STA2221 examples on CI & Testing of Hypothesis Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answer the question Provide an appropriate response. 1) Find the critical value,te for 0.99 and n-10. A) 3.250 B) 3.169 1.833 D) 2.262 2) Find the critical value to forc=0.95 and n=16. A) 2.947 B) 2.602 2120 D) 2.131 3) Find the value of E, the margin of error, for A) 1.69 B) 0.42 0.99, n=16 and s=2.6. C) 1.92 D) 0.48 4) Find the value of A) 1.80 the margin of error, forc=0.90, n=10 and s-3.1. B) 0.57 C) 1.36 D) 1.78 5) Construct the indicated confidence interval for the population mean y using the t-distribution 5 C=0.95, X 645,5 31, n 16 A) (876.2, 9815) B) (321.7,365.8) (628.5, 661.5) D) (531.2. 6129) 6) In a random sample of 28 families, the average weekly food expense was $95.60 with a standard deviation of $22.50. Determine whether a normal distribution or at-distribution should be used or whether neither of these can be used to construct a confidence interval Assume the distribution of weekly food expenses is normally shaped A) Use normal distribution. B) Cannot use normal distribution or t-distribution C) Use the t-distribution 7) For a sample of 20 IQ scores the mean score is 105 8. The standard deviation, a, is 15. Determine whether a normal distribution or a t-distribution should be used or whether neither of these can be used to construct a confidence interval. Assume that IQ scores are normally distributed A) Use the t-distribution B) Carnot use normal distribution or t-distribution C) Use normal distribution ) 8) A random sample of 15 statistics textbooks has a mean price of $105 with a standard deviation of $30.25. Determine whether a normal distribution or at-distribution should be used or whether neither of these can be used to construct a confidence interval. Assume the distribution of statistics textbook prices is not normally distributed A) Use the t-distribution B) Cannot use normal distribution or t-distribution C) Use normal distribution
9 9) Construct a 20% confidence interval for the population mean, . Assume the population has a normal distribution. A sample of 15 randomly selected students has a grade point average of 2.86 with a standard deviation of 0.78 A) (241,342) B) (2.28, 3.66) 2.37, 3.56) D) (2:51, 3.21) 10) 10) Construct a 95% confidence interval for the population mean, Asume the population has a normal distribution. A sample of 25 randomly selected students has a mean best score of 815 with a standard deviation of 10.2. A) (77.29, 85.71) B) (57.12. 98.32) (66.35, 69.99) D) 56.12,78.34) 11) 11) Construct a 95% confidence interval for the population mean, Assume the population has a normal distribution. A random sample of 16 fluorescent light bulbs has a mean life of 665 hours with a standard deviation of 31 hours. A) (321.7,365.8) B) (5762.981.5) (5312.6129) D) ( 5,661.5) SHORT ANSWER. Write the word or phrase that best completes each statement or answer the question. 12) Construct a 95% confidence interval for the population mean, Assume the population has a normal distribution. In a random sample of 25 computers, the mean repair cost was $166 with a standard deviation of $39. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answer the question 13) A random sample of 10 parking meters in a beach community showed the following incomes 13) for a day. Assume the incomes are normally distributed $3.60 $4.50 $2.80 $6.30 $2.60 $5.20 $6.75 54.25 $8.00 $3.00 Find the 95% confidence interval for the true mean A) ($1.35, $2.85) B) (53.39, 56.01) 54.81,5631) D) (52.11, 85.34) 14) 14) The grade point averages for 10 randomly selected high school students are listed below. Assume the grade point averages are normally distributed 20 3.2 18 29 0.9 4.0 3.3 2.9 3.6 0.8 Find a 9% confidence interval for the true mean A) (3.11, 4.35) B) (2.12, 3.14) (0.87,181) D) (1.55,353) 15) Find the critical value and rejection region for the type of t-test with level of significance aand sample size 15) Left-tailed test -0.1, -22 A) - 1.323;">1.323 -1.323.t-1.323 B) to-2518t<-2.518 D) -1.321; -1.321
16) Find the critical value and rejection region for the type of t-test with level of significance sample sien and 16) Right-tailed test, 0.1n-35 A) to 1.307,t<1.307 -2.441;t>2.441 B) to 1306>1.306 D) - 1.307,t>1.30 SHORT ANSWER. Write the word or phrase that best completes each statement or answer the question 17) The number of wins in a season for 32 randomly selected professional football teams 17) are listed below. Construct a 90% confidence interval for the true mean number of wins in a con 99 109 72 11 10 6 4 11 9 88 12 10 7 5 12 6 4 3 12 9 9 7 10 7 7 5 15) 18) The numbers of advertisements seen or heard in one week for 30 randomly selected people in the United States are listed below. Construct a 95% confidence interval for the true mean number of advertisements 598 481 734 494 298 588 441 135 590 595 846 540 728 764 673 690 317 727 684 649 545 486 732 486 735 582 202 677 203 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answer the question 19) Find the critical value and rejection region for the type of t-test with level of significance aand 19) sample sizen. Two-tailed test, 0.05, n-38 A) to -2.024.to - 2.024; <-2.024. 2024 B) to - 2.026;t > 2.026 to -2.026, 02.026t<-2.026,t> 2026 D) to -1.687, 1-1.587;t<-1.687,>1.687 0.01 2 0) 20) Find the standardized test statistict for a sample with n=12. = 31.25 -22 and Hou 30. Round your answer to three decimal places A) 2.001 B) 1.890 2.132 D) 1991
21) 21) Find the standardized test statistict for a sample with n-20, x=69,5-20and a = 0,058 Hau<73. Round your answer to three decimal places A) -0. 872 B )-1265 9 -1.233 D) -0.994 SHORT ANSWER. Write the word or phrase that best completes each statement or answer the question. 22) Test the claim about the population mean y at the level of significance a Assume the 22) population is normally distributed Claim y 24 -0.01. Sample statistics X-25.25 -22, n=12 23) 23) A local group claims that the police issue more than 60 speeding tickets a day in their area. To prove their point, they randomly select two weeks. Their research yields the number of tickets issued for each day. The data are listed below. At a 0.01, test the group's claim 70 48 41 68 69 55 70 57 60 83 32 60 72 58 24) - 24) A local group daims that the police issue more than 60 speeding tickets a day in their area. To prove their point, they randomly select two weeks. Their research yields the number of tickets issued for each day. The data are listed below. Atas 0.02. test the group's claim using confidence intervals. 70 48 41 68 69 55 70 57 60 83 32 60 72 58 25) 25) A local group aims that the police is more than 60 speeding tickets a day in their area. To prove their point, they randomly select two weeks. Their research yields the number of tickets issued for each day. The data are listed below. At a 0.01, test the group's claim using P-values. 70 48 41 68 69 53 70 57 60 3 32 60 72 58 26) 26) A local school district claims that the number of school days missed by its teachers due to illness is below the national average of 5. A random sample of 28 teachers provided the data below. At a 0.05, test the district's claim using P-values 0 3 6 3 3 5 4 1 3 5 7 3 1 2 3 3 2 416 25 28 31 25
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answer the question. 27) When 410 college students were surveyed 150 said they own their car. Find a point estimate 27) for p, the population proportion of students who own their cars. A) 0.634 B) 0.268 0.577 D) 0.366 28) 28) In a survey of 2450 golfers, 15% said they were left-handed. The survey's margin of error was 3%. Construct a confidence interval for the proportion of left-handed golfers. A) (0.12, 0.15) B)(0.12, 0.18) (0.11, 0.19) D) (0.18, 0.21) SHORT ANSWER. Write the word or phrase that best completes each statement or answer the question 29) A survey of 300 fatal accidents showed that 123 were alcohol related. Construct a 98% 29) confidence interval for the proportion of fatal accidents that were alcohol related MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answer the question. 30) 30) A survey of 280 homeless persons showed that 63 were veterans. Construct a 90% confidence interval for the proportion of homeless persons who are veterans A) (0.161, 0.289) B) (0.176, 0.274) (0.167, 0.283) D) (0.184, 0.266) 31) 31) 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 needed in order to be 90% confident that the sample proportion will not differ from the true proportion by more than 5%? A) 271 B) 542 09 D) 166 32) Aprivate opinion poll is conducted for a politician to determine what proportion of the population favors decriminalizing marijuana possession. 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) 13 B) 1201 601 D) 623 33) 33) Determine whether the normal sampling distribution can be used. The claim is p>0.015 and the sample size is n-150 A) Use the normal distribution B) Do not use the normal distribution 31) - 34) Determine whether the normal sampling distribution can be used. The claim is p20.675 and the sample size is n-62 A) Use the normal distribution B) Do not use the normal distribution. SHORT ANSWER. Write the word or phrase that best completes each statement or answer the question 35) Fifty-five percent of registered voters in a congressional district are registered 35) Democrats. The Republican candidate takes a poll to assess his chances in a two-candidate race. He polls 1200 potential voters and finds that 621 plan to vote for the Republican candidate. Does the Republican candidate have a chance to win? Use 0.05.
36) A recent study claimed that at least 15% of junior high students are overweight. Ina sample of 160 students, 18 were found to be overweight. Ifa -0.05, test the daim using P-values. 36) 37) 37) A telephone company claims that 20% of its customers have at least two telephone lines. The company selects a random sample of 500 customers and finds that have two or more telephone lines. Ifa -0.05, test the company's calm using confidence intervals. 38) 38) A local bank claims that the waiting time for its customers to be served is the lowest in the area. A competitor bank checks the waiting times at both banks. Assume the two samples are random and independent. Use -0.05 and a confidence interval to test the local bank's claim Local Bank nj - 45 x1 -5.3 minutes 1-1.1 minutes Competitor Bank m2 50 x2 -5.6 minutes 02-10 minute MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answer the question 39) Construct a 95% confidence interval for 1-42. Assume the two samples are random and 39) independent. The sample statistics are given below. Population statistics: o 2.5 and 02-28 Sample statistics xy - 12, n = 40 and x2 = 13. m2 - 35 A) (-1.673, 1.892) B) (-2,001,-1.873) (-2,209, 0.209) D) (-1.968, 1.561) SHORT ANSWER. Write the word or phrase that best completes each statement or answer the question 40) A researcher wishes to determine whether people with high blood pressure can lower40) their blood pressure by following a certain diet. A treatment group and a control group are selected. Assume the two samples are random and independent. Construct a 90% confidence interval for the difference between the two population means - 42. Would you recommend using this diet plan? Explain your reasoning Treatment Group n - 100 x1 - 178 01 - 35 Control Group n2-100 x2 - 193 0237
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answer the question 41) Construct a 90% confidence interval for H1-H2. Two samples are random, independent, and 41) come from populations that are normally distributed. The sample statistics are given below. Assume that c - o ng - 10 2 -12 x1 - 25 x2 =23 51-1.5 52 -1.9 A) (0.721, 3.279) B) (1.413, 3.124) (1.554, 3.651) D) (1.335, 3.012) 42) Construct a 95% confidence interval for 1-12. Two samples are random, independent, and come from populations that are normally distributed. The sample statistics are given below Assume that o-o 8 m2-7 xy-41x2-55 0.76 52 2.51 A) (2.112, 2.113) B) (-3.406, 0.606) (-1.679, 1.987) D) (-1.132. 1.563) SHORT ANSWER. Write the word or phrase that best completes each statement or answer the question 43) A sports analyst claims that the mean batting average for teams in the American League is not equal to the mean batting average for teams in the National League because a pitcher does not bat in the American League. The data listed below are random, independent, and come from populations that are normally distributed Construct a 95% confidence interval for the difference in the means 1-2. Assume the population variances are equal American League 0.279 0.274 0.271 0.265 0.254 0.240 0.268 National League 0.284 0.267 0.266 0.261 0.259 0.256 0.263 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answer the question 44) Findā. Assume the samples are random and dependent, and the populations are normally - distributed B A 13 11 A) 9,0 11 7 30 8 26 14 18 3 B) 25.2 33.1 D) -51
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 45) Test the claim that the paired sample data is from a population with a mean difference 45) of 0. Assume the samples are random and dependent, and the populations are normally distributed. Use a = 0.05. A B 30 28 28 24 47 25 43 35 31 22
Examples on I, esting of hypothesis Nune MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answer the question Provide an appropriate response. Find the critical values that corresponds to a 9% confidence level A) 1.96 D) 41.545 4 2) Determine the sampling error if the grade point averages for 10 randomly selected students from a class of 125 students has a mean of x=28. Assume the grade point average of the 125 students has a mean of 35 A) -07 5) 0.7 93.15 D) 2.45 Find the margin of error for the given values of c and = 0.98, 0.78, n = 150 A) 0.08 B) 0.15 90.11 D) 0.12 4 5 4) _ 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, Hifc0.98 A) (2.43, 3.79) B) (2.31, 3.88) 92.71,3.01) D) (2.51, 3.53) 5 $) A random sample of 56 fluorescent light bulbs has a mean life of 645 hours. Assume the population standard deviation is 31 hours. Construct a 95% confidence interval for the population mean A) (712.0, 768.0) B) (636.9,653.1) (1120, 1189) D) (539.6, 5512) SHORT ANSWER. Write the word or phrase that best completes each statement or answer the question. 5 In a random sample of 60 computers, the mean repair cost was $150. Asume the population standard deviation is $36. a) Construct the 99% confidence interval for the population mean repair cost. b) If the level of confidence was lowered to 95%, what will be the effect on the confidence interval? MULTIPLE CHOICE. Choose the one alterative that best completes the statement or answer the question 5 The standard IQ test has a mean of % and a standard deviation of 14. We want to be 99% 7) certain that we are within 4 IQ points of the true mean. Determine the required samples A) 82 B) 1 178 D) 10 SHORT ANSWER. Write the word or phrase that best completes each statement or answer the question 54 A certain confidence in interval is 7.75<<9.45. Find the sample mean and the error of estimate E 9
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answer the question In order to efficiently bid on a contract, a contractor wants to be 95% confident that his erroris 9 less than two hours in estimating the average time it takes to install tile flooring Previous contracts indicate that the standard deviation is 5 hours. How large a sample must be selected? A) 4 B) 20 05 D) 19 SHORT ANSWER. Write the word or phrase that best completes each statement or answer the question sle The number of wins in a season for randomly selected professional football teams 10) are listed below. Constructa 90% confidence interval for the true mean number of wins in a n Assume that is 26 999 8 10 9 7 2 11 10 6 4 11 9 88 12 10 7 5 12 6 4 3 12 9 9 7 10 7 7 5 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answer the question. Find the critical value,te forc=0.99 and n=10. A) 1.833 B) 3.169 3.250 D) 2.262 21 58 Find the value of the margin of error, forc=0.99.n16 and s26 A) 048 B) 0.02 91.92 D) 1.69 In a random sample of 28 families, the average weekly food expense was 595.60 with a standard deviation of $22.50. Determine whether a normal distribution or at-distribution should be used or whether neither of these can be used to construct a confidence interval Assume the distribution of weekly food expenses is normally shaped A) Use normal distribution. B) Use the distribution C) Cannot use normal distribution or distribution 14) GO A random sample of 15 statistics textbooks has a mean price of $105 with a standard deviation of $30.25. Determine whether a normal distribution ora distribution should be used or whether neither of these can be used to construct a confidence interval. Assume the distribution of statistics textbook prices is not normally distributed A) Use normal distribution B) Use the I-distribution Cannot use normal distribution or distribution
Find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject Ho for the level of significance a. 22) Two-tailed test Z -1.63 0.05 A) 0.9484; fail to reject Ho 0.1002, fail to reject Ho B) 0.0516; reject HO D) 0.0516fail to reject Ho Find the critical value and rejection region for the type of 2-test with level of significance a. 23) Right-tailed test, a 0.01 A) 20 -1.645, z> 1.645 C) 20 -2.33; z 2.33 B) zo 1.96; 2 > 1.96 D) 20 -2.575: 2 > 2.575 29 Find the critical value and rejection region for the type of 2-test with level of significance a 24 Two-tailed test, 0.01 A)-20-2.33,20 -2.33; 2<-2.33, 2 > 2.33 B) -20 -1.96, zo 1.96; z<-1.96, 2 > 1.96 C) -20 -1.645,29 -1.645, z<-1.645, 1.645 D) - 0 -2.575, 20 - 2.575 z<-2.575, 2 2.575 Test the claim about the population meanu at the level of significance a. Assume the population is normally distributed Claim: >28; a=0.05; 1.2 Sample statistics: x = 28.3, 50 A) Not enough information to decide. B) Reject Ho. There is enough evidence at the 5% level of significance to support the claim Fail to reject Ho. There is not enough evidence at the 5% level of significance to support the claim. 20 Test the claim about the population mean u at the level of significance a. Assume the population is normally distributed Claim 1400 a 0.01; 82 Sample statistics x = 1370,n 35 A) Not enough information to decide. B) Fail to reject Ho. There is enough evidence at the 1% level of significance to support the daim. Reject Ho. There is enough evidence at the 1% level of significance to reject the claim. 7 27) Find the standardized test statistict for a sample with n=12, x= 31.2,s=22, and a =0.01 if Hou 30. Round your answer to three decimal places A) 2.001 B) 1.991 C) 1.890 D) 2.132
We were unable to transcribe this image
SHORT ANSWER. Write the word or phrase that best completes each statement or answer the question. 3) Test the claim about the population meanu at the level of significance a. Assume the 28) population is normally distributed Claimu 24; 0.01. Sample statisties=252, s = 22, n=12 79 Test the claim about the population meanu at the level of significance a. Assume the population is normally distributed. 29) _ Claim > 33; a=0.005. Sample statistics.x = 34, s=3. n=25 30) 96) A local group claims that the police issue more than 60 speeding tickets a day in their area. To prove their point, they randomly select two weeks. Their research yields the number of tickets issued for each day. The data are listed below. At a 0.01, test the group's claim 70 48 41 68 69 55 70 57 60 83 32 60 72 58 31) 70 A local group claims that the police issue more than 60 speeding tickets a day in their area. To prove their point, they randomly select two weeks. Their research yields the number of tickets issued for each day. The data are listed below. At a=0.02, test the group's claim using confidence intervals. 70 48 41 68 69 55 70 57 60 83 32 60 72 58
