Deck 6: Introduction to Inference

Question 1

The heights of young American women,in inches,are Normally distributed with a mean of  and a standard deviation of  = 2.4.The margin of error for a 99% confidence interval is desired to be ±1 inch.What should be the sample size?

A)7
B)22
C)38
D)39

Answer 1

39

Question 2

The heights of a simple random sample of 400 male high school sophomores in a Midwestern state are measured.The sample mean is = 66.2 inches.Suppose that the heights of male high school sophomores follow a Normal distribution with a standard deviation of  = 4.1 inches.Suppose the heights of a simple random sample of 100 male sophomores were measured rather than 400.Which of the following statements is true?

A)The margin of error for the 95% confidence interval would increase.
B)The margin of error for the 95% confidence interval would decrease.
C)The margin of error for the 95% confidence interval would stay the same because the level of confidence has not changed.
D)The standard deviation  would decrease.

Answer 2

The margin of error for the 95% confidence interval would increase.

Question 3

To assess the accuracy of a laboratory scale,a standard weight that is known to weigh exactly 1 gram is repeatedly weighed a total of n times and the mean is computed.Suppose the scale readings are Normally distributed with an unknown mean of  and a standard deviation of  = 0.01 grams.How large should n be so that a 95% confidence interval for  has a margin of error no larger than ± 0.0001?

A)n = 100
B)n = 196
C)n = 10000
D)n = 38416

Answer 3

n = 38416

Question 4

Battery packs in radio-controlled racing cars need to be able to last pretty long.The distribution of the lifetimes of battery packs made by Lectric Co.is slightly left skewed.Assume that the standard deviation of the lifetime distribution is  = 2.5 hours.A simple random sample of 75 battery packs results in a mean of = 29.6 hours.What is a 90% confidence interval for ,the true average lifetime of the battery packs made by Lectric Co.?

A)(29.13,30.07)
B)(29.03,30.17)
C)(28.86,30.34)
D)The confidence interval cannot be calculated because the population distribution is not Normal.

Question 5

The breaking strength of yarn used in the manufacture of woven carpet material is Normally distributed with  = 2.4 psi.A random sample of 16 specimens of yarn from a production run was measured for breaking strength,and based on the mean of the sample ,a confidence interval was found to be (128.7,131.3).If we wanted to have a greater degree of confidence in the calculated interval,what would have to happen to its length?

A)The interval would be shorter.
B)The margin of error would decrease.
C)The confidence level would have a smaller value.
D)The sample size would go up.
E)The interval would increase in length.

Question 6

An agricultural researcher plants 25 plots with a new variety of yellow corn.Assume that the yield per acre for the new variety of yellow corn follows a Normal distribution with an unknown mean of  and a standard deviation of  = 10 bushels per acre.If the average yield for these 25 plots is = 150 bushels per acre,what is a 90% confidence interval for ?

A)150 ± 0.784
B)150 ± 2.00
C)150 ± 3.29
D)150 ± 3.92

Question 7

Hoping to attract more shoppers,a city builds a new public parking garage downtown.The city plans to pay for the structure through parking fees.The consultant,who advised the city on this project,randomly selected 44 weekdays.Daily fees collected averaged $126.Based on data from other parking structures,the consultant will assume parking fees at this parking garage are Normally distributed with a standard deviation of $15. If a 95% confidence interval was constructed,how would the margin of error compare to one used to create a 90% confidence interval?

A)The margin of error for the 95% confidence interval would be smaller.
B)The margin of error for the 95% confidence interval would be the same.
C)The margin of error for the 95% confidence interval would be larger.
D)This cannot be determined from the information given.

Question 8

An agricultural researcher plants 25 plots with a new variety of yellow corn.Assume that the yield per acre for the new variety of yellow corn follows a Normal distribution with an unknown mean of  and a standard deviation of  = 10 bushels per acre. Which of the following would produce a confidence interval with a smaller margin of error than the 90% confidence interval?

A)Plant only five plots rather than 25 because five are easier to manage and control.
B)Plant 10 plots rather than 25 because a smaller sample size will result in a smaller margin of error.
C)Plant 100 plots rather than 25 because a larger sample size will result in a smaller margin of error.
D)Compute a 99% confidence interval rather than a 90% confidence interval because a higher confidence level will result in a smaller margin of error.

Question 9

Suppose we wish to calculate a 90% confidence interval for the average amount spent on books by freshmen in their first year at a major university.The interval is to have a margin of error of $2.Assume that the amount spent on books by freshmen has a Normal distribution with a standard deviation of  = $30.How many observations are required to achieve this margin of error?

A)25
B)608
C)609
D)865

Question 10

Central Middle School has calculated a 95% confidence interval for the mean height ()of 11-year-old boys at their school and found it to be 56 ± 2 inches.Which of the following could be the 90% confidence interval based on the same data?

A)56 ± 1
B)56 ± 2
C)56 ± 3
D)Without knowing the sample size,any of the above answers could be the 90% confidence interval.

Question 11

The scores on the Wechsler Intelligence Scale for Children (WISC)are thought to be Normally distributed with a standard deviation of  = 10.A simple random sample of 25 children is taken,and each is given the WISC.The mean of the 25 scores is = 104.32.Based on these data,what is a 95% confidence interval for ?

A)104.32 ± 0.78
B)104.32 ± 3.29
C)104.32 ± 3.92
D)104.32 ± 19.60

Question 12

Hoping to attract more shoppers,a city builds a new public parking garage downtown.The city plans to pay for the structure through parking fees.The consultant,who advised the city on this project,randomly selected 44 weekdays.Daily fees collected averaged $126.Based on data from other parking structures,the consultant will assume parking fees at this parking garage are Normally distributed with a standard deviation of $15. What is a 90% confidence interval for the mean daily income this parking garage will generate from the parking fees?

A)($107.31,$144.69)
B)($121.57,$130.43)
C)($122.28,$129.72)
D)($125.44,$126.56)

Question 13

The heights of a simple random sample of 400 male high school sophomores in a Midwestern state are measured.The sample mean is = 66.2 inches.Suppose that the heights of male high school sophomores follow a Normal distribution with a standard deviation of  = 4.1 inches.What is a 95% confidence interval for ?

A)(58.16,74.24)
B)(59.46,72.94)
C)(65.80,66.60)
D)(65.86,66.54)

Question 14

The breaking strength of yarn used in the manufacture of woven carpet material is Normally distributed with  = 2.4 psi.A random sample of 16 specimens of yarn from a production run was measured for breaking strength,and based on the mean of the sample ,a confidence interval was found to be (128.7,131.3).What is the confidence level,C,of this interval?

A)0.95
B)0.99
C)0.90
D)0.97
E)It can't be determined with the information provided.

Question 15

Suppose that the population of the scores of all high school seniors who took the SAT Math (SAT-M)test this year follows a Normal distribution with standard deviation  = 100.You read a report that says,"On the basis of a simple random sample of 100 high school seniors that took the SAT-M test this year,a confidence interval for  is found to be 512.00 ± 25.76." What was the confidence level used to calculate this confidence interval?

A)90%
B)95%
C)99%
D)99.9%

Question 16

A nationally distributed college newspaper conducts a survey among students nationwide every year.This year,responses from a simple random sample of 204 college students to the question "About how many CDs do you own?" resulted in a sample mean of = 72.8.Based on data from previous years,the editors of the newspaper will assume that  = 7.2.Use the information given to obtain a 95% confidence interval for the mean number of CDs owned by all college students.

A)(65.6,80.0)
B)(71.8,73.8)
C)(72.0,73.6)
D)(72.3,73.3)

Question 17

Suppose a 99% confidence interval for the mean weight of high school girls (in pounds)is calculated as (102.3,106.5).If we had measured the weights of each of the girls in kilograms (2.2 pounds = 1 kilogram),then the confidence interval for the mean weight of high school girls in kilograms would have been

A)(104.5,108.7).
B)(46.5,48.4).
C)(225.06,234.3).
D)(100.1,104.3).

Question 18

The heights of young American women,in inches,are Normally distributed with a mean of  and a standard deviation of  = 2.4.A simple random sample of four young American women is selected and their heights measured.The four heights,in inches,are 63,69,62 and 66.Based on these data,what is a 99% confidence interval for ?

A)65.00 ± 1.55
B)65.00 ± 2.35
C)65.00 ± 3.09
D)65.00 ± 4.07

Question 19

The distribution of GPA scores is known to be left skewed.At a large university,an English professor is interested in learning about the average GPA score of the English majors and minors.A simple random sample of 75 junior and senior English majors and minors results in an average GPA score of 2.97.Assume that the distribution of GPA scores for all English majors and minors at this university is also left skewed with a standard deviation of 0.62.Calculate a 95% confidence interval for the mean GPA of the junior and senior English majors and minors.

A)(2.786,3.154)
B)(2.830,3.110)
C)(2.852,3.088)
D)(2.954,2.986)

Question 20

Researchers are studying the yield of a crop in two locations.The researchers are going to compute independent 90% confidence intervals for the mean yield at each location.What is the probability that at least one of the intervals will cover the true mean yields at their location?

A)0.81
B)0.19
C)0.99
D)0.95

Question 21

A 95% confidence interval __________.

A)gives the probability of 95% that the true population mean is in the interval
B)gives you an interval which you are 95% confident contains the true population mean
C)gives an interval that would contain the true population mean in 95% of all possible random samples
D)None of the above

Question 22

Outliers do not have a large effect on the formation of confidence intervals.

Question 23

The purpose of forming confidence intervals is to find the exact value of the true population mean based on a random sample.

Question 24

The basic form of a confidence interval is __________________.

A)estimate ± margin of error
B)margin of error ± estimate
C)standard error ± estimate
D)estimate ± margin

Question 25

In order to obtain a small margin of error with high levels of confidence,C,you will need ______ observations.

A)a large number of
B)a small number of
C)10
D)None of the above

Question 26

When constructing confidence intervals,the center of each interval is always _______.

A)the median
B)the margin of error
C)
D)the mode

Question 27

A sample of size 60 was selected from a population with a variance of = 121.It was found,based upon the data obtained,that the sample mean = 174.What is the 98% confidence interval estimate for ?

A)174 ± 2.33
B)174 ± 2.33
C)174 ± 2.33
D)174 ± 2.58
E)174 ± 2.58

Question 28

When constructing confidence intervals,the true population mean  will always be contained within the interval.

Question 29

When forming confidence intervals,it is very important that you only take large samples from Normal populations.

Question 30

The lifetime (in hours)of a 60-watt light bulb is a random variable that has a Normal distribution with  = 30 hours.A random sample of 25 bulbs put on test produced a sample mean lifetime of = 1038.What is the 92% confidence interval estimate for the mean lifetime ?

A)(1022.1,1053.9).
B)(1027.5,1048.5).
C)(1026.2,1049.8).
D)(1028.1,1047.9).
E)(1022.5,1053.5).

Question 31

As you increase the margin error of a confidence interval,the confidence level _________.(Note: Assume the sample size is fixed. )

A)increases
B)decreases
C)remains the same

Question 32

The lifetime (in hours)of a 60-watt light bulb is a random variable that has a Normal distribution with  = 30 hours.A random sample of 25 bulbs put on test produced a sample mean lifetime of = 1038.Construct a 92% confidence interval estimate for the mean lifetime .If it were desired to cut the confidence interval to half its length while keeping the same 92% level,what size sample would be required to achieve this?

A)50
B)13
C)75
D)100
E)41

Question 33

The margin of error in a confidence interval captures errors that are present from random sampling only.

Question 34

A research team conducted a critical study,and using the data they gathered in their random experiment,a 95% confidence interval for the population mean was constructed.The team was not happy with the result because they felt the margin of error was much too large.All other things being equal,if they were to repeat the study,what could they do to reduce the margin of error?

A)They could construct the confidence interval with a lower confidence level than they previously used.
B)They could include a greater number of subjects in the experiment.
C)They could reduce the population standard deviation .
D)All of the above are possible things for them to try.
E)None of the above will work because of the randomness in the experiment.

Question 35

A study was conducted on the reaction time of female subjects over the age of 50 to a particular light stimulus using a specific type of red light.A random sample of 45 female subjects from this age group in the population was selected and the subject's reaction time (in seconds)determined.Based on the test data,the 99% confidence interval estimate for  was determined to be (0.66,0.78).From this interval we can conclude that

A)this interval contains the sample mean with probability 0.99.
B)this interval has a probability of 0.99 of enclosing the true mean .
C)this interval,in the long run,will contain the true mean  99% of the time.
D)we have 99% confidence in this interval because,in repeated sampling from the population,the method used to determine such confidence intervals will produce intervals 99% of which will contain .
E)we have 99% confidence that this interval contains  because,if we repeated testing over and over again,99% of the time this interval will contain .

Question 36

The lifetime (in hours)of a 60-watt light bulb is a random variable that has a Normal distribution with  = 30 hours.A random sample of 25 bulbs put on test produced a sample mean lifetime of = 1038.If in the study of the lifetime of 60-watt light bulbs it was desired to have a margin of error no larger than 6 hours with 99% confidence,how many randomly selected 60-watt light bulbs should be tested to achieve this result?

A)13
B)97
C)165
D)42
E)Not within ± 2 of any of the above

Question 37

How do you form a confidence interval when taking a small sample from a non-Normal population?

A)You can use the bootstrap procedure.
B)You will not be able to form a confidence interval.
C)You can use the central limit theorem.
D)None of the above

Question 38

Small margins of error with high levels of confidence will require _________.

A)a small number of observations
B)a large number of observations
C)discrete data
D)a large population

Question 39

The larger the level of confidence,C,the ______ the confidence interval.

A)smaller
B)larger
C)None of the above

Question 40

Since confidence intervals are based on the sampling distribution of the sample mean,it is possible to form confidence intervals when sampling from slightly skewed distributions due to the central limit theorem.

Question 41

Suppose a study was done to determine if the average amount of sleep that students get the day before an exam is less than 6 hours.An SRS of 100 students from a university was taken and a mean of 5.5 hours was computed from the sample.The figure below provides the results of the analysis. What is the value of the test statistic?

A)-2.5
B)0
C).006
D)This can't be determined from the given information.

Question 42

Suppose a study was done to determine if the average amount of sleep that students get the day before an exam is less than 6 hours.An SRS of 100 students from a university was taken and a mean of 5.5 hours was computed from the sample.The figure below provides the results of the analysis. What is the P-value?

A)-2.5
B)0
C).006
D)This can't be determined from the given information.

Question 43

Suppose we are interested in determining the average amount of money students spend on car maintenance every year.If we obtained 120 SRS of size 100 and constructed an 80% confidence interval for each SRS,we would expect ______ of the confidence intervals to contain the true population mean.

A)96
B)80
C)20
D)24

Question 44

What is needed to compute a margin of error?

A)Sample size,standard deviation,and z*
B)Sample mean,sample size,and z*
C)Sample median,sample mean,and sample size
D)Sample median,sample size,standard deviation,and z*

Question 45

The P-values based on a one-sided alternative hypothesis will always be ______ the P-value based on a two-sided alternative hypothesis on the same data.

A)larger than
B)smaller than
C)the same as

Question 46

The null hypothesis is a statement about the ________.

A)population parameter
B)sample statistics
C)sample mean
D)margin of error

Question 47

When choosing between a one-sided alternative hypothesis and a two-sided alternative hypothesis,you should base the decision on _______.

A)the data
B)the research question
C)the results of the P-value
D)All of the above

Question 48

Confidence intervals are resistant to outliers in the data set.

Question 49

Confidence intervals are useful when trying to estimate _______.

A)unknown parameters
B)known parameters
C)unknown statistics
D)known statistics

Question 50

The P-values based on a two-sided alternative hypothesis will always be ______ the P-value based on a one-sided alternative hypothesis on the same data.

A)larger than
B)smaller than
C)the same as

Question 51

Suppose a study was done to determine if the average amount of sleep that students get the day before an exam is less than 6 hours.An SRS of 100 students from a university was taken and a mean of 5.5 hours was computed from the sample.The figure below provides the results of the analysis. The alternative hypothesis is ________.

A)one-sided
B)two-sided
C)three-sided
D)four-sided

Question 52

A 95% confidence interval was computed to estimate a population mean of 10.The resulting confidence interval is (5,15).Does this appear to be a valid confidence interval?

A)Yes,the population mean is in the center of the interval.
B)No,the interval is too wide for a 95% confidence interval.
C)No,the population mean should not be in the interval.
D)It can't be determined from the given information.

Question 53

What is needed to compute a sample size,n,to obtain a confidence interval with a specified margin of error,m?

A)Standard deviation,m,and z*
B)Sample mean,Standard deviation,m,and z*
C)m and z*
D)Population mean,standard deviation,m,and z*

Question 54

The margin of error in a confidence interval is necessary to account for _________.

A)random sampling errors
B)undercoverage
C)nonresponse
D)design errors

Question 55

You perform 2000 significance tests using a significance level,,of 0.10.Assume that all of the null hypotheses for the 2000 significance tests are true.How many of the 2000 significance tests would be statistically significant?

A)200
B)1800
C)2000
D)0

Question 56

Suppose a study was done to determine if the average amount of sleep that students get the day before an exam is less than 6 hours.An SRS of 100 students from a university was taken and a mean of 5.5 hours was computed from the sample.The figure below provides the results of the analysis. What is the alternative hypothesis?

A)H_a:  = 6
B)H_a:  < 6
C)H_a:  < 5.5
D)H_a:  = 5.5
E)H_a:  > 6

Question 57

A test of significance can be used to test differences in categorical data.

Question 58

Confidence intervals are based on the ________ distribution.

A)sampling
B)population
C)uniform
D)None of the above

Question 59

When computing P-values,if the P-value is smaller than the significance level ,we say the results are _________.

A)Normal
B)important
C)statistically significant
D)statistically beneficial

Question 60

A 95% confidence interval was computed around a sample mean of 10.The resulting confidence interval is (5,11).Does this appear to be a valid confidence interval?

A)Yes,the confidence interval includes the sample mean.
B)Yes,the confidence interval is small enough to be a 95% confidence interval.
C)No,the confidence interval should be symmetric around the sample mean.
D)No,the confidence interval cannot contain the sample mean.

Question 61

When performing significance tests at level ,if the P-value obtained is _____ ,the null hypothesis will be rejected.

A)larger than
B)smaller or the same as
C)None of the above

Question 62

Suppose a study was done to determine if the average amount of sleep that students get the day before an exam is less than 6 hours.An SRS of 100 students from a university was taken and a mean of 5.5 hours was computed from the sample.The figure below provides the results of the analysis. Suppose the alternative hypothesis is H_a:   6.What would be the P-value?

A).006
B).012
C)-2.5
D)5

Question 63

The ____ the P-value,the stronger the evidence against the null hypothesis provided by the data.

A)larger
B)smaller

Question 64

When we state the alternative hypothesis to look for a difference in a parameter in one direction,we are doing a _____.

A)one-sided test
B)two-sided test
C)None of the above

Question 65

Suppose a study was done to determine if the average amount of sleep that students get the day before an exam is less than 6 hours.An SRS of 100 students from a university was taken and a mean of 5.5 hours was computed from the sample.The figure below provides the results of the analysis. Suppose the alternative hypothesis is H_a:   6.Would the null hypothesis be rejected at the .01 level?

A)Yes
B)No

Question 66

Suppose a study was done to determine if the average amount of sleep that students get the day before an exam is less than 6 hours.An SRS of 100 students from a university was taken and a mean of 5.5 hours was computed from the sample.The figure below provides the results of the analysis. Based on the results,the null hypothesis would ______ at the .10 significance level.

A)be rejected
B)not be rejected

Question 67

The results obtained from a test of significance can always be trusted as long as the data collection methods are correct.

Question 68

When performing significance tests at level ,if the P-value obtained is _____ ,the null hypothesis will not be rejected.

A)larger than
B)smaller than
C)the same as
D)None of the above

Question 69

The results obtained from a test of significance can always be trusted as long as you use a random sample.

Question 70

Suppose a study was done to determine if the average amount of sleep that students get the day before an exam is less than 6 hours.An SRS of 100 students from a university was taken and a mean of 5.5 hours was computed from the sample.The figure below provides the results of the analysis. Suppose the alternative hypothesis is H_a:   6.Would the null hypothesis be rejected at the .05 level?

A)Yes
B)No

Question 71

Suppose a study was done to determine if the average amount of sleep that students get the day before an exam is less than 6 hours.An SRS of 100 students from a university was taken and a mean of 5.5 hours was computed from the sample.The figure below provides the results of the analysis. What is your conclusion based on the results of this study? (Assume a significance level of .05. )

A)On average,students typically get less than 6 hours of sleep the day before an exam.
B)On average,students typically get 6 hours of sleep the day before an exam.
C)On average,students typically get more than 6 hours of sleep the day before an exam.
D)On average,students typically get 5.5 hours of sleep the day before an exam.

Question 72

Suppose a study was done to determine if the average amount of sleep that students get the day before an exam is less than 6 hours.An SRS of 100 students from a university was taken and a mean of 5.5 hours was computed from the sample.The figure below provides the results of the analysis. Based on the results,the null hypothesis would ______ at the .05 significance level.

A)be rejected
B)not be rejected

Question 73

The null and alternative hypotheses are stated in terms of the statistics from the random sample.

Question 74

The results obtained from a test of significance can always be trusted as long as there are no outliers in the data.

Question 75

When we state the alternative hypothesis to look for a difference in a parameter in any direction,we are doing a _____.

A)one-sided test
B)two-sided test
C)None of the above

Question 76

Given that a test of significance was done for a one-sided test and the P-value obtained was 0.02,what would be the P-value for a two-sided significance test?

A)0.02
B)0.04
C)0.01
D)0

Question 77

Given that a test of significance was done for a two-sided test and the P-value obtained was 0.02,what would be the P-value for a one-sided significance test?

A)0.02
B)0.04
C)0.01
D)0

Question 78

The P-value obtained from a two-sided significance test will be twice as the large as the P-value that would come from the same one-sided test.

Question 79

Confidence intervals and two-sided significance tests are linked in the sense that a two-sided test at a significance level  can be carried in the form of a confidence interval with confidence level 1 - .

Question 80

Suppose a study was done to determine if the average amount of sleep that students get the day before an exam is less than 6 hours.An SRS of 100 students from a university was taken and a mean of 5.5 hours was computed from the sample.The figure below provides the results of the analysis. What is the null hypothesis?

A)H₀:  = 6
B)H₀:  = 5.5
C)H₀:  > 6
D)H₀:  < 6
E)H₀:  < 5.5