stats final

Every fifth adult entering an airport is checked for extra security screening. What sampling technique is used? A) cluster B) simple random C) convenience D) systematic E) stratified

systematic

Find the standardized test statistic t for a sample with n = 25, x bar= 26, s = 3, and α = 0.05 if H1: μ > 25. Round your answer to three decimal places.

t=(26-25)/3/sqrt(25)) t=1.67

A poll used a sample of 100 randomly selected car owners. Within the​ sample, the mean time of ownership for a single car was 7.45 years with a standard deviation of 3.62 years. Test the claim by the owner of a large dealership that the mean time of ownership for all cars is less than 7.5 years. Use a 0.05 significance level

t=(7.45-7.5)/(3.62/sqrt(10)) t=-0.04368

The analysis of variance is an inferential method that is used to test the equality of A) three or more population means. B) three or more population variances C) two population means. D) two population variances

three or more population means

Decide whether the statement makes sense​ (or is clearly​ true) or does not make sense​ (or is clearly​ false). Explain. In a test for equality of mean skull breadths of ancient males from three different​ epochs, the​ P-value of 0.055 is obtained. Because the​ P-value greater than .05, fail to reject the null hypothesis of equal means and conclude there is not sufficient evidence that at least one of the means is different

true

A manufacturer claims that the mean lifetime of its lithium batteries is 1100 and the standard deviation of the population is 80 hours. A homeowner selects 25 of these batteries and finds the mean lifetime to be 1080 hours. Test the manufacturer's claim. Use α = 0.05. Round the test statistic to the nearest thousandth

z=(1080-1100)/(80/sqrt(25))=-20/16=-1.25 Only need to find test statistic for this one

The length of time it takes college students to find a parking spot in the library parking lot follows a normal distribution with a mean of 6.5 minutes and a standard deviation of 1 minute. Find the probability that a randomly selected college student will take between 5.0 and 7.5 minutes to find a parking spot in the library lot

z=(5-6.5)/1=-1.5 z=(7.5-6.5)/1=1 Look up -1.5 and 1 and subtract the smaller from the larger. Area is .0668. Area is .8413. Answer=.8413-.0668=.7745

The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 2900 miles. What is the probability a particular tire of this brand will last longer than 57,100 miles?

z=standard score=(57,100-60,000)/2900=-1 Look up -1 on the z table. Area is .1587. Because it says "last longer", subtract from 1. So, the answer is (1-.1587)=.8413

State three properties of , the correlation coefficient.

-r is unitless -r is between -1 & 1 & the closer it is to 1 or -1 the stronger the association -if r>0 it is positive association -if r<0 it is negative association

What are the three methods for determining probabilities

Classical/Theoretical Empirical/Relative Frequency Subjective

flip 1) 83 2) 156 3) 73 4) 60/83*100=72.29% 5) 67/73=91.78%

1) how many patients were treated with splints 2) how many subjects were included in the study 3) how many patients were treated with sugery 4) For the patients treated with splints, what was the success rate? 5) For the patients treated with surgery, what was the success rate?

A researcher at a major clinic wishes to estimate the proportion of the adult population of the United States that has sleep deprivation. How large a sample is needed in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 4%?

1/(.04)^2=625

What is the difference between a prospective study and retrospective study?

A prospective study looks forward in time whereas a retrospective study looks back in time.

The output below gives the mean and median for the national dropout rates of high school students in 2010 and 2012 Drop 2010 Drop 2012 N 51 51 MEAN 28.38 26.76 MEDIAN 27.94 25.54 Use the sample information to determine the shape of the distributions of the high school dropout rates in 2010 and 2012.

Because the mean is approximately the median, both are normally distributed. If the mean was greater than the median, it would be right skewed. If the mean was less than the median, it would be left skewed.

What is bias in statistics?

Bias is when the sample overestimates or underestimates a particular part of the population. Or, the expected value of the statistic overestimates or underestimates the population value

The mean cost of textbooks for one class is greater than $130. Identify the type I and type II errors for the hypothesis test of this claim & the H0 & HA

H0 u=130 HA u>130 Type I error is rejecting the null when the null is true. It would be saying the mean is greater than 130, when in fact, it is 130. Type II error would be failing to reject the null when the alternative is true. It would be saying the mean is 130, when in fact, it is greater than 130

Samples of airline departure times are obtained and compared to the scheduled departure times. Four major airlines are compared and their mean delay times are recorded. Identify the null and alternative hypotheses for applying an analysis of variance.

H0: mu1=mu2=mu3 HA: at least 1 mean is different

the mean repair bill of cars is greater than $150. Write the null and alternative hypotheses.

H0: u=$150 HA: u>$150

The mean annual return for an employeeʹs IRA is at most 5.4 percent. Write the null and alternative hypotheses.

H0: u=5.4 HA: u<5.4

The mean age of lawyers in New York is 50.7 years. Write the null and alternative hypotheses.

H0: u=50.7 HA: u does not equal 50.7

The mean age of judges in Los Angeles is 56.3 years. Identify the type I and type II errors for the hypothesis test of this claim & find the H0 & HA

H0: u=56.3 HA: u does not equal 56.3 type 1: rejecting the null when the null is true. It would be saying the mean is not equal to 56.3 years, when in fact, it is 56.3 years type 2: failing to reject the null when the alternative is true. It would be saying the mean is 56.3 years when in fact, it is not 56.3 years.

A student scores 74 on a geography test and 282 on a mathematics test. The geography test has a mean of 80 and a standard deviation of 5. The mathematics test has a mean of 300 and a standard deviation of 12. If the data for both tests are normally distributed, on which test did the student score better relative to the other students in each class?

Standard score for geography=(74-80)/5=-1.2 Standard score for mathematics=(282-300)/12=-1.5 The student scored better on the geography test.

What is meant by "statistical significance"?

Statistical significance means not likely to have occurred by chance

What is the placebo effect?

Effect of a placebo (innocuous medication) on the individual that can't be attributed to the medicine, but rather, the beliefs about the medicine.

The book cost (in dollars) for one semesterʹs books are given below for a sample of five college students. Calculate the sample variance and sample standard deviation of the book costs. 200, 130, 400, 500, 345

Find the mean. Mean=(200+130+400+500+345)/5=315 Now, find the variance and standard deviation. Variance=((200-315)^2+(130-315)^2+(400-315)^2+(500-315)^2+(345-315)^2)/4=22450 Std. dev.=sqrt(22450)=149.83

the cholesterol levels of a group of adults the day after Thanksgiving-continuous or discrete

continuous

the low temperature in degrees Fahrenheit on January 1st in Cheyenne, Wyoming-continuous or discrete

continuous

Each year advertisers spend billions of dollars purchasing commercial time on network sports television. In the first 6 months of 1988, advertisers spent $1.1 billion. A recent article listed the top 10 leading spenders (in millions of dollars): Company A $70.3 B 60.5 C 57.9 D 54.7 E 29.3 F 26.4 G 24.6 H 21.1 I 22.4 J 20.9 Calculate the mean amount spent.

Mean=(70.3+60.5+57.9+54.7+29.3+26.4+24.6+21.1+22.4+20.9)/10=388.1/10=38.81 million

Consider rolling two die, what is the probability of getting doubles? What is the probability of not getting doubles?

P(doubles)=6/36=1/6 P(not doubles)=36/36-6/36=30/36=5/6

What is the difference between precision and accuracy?

Precision is when all measurements are about the same. Accuracy is when the measurements are close to a known value.

1) An industrial psychologist is investigating the effects of work environment on employee attitudes. A group of 20 recently hired sales trainees were randomly assigned to one of four different ʺhome roomsʺ - five trainees per room. Each room is identical except for wall color. The four colors used were light green, light blue, gray and red. The psychologist wants to know whether room color has an effect on attitude, and, if so, wants to compare the mean attitudes of the trainees assigned to the four room colors. At the end of the training program, the attitude of each trainee was measured on a 60-pt. scale (the lower the score, the poorer the attitude). The data was subjected to a one-way analysis of variance. At α = 0.05, what would be the best interpretation?

Pvalue of 0. Reject the null hypothesis

the speed of a car on a Boston tollway during rush hour traffic-continuous or discrete

continuous

the number of bottles of juice sold in a cafeteria during lunch-continuous or discrete

discrete

the number of goals scored in a hockey game-continuous or discrete

discrete

the number of phone calls to the police department on any given day-continuous or discrete

discrete

the number of pills in an aspirin bottle-continuous or discrete

discrete

What is meant when we say two events are independent?

The probability of an event is not affected by the occurrence of the other event

What is meant when we say two events are mutually exclusive or disjoint?

They have no outcomes in common

How much money does the average professional hockey fan spend on food at a single hockey game? That question was posed to 10 randomly selected hockey fans. The sampled results show that sample mean and standard deviation were $16.00 and $2.6, respectively. Use this information to create a 95% confidence interval for the mean

Upper bound: 16+2.262*(2.6/sqrt(10)) Lower bound: 16-2.262*(2.6/sqrt(10))

Construct a 95% confidence interval for the population mean, μ. Assume the population has a normal distribution. In a recent study of 22 eighth graders, the mean number of hours per week that they played video games was 19.6 with a standard deviation of 5.8 hours. Round to the nearest hundredth

Upper bound: 19.6+1.96*(5.8/sqrt(22))=22.02 Lower bound: 19.6-1.96*(5.8/sqrt(22))=17.18

A small computing center has found that the number of jobs submitted per day to its computers has a distribution that is approximately bell shaped, with a mean of 84 jobs and a standard deviation of 10. Where do we expect most (approximately 95%) of the distribution to fall?

Upper limit: 84+2(10)=104 Lower limit: 84-2(10)=64 They should fall between 64 and 104.

A medical researcher obtains a sample of adults suffering from diabetes. She randomly assigns 73 people to a treatment group and 73 to a placebo group. The treatment group receives a medication over a period of three months and the placebo group receives a placebo over the same time frame. At the end of three months the patientsʹ symptoms are evaluated experiment or observational study

experiment

A local hardware store claims that the mean waiting time in line is less than 3.5 and the standard deviation is .8 minutes. A random sample of 20 customers has a mean of 3.7 minutes. If α = 0.05, test the storeʹs claim using P-values

Z=(3.7-3.5)/(.8/sqrt(20))=.2/.179=1.12 Look up a pvalue of 1.12 on chart Area from table is .8686. Fail to reject the null

A new phone system was installed last year to help reduce the expense of personal calls that were being made by employees. Before the new system was installed, the amount being spent on personal calls follows a normal distribution with an average of $900 per month and a standard deviation of $50 per month. Refer to such expenses as PCEʹs (personal call expenses). Find the probability that a randomly selected month had a PCE that falls below $750

Z=(750-900)/50=-3 Look up a standard score of -3. Answer is .0013

World population in 1950 was 2.6 billion. By the of 2015, it had reached 7.3 billion. Describe the absolute and relative change in world population from 1950 to 2015

absolute: 7.3billion-2.6billion=4.7 billion relative change (7.3-2.6)/2.6 x 100=180.77% increase increase

What does "And" mean in probability? What about "Or"?

and=multiply or=add

The following data represent the bachelor degrees of CEOʹs at area small businesses. Determine the mode degree accounting: 29 business: 42 liberal arts: 5 marketing: 24 other: 7

business???? why

At a local technical school, five auto repair classes are randomly selected and all of the students from each class are interviewed. What sampling technique is used? A) simple random B) convenience C) systematic D) stratified E) cluster

cluster

The weight of a player on the wrestling team-continuous or discrete

continuous

the age of the oldest employee in the data processing department-continuous or discrete

continuous

A medical researcher obtains a sample of adults suffering from diabetes. She randomly assigns 73 people to a treatment group and 73 to a placebo group. The treatment group receives a medication over a period of three months and the placebo group receives a placebo over the same time frame. At the end of three months the patientsʹ symptoms are evaluated. experiment or observational study

experiment

A scientist was studying the effects of a new fertilizer on crop yield. She randomly assigned half of the plots on a farm to group one and the remaining plots to group two. On the plots in group one, the new fertilizer was used for a year. On the plots in group two, the old fertilizer was used. At the end of the year the average crop yield for the plots in group one was compared with the average crop yield for the plots in group two experiment or observational study

experiment

A scientist was studying the effects of a new fertilizer on crop yield. She randomly assigned half of the plots on a farm to group one and the remaining plots to group two. On the plots in group one, the new fertilizer was used for a year. On the plots in group two, the old fertilizer was used. At the end of the year the average crop yield for the plots in group one was compared with the average crop yield for the plots in group two. experiment or observational study

experiment

the day of the month

interval

The annual profits of five large corporations in a certain area are given below. Which measure of central tendency should be used? $135,000 $143,000 $163,000 $133,000 $1,213,000

median

the musical instrument played by a music student

nominal

the native language of a tourist

nominal

A poll is conducted in which professional musicians are asked their ages experiment or observational study

observational study

A researcher obtained a random sample of 100 smokers and a random sample of 100 nonsmokers. After interviewing all 200 participants in the study, the researcher compared the rate of depression among the smokers with the rate of depression among nonsmokers experiment or observational study

observational study

An officer's rank in the military

ordinal

The medal received (gold, silver, bronze) by an Olympic gymnast

ordinal

The following data represent a random sample of 15 complaints registered with the customer service department of a store. Determine the mode complaint defective product rude personnel messy store other defective product defective product other excessive waiting time other defective product other other rude personnel defective product other

other

A survey of 700 non-fatal accidents showed that 163 involved uninsured drivers. Construct a 95% confidence interval for the proportion of fatal accidents that involved uninsured drivers. Round to the nearest thousandth

p-hat=163/700=.23 Upper bound: .23+1.96*sqrt((.23*.77)/700) Lower bound: .23-1.96*sqrt((.23*.77)/700) Upper bound: .23+.03=.26 Lower bound: .23-.03=.20

A recent study claimed that at least 15% of junior high students are overweight. In a sample of 160 students, 18 were found to be overweight. At α = 0.05, test the claim

p-hat=18/160=.1125 z=(.1125=.15)/(sqrt(.15*..85)/160) z=-1.32 Look up z=-1.33 on the z chart. Area from table is: .0918

An airline claims that the no-show rate for passengers is less than 5%. In a sample of 420 randomly selected reservations, 19 were no-shows. At α = 0.01, test the airline's claim. Round to the nearest thousandth when calculating the test statistic

p-hat=19/420=.045 z=(.045-.05)/sqrt((.05*.95)/420)=-.47 Look up z=-.47 on the standard normal table. Area from the table is: .3192. Fail to reject the null

The average age of the 65 students in Ms. Hopeʹs political science class is 21 years 7 months is the 21 years 7 months a parameter or statistic?

parameter

the bank account numbers of the students in a class

qualitative

the colors of book covers on a bookshelf-qualitative or quantitative

qualitative

the numbers on the shirts of a boy's football team-qualitative or quantitative

qualitative

the number of calls received at a companyʹs help desk-qualitative or quantitative

quantitative

the number of seats in a school auditorium-qualitative or quantitative

quantitative

height of a tree

ratio

weight of rice bought by a customer

ratio

If the mean was greater than the median, it would be ___________. If the mean was less than the median, it would be ________________.

right skewed left skewed

A (hypothetical) study seeks to determine whether vitamin C has an effect in preventing colds. Among a sample of 220 people, 105 randomly selected people took a vitamin C pill daily for a period of 10 weeks and the remaining 115 people took a placebo daily for 10 weeks. At the end of 10 weeks, the number of people who got colds was recorded. Table 10.6 summarizes the results. State the hypotheses and determine the test statistic

see study guide 3

A study of 3700 college students in the city of Pemblington found that 8% had been victims of violent crimes. is the 8% a parameter or statistic?

statistic

In a survey conducted in the town of Atherton, 25% of adult respondents reported that they had been involved in at least one car accident in the past ten years is the 25% a parameter or statistic?

statistic

Telephone interviews of 372 employees of a large electronics company found that 65% were dissatisfied with their working conditions is the 65% a parameter or statistic?

statistic

A writer for an art magazine randomly selects and interviews fifty male and fifty female artists. What sampling technique is used? A) simple random B) convenience C) systematic D) stratified E) cluster

stratified