MAS291

Suppose that n = 100 random samples of water from a fresh water lake were taken and the calcium concentration measured. The 95% confidence interval on the mean calcium concentration is (0.49 ; 0.82). Which of the following statement is true (i) the 99% confidence interval from the same sample data is longer. (ii) the sample mean is 0.655 (iii) There is a 95% chance that the true mean calcium concentration is between 0.49 and 0.82

(i) and (iii)

The mean pull-off force of a connector depends on cure time. State the null and alternative hypotheses used to demonstrate that the pull-off force is below 25 newtons (i) >25 ; =25 (ii) =25 ; >25 (iii) = 25 ; < 25 (iv) <25 ; = 25

(iii) = 25 ; < 25

To test the null hypothesis H0: m = 1000 H1: m < 1000 alpha = 0.01 a random sample of n = 17 observations is selected from a normal population. Specify the rejection region. (i) t0 < 2.921 (ii) t0 < -2.583 (iii) t0 < 2.583 (iv) t0 < -2.921

(iii) t0 < 2.583

The data below are the temperatures on randomly chosen days during a summers class and the number of absences on those days. Find the equation for the regression line for the given data X 73 85 91 Y 3 8 10 (i) y = 0.274X + 0.449 (ii) y = 0.449X + 30.27 (iii) y = 0.532X - 0.449 (iv) y = 0.393X - 25.067

(iv) y = 0.393X - 25.067

Suppose we want to test H0: m = 0.80 H1: m ≠ 0.80 alpha = 0.05 Specify the rejection region assuming that the sample size will be sufficient to guarantee the approximate normality of the sampling distribution of X. Let Z0.05 = 1.645 and Z0.025 = 1.96 (i) Z0 < -1.645 (ii) Z0 > 1.96 (iii) |Z0| > 1.645 (iv) |Z0| > 1.96

(iv) |Z0| > 1.96

The grade point averages for 10 randomly selected students in a statistic class with 125 students are listed below 2.0 3.2 1.8 2.9 4.0 3.3 2.9 3.6 0.8 What is the effect on the width of the confidence interval if the sample size is increased to 20? A. It is impossible to tell without more information B. The width decreases. C. The width remains the same D. The width increases

A

A local bank needs information concerning the checking account balances of its customers. A random sample of 15 accounts was checked. The mean balance was 686.75 with a standard deviation of 256.20. Find a 98% confidence interval for the true mean. Assume that the account balances are normally distributed. A. ( 513.17 , 860.33 ) B. None of the other choices is correct C. ( 487.31 , 563.80 ) D. ( 238.23 , 326.41 ) E. ( 326.21 , 437.90 )

A. ( 513.17 , 860.33 )

An article reported on the topics that teenagers most want to discuss with their parents. The findings, the result of a poll, showed that 33% would like more discussion about family's finacial situation, 37% would like to talk about school, and 30% would like to talk about religion. These and other percentages were based on a national sampling of 549 teenagers. Estimate the proportion of all teenagers who want more family discussion about school. Use a 99% confidence level. A. 0.317 ; 0.423 B. 0.628 ; 0. 632 C. 0.577 ; 0.683 D. 0.368 ; 0.372 E. None

A. 0.317 ; 0.423

The following confidence interval is obtained for a population proportion, p: 0.817<p<0.855 . Use these confidence interval limits to find the point estimate of p. A. 0.836 B. NONE C. 0.817 D. 0.839 E. 0.833

A. 0.836

A police authority conducts as eight week experiment. In each week it records the number of foot patrole x, madwe in a ... towns and the number of reported crime y, in that town. The data are summarized as follows ... Estimate the correlation coefficient

Anh cua thao linh cau 2 mo` ko co dap an

Suppose a 95% confidence interval for m turn out tobe (1000 ; 2000). Give a definition of what it mean to be 95% confident in an inference. A. 95% of the observations in the entire population fall in the given interval. B. In repeated sampling. 95% of the intervals constructed would contain the population mean. C. 95% of the observations in the sample fall in the given interval D. In repeated sampling, the population parameter would fall in the given interval 95% of the time.

B

When calculating a confidence interval for the standard deviation, which distribution is used? A. Student's t-distribution B. Chi-square distribution C. Normal distribution D. Binomial distribution

B

Which of the following statements is false? A. Other things being equal, as the confidence level for a confidence interval increases, the width of the interval increases. B. A population parameter is used to estimate a confidence interval C. A point estimate consists of a single sample statistic that is used to estimate the true population parameter. D. None of the other choices is correct

B

Find the value the test statistic to test the claim that less than 50% of the people following a particular diet will experience increased energy. Of 100 randomly selected subjects who followed the diet, 47 noticed an increase in their energy level A. 1.21 B. -0.60 C. -3.47 D. NONE E. 1.65

B. -0.60

A random sample of 150 students has a grade point average with a mean of 2.86. Assume the population standard deviation is 0.78. Construct the confidence interval for the population mean. Use a 98% confidence level. A. 2.31 ; 3.88 B. 2.71 ; 3.01 C. NONE D. 2.51 ; 3.53 E. 2.43 ; 3.79

B. 2.71 ; 3.01

It is believed that, the average numbers of hours spent studying perday during undergraduate education should have the possitive linear relationship with the starting salary..... ANOVA The error sum of squares (SSe) of the above agression is A. 1.8782 B. 92.0326 C. 427.0798 D. 335.0472 E. none

B. 92.0326

A sample of 250 accidents showed that 140 were caused by drunk driving. Let Z0.025 = 1.96, Z0.05 = 1.645. Use the data to test H0: p = 0.5 with α = 0.05 the result is ____________ A. Reject H0 B. Fail to reject H0 C. Not determined D. None of the other choices is correct

B. Fail to reject H0

You are interested in the retation between the number of years working for a particular company and income. You survey 80 workers at this company and figure a correlation between these two variables of -0.97. This is considered a ___________ : A. weak negative linear correlation B. strong negative linear complation C. Strong possitive linear correlation D. Weak possitive linear correlation

B. Strong negative linear complation

The weight and blood pressure of 4 random selected woman in age 25-30 are shown in following table: Weight 60 45 58 53 BP 125 100 110 100 Which following statement is true about this sample? A. r = 0.802, negative correlation B. r = 0.802, positive correlation C. r = -0.802, positive correlation D. NONE E. r = -0.802, negative correlation

B. r = 0.802, positive correlation

Past experience indicates that the time for high school seniors to complete a standardized test is a normal random variable with a mean of 35 minutes. If a random sample of 20 high school seniors took nan average of 33.1 minutes to complete this test wih a standard deviation of 4.3 minutes, test the hypothesis at the 0.025 level of significance that μ = 35 minutes against the alternative that μ < 35 minutes. Let t0.025,19 = 2.09 . A. t0 = -1.98, reject H0 B. t0 = -1.98, fail to reject H0 C. t0 = -0.099, reject H0 D. t0 = -0.099, fail to reject H0 E. none of the other choices is correct

B. t0 = -1.98, fail to reject H0

A researcher at a major hospital wishes to estimate the proportion of the adult population of the United States that has high blood pressure. How large a sample is need in order to be 99% confident that the sample proportion will not differ from the true proportion by more than 4%? Let Z0.005 = 2.575 A. 849 B. None of the other choices is correct C. 1037 D. 17 E. 2073

C

A major department store chain is interested in estimating the Average amount its credit card customers spent on their first visit to the chain's new store in the mall. Fifty credit card accounts were randomly sampled and analyzed with the mean 80$. Construct a 95% confidence interval for the average amount tis credit card customers spent on their first visit to the chain's new store in the mall, assuming that the amount spent follows a normal distribution with the population standard deviation of 20$. Let Z0.025 = 1.96 ; t0.025,49 = 2.01 ; Z0.05 = 1.65 ; t0.05,49 = 1.68 A. ( 74.31 ; 85.69 ) B. ( 75.33 ; 84.67 ) C. ( 74.46 ; 85.54 ) D. ( 75.25 ; 84.75 ) E. None of the other choices is correct

C. ( 74.46 ; 85.54 )

Expedia would like to test the hypothesis that the propotion of United Airline flights that arive on-time is less than 0.80. A random sample of 110 United Airline flights found that 82 arrived on-time. Expedia would like to set the significant level to be 0.02. The test statistic for the hypothesis test would be ___________ A. -2.30 B. -1.87 C. -1.43 D. -2.77 E. None

C. -1.43

Listed below are the top 10 salaries ( in millions of dollars ) of television personalities in a recent year 38 36 35 27 15 13 12 10 9.6 8.4 We want to construct a 98% two-sided confidence tinterval on the variance, find the critical value. A. 2.09 B. 19.68 and 2.53 C. 21.67 and 2.09 D. None of the other choices is correct E. 19.68

C. 21.67 and 2.09

The mean replacement time for a random sample of 12 microwave ovens is 8.6 years with a standard deviation of 2.7 years. Construct the 98% confidence interval for the population variance. Assume the data are normally distributed. A. 1.8 ; 5.1 B. NONE C. 3.2 ; 26.3 D. 3.1 ; 22.5 E. 1.2 ; 9.7

C. 3.2 ; 26.3

Which of the following is FALSE about the slope of regression line? A. The slope of estimated regression line is an unbiased estimator for the slope of population regression line B. The slope of estimated regression line has Student's t distribution with degree of freedom n-2 C. The slope of estimated regression line has Student's t distribution with degree of freedom n-1

C. n-1

In a regression analysis if SSe = 180 and SSr = 450 then the coefficient of determination is ________ A. 0.7 B. 0.3 C. None D. 0.6 E. 0.4

Chua co

Entertainment Software Association would like to test if the standard deviation for the age of gamers is equal to 5.0 years. The standard deviation for the age from a random sample of 20 gamers is 5.6 years . Using the significance level of 0.10 , fidn the upper percentage point for this hypothesis test. Let X... = 30.114 ; X... = 10.117 ; X... = 11.651 ; X.... = 27.204 A. none of B. 11.651 C. 30.144 D. 27.204 E. 10.117

Chua co ( cau 14/15 de thaolin)

A restaurant claims that the standard deviation of the waiting time in line is less than 1.2 minutes. A random sample of 35 customers has a mean of 5.4 minutes with a standard deviation of 1.1 minute. Find the test statistic to test the restaurant's claim at teh significant level of 0.1. A. 13.4 B. 22.5 C. 12.8 D. 28.6 E. NONE

Chua co dap an

Construct a 95% confidence interval for the population standard deviation of a random sample of 15 men who have a mean weight of 165.2 pounds with a standard deviation of 10.3 pounds. Assume the population is normally distribute A. ( 2.3 ; 5.1 ) B. ( 7.9 ; 15.0 ) C. ( 7.5 ; 16.2 ) D. None of thje other choices is correct E. ( 56.9 ; 263.9 )

Chua co dap an

In a sample of 10 randomly selected woman, it was found that their mean height was 63.4 inches. From previous studies, it is assumed that the standard deviation of the population is 2.4 inches. Construct the 95% confidence interval for the population mean. A. 58.1 ; 67.3 B. None C. 60.8 ; 65.4 D. 59.7 ; 56.5 E. 61.9 ; 64.9

Chua co dap an ( 12/15 tlin)

The National Center for Education Statistics would like to test the hypothesis that the proportion of Bachelor's degrees that were earned by women equals 0.90 . A random sample of 140 college graduates wich bachelor degrees found that 75 were women. The National Center for Education Statistics would like to set the significant level to be 0.10 . What is the value of the test statistic for this hypothesis test ? A. None B. -1.55 C. -1.21 D. 1.43 E. 2.18

Chua co dap an ( cau 15/15 thaolin)

An article described a study of investigating the relationship between the age (x) and length (y) of 5 captured dugongs: x 1.0 1.5 1.5 2.5 4.0 y 1.80 1.85 1.87 2.02 2.27 Find the best point estimate of the y-intercept of regression line between x and y A. 0.1595 B. 0.9962 C. 0.1455 D. None of the other choices is correct E. 1.6271

D

If an economist wishes to determine whether there is evidence that average family income in a community exceeds $25000 _______________ A. a two-tailed test should be ultilized B. either a one-tailed or two-tailed test could be used with equivalent results. C. None of the other choices is correct D. a one-tailed test should be ultilized

D

In an effort to estimate the mean dollars spent per visit by customers of a food store, the manager has selected a random sample of 100 cash register receipts. The mean of these was $45.67 with a sample standard deviation equal to $12.30. assuming that he wants to develop a 90 percent confidence interval estimate, which of the follwing is the width of confidence interval that will be reported? A. About 1.43 B. About 1.645 C. None of the other choices D. About 4.04 E. Nearly $50.20

D

Suppose you want to test the claim that μ ≠ 3.5 . Given a sample size of n = 41 and a level of significance of alpha = 0.10, when should you reject H0 ? Let Z0.025 = 1.96 ; Z0.005 = 2.575 ; Z0.05 = 1.645 ; Z0.01 = 2.33 A. Reject H0 if the standardized test statistic is greater than 2.575 or less than -2.575 B. NONE C. Reject H0 if the standardized test statistic is greater than 1.96 or less than -1.96 D. Reject H0 if the standardized test statistic is greater than 1.645 or less than -1.645 E. Reject H0 if the standardized test statistic is greater than 2.3 or less than -2.33

D

Suppose you want to test the claim that μ≠31.5 , with known sigma, if the sample size is n = 81 and the level of significance α = 0.1 , when should you reject H0? Let Z0,005 = 2.575 ; Z0,01 =2.33 ; Z0.025 = 1.96 and Z0.05 = 1.645 : A. Reject H0 if the test statistic is greater than 2.33 or less than -2.33. B. None of the other choices is correct. C. Reject H0 if the test statistic is greater than 2.575 or less than -2.575. D. Reject H0 if the test statistic is greater than 1.645 or less than -1.645. E. Reject H0 if the test statistic is greater than 1.96 or less than -1.96.

D

The height y and base diameter X of four trees of a certain variety produced the following data x 2 2 3 5 y 31 36 94 127 Compute the correlation coefficient A. 0.899 B. 0.245 C. 0.764 D. 0.948 E. NONE

D. 0.948

The grade point averages for 10 randomly selected high school students are listed below, which implies a sample mean of 2.54 and a sample standard deviation of 1.11. Assume the grade point averages are normally distributed. 2.0 3.2 1.8 2.9 4.0 3.3 2.9 3.6 0.8 Find a 98% confidence interal for the true mean. A. 0.67 ; 1.81 B. 3.11 ; 4.36 C. 2.12 ; 3.14 D. 1.55 ; 3.53 E. NONE

D. 1.55 ; 3.53

Suppose we have the following information from a simple regression n=20 ; Σx = 23.92 ;Σy = 1943.21; Σy^2 = 170044.5321; Σx^2 = 29.2892 . Find the total sum of squares,SSt : A. 1610.53 B. 185.435 C. None of the other choices is correct D. 173.37 E. 198.56

D. 173.37

Medicare would like totest the hypothesis that the average monthly rate for one-bedroom assisted-living facility is equal to $3,300 . A random sample of 12 assisted-living facilities had an average of $3,690 permonth and a standard of $530. It is believed that the monthly rate for one-bedroom .... . Use the significance level of 0.05 for this hypothesis test, what is the critical value? A. 2.761 ; -2.761 B. 1.985 ; -1.985 C. NONE D. 2.201 ; -2.201 E. 1.645 ; -1.645

D. 2.201 ; -2.201

A manufacturer of golf equipment wishes to estimate the number of left-handed golfers. 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%? A previous study indicates that the proportion of left-handed golfers is 10%. Let Z0.025 = 1.96 A. 15 B. none of the other choices is correct C. 241 D. 217 E. 153

D. 217

Given a sample with r = 0.823, n = 10 and α=0.05, determine the standardized test statistic t necessary to test the claim p = 0. A. 3.816 B. None of the other choices is correc C. 1.782 D. 4.098 E. 2.891

D. 4.098

A golfer would like to test the hypothesis that the variance of his golf score equals 12.0 . A random sample of 25 rounds of golf had a sample standard deviation of 4.6 . The test statistic for this hypothesis test would be ____________: A. 45.66 B. 30.15 C. 12.57 D. 42.32 E. None of the other choices is true

D. 42.32

A random sample of 16 fluorescent light bulbs has a mean life of 645 hours with a standard deviation of 31 hours. Construct a 95% confidence interal for the population mean. Assume the population has a normal distribution. Let Z0.025 = 1.96 ; Z0.05 = 1.65 t0.025,15 = 2.13 ; t0.05,15 = 1.75 A. 321.7 ; 365.8 B. 876.2 ; 981.5 C. 531.2 ; 612.9 D. None E. 628.5 ; 661.5

E

Find the value of the test statistic X0 based on the given information H0 : sigma^2 = 0.01 ; n = 20 ; S^2 = 0.0153 A. None B. 28.01 C. 30.98 D. 30.27 E. 29.07

E

Lacne walker owns a construcion company and has designed a gazebo. He has estimated the time needed for two employees to build the gazebo to be 14 hours. Lance would like to know if the mean time is less than 14 hours. Fifty gazebos were built, and the sample mean was 12.5 hours. Set up the null and alternative hypotheses for the test. A. (iv) ....H1: m ≠ 12.5 B. None C. (ii) ....H1: m ≠ 14 D. (iii) ....H1: m <12/5 E. (i) ....H1: m < 14

E

Anna collected the scores of a random sample 50 students on the first exam in a certain class and their coreresponding scores on the second exam in that class. Here is computer output on the sample data. ... Assume that all condition for iniferrence have been met. Find the test statistic for testing the null hypothesis that the population y-intercept is 6.5. A. 0.73 B. NONE C. 0.11 D. 2.13 E. 0.38

E. 0.38

A study is to be conducted of the percentage of homeowners who own at least two television sets. how large a sample is required if we wish to be 99% confident that the error in estimating this quantity is less than 0.04? Let Z0.005 = 2.58 and Z0.01 = 2.33 A. 849 B. 848 C. NONE D. 1040 E. 1041

E. 1041

A mail-order firm is interetd in estimating the number of order that need to be processed on a given day from the weight of the mail received. A close monitoring of the mail on 4 randomly selected business days produced the results below. Find the equation of the least squares regression line A. -5 + 0.23X B. -5X - 0.23 C. 5.5X + 0.23 D. None E. 5.5 + 0.23X

E. 5.5 + 0.23X

A random sample of 20 observations was made on the diameter of spot welds and the corresponding weld shear strength. Given thta r = 0.75, what is the critical value if we want to test the hypothesis that H0 p=0 versus H1: p≠0 , use alpha = 0.02. Let t0.01,19 = 2.539 ; t0.01,18 =2.552 ; t0.02,19 = 2.205 ; t0.02,18 = 2.214 A. 2.205 B. None C. 2.214 D. 2.552 E. 2.539

Hai chon C Tuan chon D

A teacher wants to report the most fail rate on a test with 90% confidence, construct the appropriate one-sided confidence interval. Assume that a simple random sample of 58 student results in 6 who fail the test. Let Z0.05 = 1.65 ; Z0.1 = 1.28 A. (ii) p<= 0.052 B. (iv) p >= 0.052 C. (iii) p<= 0.155 D. (i) p >= 0.155 E. none

Hai dap an B Tuan dap an C

Weight of women in one age group are normally distributed with a standard deviation of 13lb. A researcher wishes to estimate the mean weight of all women in this age group. Find how large a sample must be 90 percent confident that the sample mean will will not differ from the population mean by more than 3.5 lb. A. 44 B. None of the other choices is correct C. 38 D. 32 E. 23

Tuan chon C Hai chon D

A university is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are recieiving financial aid. Use a 95% confidence interval to estimate the true proportion of students on financial aid. A. ( 0.588 , 0.592 ) B. ( 0.116 , 1.064 ) C. None of the other choices is correct D. ( 0.585 , 0.595 ) E. ( 0.522 , 0.658 )

Tuan chon E Hai chon D

Find the critical value for a two-tailed test H1: μ ≠ 10 ; alpha = 0.01 ; n = 30 Assume that the data are normally distributed A. 2.33 ; -2.33 B. 1.645 ; -1.645 C. None of the other choices is correct D. 2.756 ; -2.756 E. 1.96 ; -1.96

chua co dap an