quiz 7
The degrees of freedom for a contingency table with 6 rows and 3 columns is
10
Exhibit 10-13 In a completely randomized experimental design involving five treatments, thirteen observations were recorded for each of the five treatments. The following information is provided. SSTR = 200 (Sum Square Between Treatments) SST = 800 (Total Sum Square) Refer to Exhibit 10-13. The number of degrees of freedom corresponding to within treatments is
60
An experimental design where the experimental units are randomly assigned to the treatments is known as
completely randomized design
In the ANOVA, treatment refers to
different levels of a factor
In the hypothesis testing procedure, α is
level of significance
For a sample size of 30, changing from using the standard normal distribution to using the t distribution in a hypothesis test,
will result in the rejection region being smaller
Exhibit 11-6The results of a recent poll on the preference of shoppers regarding two products are shown below. Product Shoppers Surveyed Shoppers FavoringThis Product A 800 560 B 900 612 Refer to Exhibit 11-6. The point estimate for the difference between the two population proportions in favor of this product is
.02
For a two-tailed hypothesis test with a test statistic value of z = 2.05, the p-value i
.0404
Exhibit 11-3In order to determine whether or not a particular medication was effective in curing the common cold, one group of patients was given the medication, while another group received sugar pills. The results of the study are shown below. PatientsCured PatientsNot Cured Received medication 70 10 Received sugar pills 20 50 We are interested in determining whether or not the medication was effective in curing the common cold. Refer to Exhibit 11-3. The number of degrees of freedom associated with this problem is
1
Read the t statistic from the table of t distributions and circle the correct answer. A two-tailed test, a sample of 20 at a .20 level of significance; t =
1.328
Exhibit 10-1Salary information regarding male and female employees of a large company is shown below. Male Female Sample Size 64 36 Sample Mean Salary (in $1,000) 44 41 Population Variance 128 72 Refer to Exhibit 10-1. If you are interested in testing whether or not the average salary of males is significantly greater than that of females, the test statistic is
1.5
Exhibit 11-2Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification. Freshmen 83 Sophomores 68 Juniors 85 Seniors 64 We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. Refer to Exhibit 11-2. The calculated value for the test statistic equals
1.6615
Read the t statistic from the table of t distributions and circle the correct answer. A one-tailed test (upper tail), a sample size of 18 at a .05 level of significance t =
1.740
The degrees of freedom for a contingency table with 12 rows and 12 columns is
121
In an analysis of variance problem involving 3 treatments and 10 observations per treatment, SSE = 399.6. The MSE for this situation is
14.8
Exhibit 11-1When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained. Do You SupportCapital Punishment? Number ofIndividuals Yes 40 No 60 No Opinion 50 We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. Refer to Exhibit 11-1. The number of degrees of freedom associated with this problem is
2
Exhibit 10-1Salary information regarding male and female employees of a large company is shown below. Male Female Sample Size 64 36 Sample Mean Salary (in $1,000) 44 41 Population Variance 128 72 Refer to Exhibit 10-1. The point estimate of the difference between the means of the two populations is
3
The critical F value with 8 numerator and 29 denominator degrees of freedom at α = 0.01 is
3.20
Exhibit 11-3In order to determine whether or not a particular medication was effective in curing the common cold, one group of patients was given the medication, while another group received sugar pills. The results of the study are shown below. PatientsCured PatientsNot Cured Received medication 70 10 Received sugar pills 20 50 We are interested in determining whether or not the medication was effective in curing the common cold. Refer to Exhibit 11-3. The hypothesis is to be tested at the 5% level of significance. The critical value from the table equals
3.84
An ANOVA procedure is applied to data obtained from 6 samples where each sample contains 20 observations. The degrees of freedom for the critical value of F are
5 numerator and 114 denominator degrees of freedom
Exhibit 11-4 In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. Refer to Exhibit 11-4. The hypothesis is to be tested at the 5% level of significance. The critical value from the table equals
5.99
The degrees of freedom for a contingency table with 10 rows and 11 columns is
90
In an analysis of variance where the total sample size for the experiment is nT and the number of populations is k, the mean square within treatments is
SSE/(nT - k)
When an analysis of variance is performed on samples drawn from k populations, the mean square between treatments (MSTR) is
SSTR/(k-1)
The probability of making a Type I error is denoted by
a
The equality part of the expression (in either <, >, or =)
always appears in the null hypothesis
Exhibit 11-1When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained. Do You SupportCapital Punishment? Number ofIndividuals Yes 40 No 60 No Opinion 50 We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. Refer to Exhibit 11-1. The conclusion of the test is that the
distribution is uniform
In order to determine whether or not the means of two populations are equal,
either a t test or an analysis of variance can be performed
A term that means the same as the term "variable" in an ANOVA procedure is
factor
A statistical test conducted to determine whether to reject or not reject a hypothesized probability distribution for a population is known as a
goodness of fit test
For a one-tailed test (upper tail) with a sample size of 900, the null hypothesis will be rejected at the .05 level of significance if the test statistic is
greater than or equal to 1.645
A two-tailed test is a
hypothesis test in which rejection region is in both tails of the sampling distribution
An example of statistical inference is
hypothesis testing
The rejection region for a one-tailed hypothesis test
is in the tail that supports the alternative hypothesis
The level of significance is the
maximum allowable probability of Type I error
A population where each element of the population is assigned to one and only one of several classes or categories is a
multinomial population
In hypothesis testing if the null hypothesis is rejected,
none of the other answers are correct
Statisticians suggest, as a guideline, that a p-value less than .01 be interpreted as _______ evidence to conclude that Ha is true.
overwhelming
Exhibit 11-4 In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. Refer to Exhibit 11-4. The conclusion of the test is that the
proportions have not changed significantly
The level of significance in hypothesis testing is the probability of
rejecting a true null hypothesis
Exhibit 10-8In order to determine whether or not there is a significant difference between the hourly wages of two companies, the following data have been accumulated. Company A Company B Sample size 80 60 Sample mean $6.75 $6.25 Population standard deviation $1.00 $0.95 Refer to Exhibit 10-8. The null hypothesis
should be rejected
A two-tailed test is performed at a 5% level of significance. The p-value is determined to be 0.09. The null hypothesis
should not be rejected
Exhibit 9-6A random sample of 100 people was taken. Eighty of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 75%. Refer to Exhibit 9-6. At a .05 level of significance, it can be concluded that the proportion of the population in favor of candidate A is
significantly greater than 75%
Exhibit 9-4A random sample of 16 students selected from the student body of a large university had an average age of 25 years. We want to determine if the average age of all the students at the university is significantly different from 24. Assume the distribution of the population of ages is normal with a standard deviation of 2 years. Refer to Exhibit 9-4. At a .05 level of significance, it can be concluded that the mean age is
significantly less than 24
Independent simple random samples are taken to test the difference between the means of two populations whose variances are not known. The sample sizes are n1 = 32 and n2 = 40. The correct distribution to use is the
t distribution with 70 degrees of freedom
The mean square is the sum of squares divided by
the corresponding degrees of freedom
Which of the following does not need to be known in order to compute the p-value?
the level of significance
In hypothesis testing, the hypothesis tentatively assumed to be true is
the null hypothesis
The chi-square test for independence involves
two categorical variables
Exhibit 11-2Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification. Freshmen 83 Sophomores 68 Juniors 85 Seniors 64 We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. Refer to Exhibit 11-2. The hypothesis is to be tested at the 5% level of significance. The critical value from the table equals
unknown
