Class Examples                                                           Confidence Intervals

 

1)  Compute the critical value  Zα/2 that corresponds to a  94 % level of confidence.

 

A) 1.96          B) 1.645        C)  1.88         D)  2.33

 

2)  In a sample of 10 randomly selected women, it was found that their mean height was 63.4 inches. From previous studies, it is assumed that the standard deviation,  s = 2.4. Construct the 95% confidence interval for the population mean.

 

A) (60.8, 65.4)        B) (58.1, 67.3)      C)  (61.9, 64.9)            D)  (59.7, 66.5)

 

3)  A random sample of 40 students has a mean annual earnings of $3120 and a population standard deviation of $677. Construct the confidence interval for the population mean,   if    α  = 0.05.

 

A) ($1987, $2346)     B)  ($210, $110)         C)  ($2910, $3330)      D)  ($4812, $5342)

 

4)  A group of 49 randomly selected students has a mean age of 22.4 years with a population standard deviation of 3.8. Construct a 98% confidence interval for the population mean.

 

A) (19.8, 25.1)       B)  (21.1, 23.7)        C)  (18.8, 26.3)          D)  (20.3, 24.5)

 

5)  In a random sample of 60 computers, the mean repair cost was $150 with a population standard deviation of $36. Construct a 99% confidence interval for the population mean.

 

A) ($138, $162)        B)  ($238, $274)       C)  ($537, $654)        D)   ($18, $54)

 

6)  In a recent study of 42 eighth graders, the mean number of hours per week that they watched television was 19.6 with a population standard deviation of 5.8 hours. Find the 98% confidence interval for the population mean.

                                A) (17.5, 21.7)       B)  (18.3, 20.9)       C)  (14.1, 23.2)            D)  (19.1, 20.4)

 

7)  A 90% confidence interval for the mean percentage of airline reservations being canceled on the day of the flight is (3.2 %, 7 %). What is the point estimator of the mean percentage of reservations that are canceled on the day of the flight?

                                                           A) 3.50%     B)  1.90%      C)  3.8%           D)  5.10%

 

8)  Suppose a  90% confidence interval for μ turns out to be ( 110,  260). Based on the interval, do you believe the average is equal to  270?

 

A) Yes, and I am 100% sure of it.            B)  Yes, and I am  90% sure of it.                           C) No, and I am  90% sure of it.               D)  No, and I am 100% sure of it.

 

9)  A random sample of  120 students has a test score average with a standard deviation of  9.1. 

Find the margin of error if  α =  0.10   

                                

                    A) 0.12        B)  0.83             C)  0.75            D)  1.37

 

10)  A nurse at a local hospital is interested in estimating the birth weight of infants. How large a sample must she select if she desires to be  90% confident that the true mean is within  4 ounces of the sample mean? The standard deviation of the birth weights is known to be  6 ounces.

                     A) 7        B)  2         C)  6       D)  3

 

11)  The grade point averages for 10 randomly selected students in a statistics class with 125 students are listed below.

 

                            2.0    3.2    1.8    2.9    0.9    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) The width decreases.                    B) It is impossible to tell without more information.

C) The width remains the same.       D) The width increases.

 

12)  B = 3,  s2 = 60,  (1 - α) = .95.          Find the sample size needed to estimate μ.

 

A) 77      B)  26               C)  19            D)  1537

 

13)  Suppose a  98 % confidence interval for μ  turns out to be  (1000, 2100). If this interval was based on a sample of size        n =  19 explain what assumptions are necessary for this interval to be valid.

 

A) The sampling distribution must be biased with  18 degrees of freedom.

B) The sampling distribution of the sample mean must have a normal distribution.

C) The population must have an approximately normal distribution.

D) The population of salaries must have an approximate t distribution.

 

14) The principal at Lakewood Elementary would like to estimate the mean length of time each  day that it takes all the buses to arrive and unload the students. How large a sample is needed if the principal would like to assert with 90% confidence that the sample mean is off by, at most, 7 minutes.  Assume s = 14 minutes.

 

15)  Find the critical t-value that corresponds to α = 0.01 and n = 10.

 

A) 2.262              B)  1.833          C)  2.2821            D)  3.250

 

16)  Find the critical t-value that corresponds to α = 0.10 and n = 15.

 

A) 2.145    B)  1.345       C)  2.624         D)  1.761

 

17)  Construct a 95% confidence interval for the population mean, μ. Assume the population has a normal distribution. A sample of 20 college students had mean annual earnings of $3120 with a standard deviation of $677.

               A) ($2135, $2567)       B)  ($2657, $2891)        C)  ($2803, $3437)            D)  ($1324, $1567)

 

18)  Construct a 95% confidence interval for the population mean, μ. Assume the population has a normal distribution. A sample of 25 randomly selected students has a mean test score of 81.5 with a standard deviation of 10.2.

                            A) (87.12, 98.32)     B)  (66.35, 69.89)     C)  (77.29, 85.71)        D)  (56.12, 78.34)

 

19)  Construct a 99% confidence interval for the population mean, μ. Assume the population has a normal distribution. A group of 19 randomly selected students has a mean age of 22.4 years with a standard deviation of 3.8 years.

 

                          A) (18.7, 24.1)      B)  (19.9, 24.9)      C)  (16.3, 26.9)          D)  (17.2, 23.6)

 

20)  A random sample of 10 parking meters in a beach community showed the following incomes for a day. Assume the incomes are normally distributed.

 

$3.60       $4.50     $2.80      $6.30     $2.60     $5.20    $6.75     $4.25      $8.00    $3.00

 

Find the 95% confidence interval for the true mean.

 

A) ($2.11, $5.34)      B)  ($1.35, $2.85)      C)   ($4.81, $6.31)               D)  ($3.39, $6.01)

 

21)  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) ($487.31, $563.80)                         B)  ($238.23, $326.41)

                   C) ($513.17, $860.33)                          D)  ($326.21, $437.90)

 

22)  A survey of 100 fatal accidents showed that  43 were alcohol related. Find a point estimate for p, the population proportion of accidents that were alcohol related.

 

A) 0.301                        B)  0.43              C)  0.57               D)  0.754

 

23)  A survey of  2290 golfers showed that  306 of them are left-handed. Find a point estimate for p, the population proportion of golfers that are left-handed.

 

A) 0.866                   B)  0.118                  C)  0.154                         D)  0.134

 

24)  Many people think that a national lobby's successful fight against gun control legislation is reflecting the will of a minority of Americans. A random sample of 4000 citizens yielded  2280 who are in favor of gun control legislation. Find the point estimate for estimating the proportion of all Americans who are in favor of gun control legislation                                                                                                                             

 

A) 4000          B)  0. 4300               C)  0. 5700                  D)  2280

 

25)  A survey of  400 non-fatal accidents showed that  141 involved the use of a cell phone. Construct a 99% confidence interval for the proportion of fatal accidents that involved the use of a cell phone.

 

26)  An article a Florida newspaper reported on the topics that teenagers most want to discuss with their parents. The findings, the results of a poll, showed that 46% would like more discussion about the family's financial 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 discussions about school. Use a  99% confidence level.

 

A) .37 .053                                 B)  .63   .002                 C)  .37 .002                      D)  .63 .053

 

27)  A university dean 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 receiving financial aid. Use a  98% confidence interval to estimate the true proportion of students on financial aid.

 

A) .59 .564                   B)  .59 .006                 C)  .59 .081           D)  .59 .003

 

 

28)  A pollster wishes to estimate the proportion of United States voters who favor capital punishment. 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  2%?

 

A) 1692                   B)  3383                 C)  21                               D)  1024

 

29)  A researcher wishes to estimate the number of households with two cars. How large a sample is needed in order to be  98% confident that the sample proportion will not differ from the true proportion by more than  5%? A previous study indicates that the proportion of households with two cars is  20%.

 

A) 246                        B)  435                           C)  348                              D)  7

 

30)  A confidence interval was used to estimate the proportion of statistics students that are female. A random sample of 72 statistics students generated the following confidence interval:  (0.438, 0.642).

 Using the information above, what size sample would be necessary if we wanted to estimate the true proportion to within  5% using  95% reliability?

 

A) 385                   B)  382                      C)  400                           D)  369

 

                                              Answers

1)  C   2)  C   3)  C    4)  B   5)  A    6)  A    7)  D   8)  C   9)  D   10)  A  11)  A   12)  B   13)  C   14)  11   15)  D   16)  D      17)  C   18)  C   19)  B    20)  D  21)  C    22)  B    23)  D    24)  C    25)  ( 0.291,  0.414)    26)  A     27)  C    28)  A  29)  C     30)  B