus? Check all that apply.

n*^p is not greater than 10. The actual count of bike riders is too small. The sample needs to be random but we don't know if it is.

Concert marketing: GSU's Rialto Center for the Performing Arts wanted to investigate why ticket sales for the upcoming season significantly decreased from last year's sales. The marketing staff collected

n^p is not greater than 10. The sample needs to be random, but we don't know if it is. The actual count of community residents who received the concert brochure by mail is too small.

A Gallup survey of 2322 adults (at least 18 years old) in the U.S. found that 408 of them have donated blood in the past two years. Construct a 90% confidence interval for the population proportio

phat= 408/2322 n =2322 x= 408 std err= sqrt(phat*(1-phat)/n) z =1.645 moe= z* st error lwr phat - moe upper phat + moe

Suppose that the distribution for total amounts spent by students vacationing for a week in Florida is normally distributed with a mean of 650 and a standard deviation of 120. Suppose you take a simple random sample (SRS) of 35 students from this distribution. What is the probability that a SRS of 35 students will spend an average of between 600 and 700 dollars?

std 120/sqrt(35) norm.dist(700,650,std,1)-norm.dist(600,650,std,1)

A machine is designed to fill 16-ounce bottles of shampoo. When the machine is working properly, the amount poured into the bottles follows a normal distribution with mean 16.05 ounces with a standard deviation of .4 ounces. If four bottles are randomly selected each hour and the number of ounces in each bottle is measured, then 95% of the means calculated should occur in what interval?

std =.400/sqrt(4) lower = 16.05-2*std upper = 16.05+2*std