# MATHEMATICS

**7.** TABLE 12-2

Many companies use well-known celebrities as spokespersons in their TV advertisements. A study was conducted to determine whether brand awareness of female TV viewers and the gender of the spokesperson are independent. Each in a sample of 300 female TV viewers was asked to identify a product advertised by a celebrity spokesperson. The gender of the spokesperson and whether or not the viewer could identify the product was recorded. The numbers in each category are given below.

Referring to Table 12-2, at 5% level of significance, the critical value of the test statistic is:

[removed]A) 3.8415

[removed]B) 13.2767

[removed]C) 5.9914

[removed]D) 9.4877

**8.** TABLE 12-18

An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants all 3 varieties of the seeds on each of 5 different patches of fields. She then measures the crop yield in bushels per acre. Treating this as a randomized block design, the results are presented in the table that follows.

Referring to Table 12-18, the null hypothesis for the Friedman rank test is

[removed]A) *H*_{0}: *M*_{Field1} = *M*_{Field2} = *M*_{Field3} = *M*_{Field4} = *M*_{Field5}

[removed]B) *H*_{0}: *M*_{Smith} = *M*_{Walsh} = *M*_{Trevor}

[removed]C) *H*_{0}: *μ*_{Field1} = *μ*_{Field2} = *μ*_{Field3} = *μ*_{Field4} = *μ*_{Field5}

[removed]D) *H*_{0}: *μ*_{Smith} = *μ*_{Walsh} = *μ*_{Trevor}

**9.** TABLE 12-10

Parents complain that children read too few storybooks and watch too much television nowadays. A survey of 1,000 children reveals the following information on average time spent watching TV and average time spent reading storybooks.

Average time spent reading story books

Average time spent watching TV | Less than 1 hour |
Between 1 and 2 hours |
More than 2 hours |

Less than 2 hours | 90 | 85 | 130 |

More than 2 hours | 655 | 32 | 8 |

Referring to Table 12-10, we want to test whether there is any relationship between average time spent watching TV and average time spent reading storybooks. Suppose the value of the test statistic was 164 (which is not the correct answer) and the critical value was 19.00 (which is not the correct answer), then we could conclude that

[removed]A) there is no connection between time spent reading storybooks and time spent watching TV.

[removed]B) there is connection between time spent reading storybooks and time spent watching TV.

[removed]C) more time spent watching TV leads to less time spent reading storybooks.

[removed]D) more time spent reading storybooks leads to less time spent watching TV.

**10.** TABLE 12-3

A computer used by a 24-hour banking service is supposed to randomly assign each transaction to one of 5 memory locations. A check at the end of a day’s transactions gave the counts shown in the table for each of the 5 memory locations, along with the number of reported errors.

The bank manager wanted to test whether the proportion of errors in transactions assigned to each of the 5 memory locations differ.

Referring to Table 12-3, the critical value of the test statistic at 1% level of significance is:

[removed]A) 13.2767

[removed]B) 7.7794

[removed]C) 23.2093

[removed]D) 20.0902

**11.** When testing for independence in a contingency table with 3 rows and 4 columns, there are ________ degrees of freedom.

[removed]A) 12

[removed]B) 5

[removed]C) 7

[removed]D) 6

**12.** TABLE 13-1

A large national bank charges local companies for using their services. A bank official reported the results of a regression analysis designed to predict the bank’s charges (*Y*)—measured in dollars per month—for services rendered to local companies. One independent variable used to predict the service charge to a company is the company’s sales revenue (*X*)—measured in millions of dollars. Data for 21 companies who use the bank’s services were used to fit the model:

*E*(*Y*) = *β*_{0} + *β*_{1}*X*

The results of the simple linear regression are provided below.

= -2,700 + 20*X*, S* _{YX}* = 65, two-tailed

*p*value = 0.034 (for testing

*β*

_{1})

Referring to Table 13-1, interpret the estimate of σ, the standard deviation of the random error term (standard error of the estimate) in the model.

[removed]A) For every $1 million increase in sales revenue, we expect a service charge to increase $65.

[removed]B) About 95% of the observed service charges equal their corresponding predicted values.

[removed]C) About 95% of the observed service charges fall within $130 of the least squares line.

[removed]D) About 95% of the observed service charges fall within $65 of the least squares line.

**13.** In a simple linear regression problem, *r* and *b*_{1}

[removed]A) must have opposite signs.

[removed]B) may have opposite signs.

[removed]C) must have the same sign.

[removed]D) are equal.