Homework SourseCHAP 13 OIS 3440STAT Question A chisquare test for goodnesso
CHAP 13
OIS 3440-STAT
Question
A chi-square test for goodness-of-fit is used to test whether or not there are any preferences among 3 brands of peas. If the study uses a sample of n = 60 subjects, then the expected frequency for each category would be:
60
20
33
30
Question,
When the variables of interest are both categorical and the decision maker is interested in determining whether a relationship exists between the two, a statistical technique known as contingency analysis is useful.
True
False
Question
A survey was recently conducted in which males and females were asked whether they owned a laptop personal computer. The following data were observed:
Males
Females
Have Laptop
120
70
No Laptop
50
60
Given this information, if an alpha level of .05 is used, the test statistic for determining whether having a laptop is independent of gender is approximately 14.23.
True
False
Question
In conducting a test of independence for a contingency table that has 4 rows and 3 columns, the number of degrees of freedom is 11.
True
False
Question
If a contingency analysis test is performed with a 4 × 6 design, and if alpha = .05, the critical value from the chi-square distribution is 24.9958
True
False
Question
A walk-in medical clinic believes that arrivals are uniformly distributed over weekdays (Monday through Friday). It has collected the following data based on a random sample of 100 days.
Frequency
Mon
25
Tue
22
Wed
19
Thu
18
Fri
16
Total
100
Assuming that a goodness-of-fit test is to be conducted using a 0.10 level of significance, the critical value is:
7.7794
9.4877
11.0705
9.2363
Question.
A walk-in medical clinic believes that arrivals are uniformly distributed over weekdays (Monday through Friday). It has collected the following data based on a random sample of 100 days.
Frequency
Mon
25
Tue
22
Wed
19
Thu
18
Fri
16
Total
100
To conduct a goodness-of-fit test, what is the expected value for Friday?
20
25
100
16
Question
A walk-in medical clinic believes that arrivals are uniformly distributed over weekdays (Monday through Friday). It has collected the following data based on a random sample of 100 days.
Frequency
Mon
25
Tue
22
Wed
19
Thu
18
Fri
16
Total
100
Based on these data, conduct a goodness-of-fit test using a 0.10 level of significance. Which conclusion is correct?
Arrivals are uniformly distributed over the weekday because (test statistic) > (critical value).
Arrives are uniformly distributed over the weekday because (test statistic) < (critical value).
Arrivals are not uniformly distributed over the weekday because (test statistic) > (critical value).
Arrivals are not uniformly distributed over the weekday because (test statistic) > (critical value).
Question
We are interested in determining whether the opinions of the individuals on gun control (as to Yes, No, and No Opinion) are uniformly distributed.
A sample of 150 was taken and the following data were obtained.
Do you support gun control
Number of Responses
Yes
40
No
60
No Opinion
50
The conclusion of the test with alpha = 0.05 is that the views of people on gun control are:
inconclusive.
uniformly distributed.
not uniformly distributed.
None of the above
Question
The goodness-of-fit test is always a one-tail test with the rejection region in the upper tail.
True
False
Question
A survey was recently conducted in which males and females were asked whether they owned a laptop personal computer. The following data were observed:
Males
Females
Have Laptop
120
70
No Laptop
50
60
Given this information, if having a laptop is independent of gender, the expected number of males with laptops in this survey is 150.
True
False
Question
The logic behind the chi-square goodness-of-fit test is based on determining how far the actual observed frequencies are from the expected frequencies.
True
False
Question
The Conrad Real Estate Company recently conducted a statistical test to determine whether the number of days that homes are on the market prior to selling is normally distributed with a mean equal to 50 days and a standard deviation equal to 10 days. The sample of 200 homes was divided into 8 groups to form a grouped data frequency distribution. The degrees of freedom for the test will be 7.
True
False
Question
Consider a goodness-of-fit test with a computed value of chi-square = 1.273 and a critical value = 13.388, the appropriate conclusion would be to:
reject H0.
take a larger sample.
take a smaller sample.
fail to reject H0.
Question
A walk-in medical clinic believes that arrivals are uniformly distributed over weekdays (Monday through Friday). It has collected the following data based on a random sample of 100 days.
Frequency
Mon
25
Tue
22
Wed
19
Thu
18
Fri
16
Total
100
What is the value of the test statistic needed to conduct a goodness-of-fit test?
7.7794
2.46
8.75
2.50
Question
A walk-in medical clinic believes that arrivals are uniformly distributed over weekdays (Monday through Friday). It has collected the following data based on a random sample of 100 days.
Frequency
Mon
25
Tue
22
Wed
19
Thu
18
Fri
16
Total
100
Based on this information how many degrees for freedom are involved in this goodness of fit test?
4
99
100
5
Question
If the test statistic for a chi-square goodness-of-fit test is larger than the critical value, the null hypothesis should be rejected.
True
False
Question
A survey was recently conducted in which males and females were asked whether they owned a laptop personal computer. The following data were observed:
Males
Females
Have Laptop
120
70
No Laptop
50
60
Given this information, if an alpha level of .05 is used, the critical value for testing whether the two variables are independent is x2= 3.8415.
True
False
Question
A researcher is using a chi-square test to determine whether there are any preferences among 4 brands of orange juice. With alpha= 0.05 and n = 30, the critical region for the hypothesis test would have a boundary of:
8.17
7.81
42.25
8.71
Question 20
A survey was recently conducted in which males and females were asked whether they owned a laptop personal computer. The following data were observed:
Males
Females
Have Laptop
120
70
No Laptop
50
60
Given this information, if an alpha level of .05 is used, the sum of the expected cell frequencies will be equal to the sum of the observed cell frequencies.
True
False
……………………………………………………………..
| 60 | |
| 20 |
Solution
( answers in bold)
CHAP 13
OIS 3440-STAT
Question
A chi-square test for goodness-of-fit is used to test whether or not there are any preferences among 3 brands of peas. If the study uses a sample of n = 60 subjects, then the expected frequency for each category would be:
60
20
33
30
Question,
When the variables of interest are both categorical and the decision maker is interested in determining whether a relationship exists between the two, a statistical technique known as contingency analysis is useful.
True
False
Question
A survey was recently conducted in which males and females were asked whether they owned a laptop personal computer. The following data were observed:
Males
Females
Have Laptop
120
70
No Laptop
50
60
Given this information, if an alpha level of .05 is used, the test statistic for determining whether having a laptop is independent of gender is approximately 14.23.
True
False
Question
In conducting a test of independence for a contingency table that has 4 rows and 3 columns, the number of degrees of freedom is 11.
True
False
( Df= 3*2=6)
Question
If a contingency analysis test is performed with a 4 × 6 design, and if alpha = .05, the critical value from the chi-square distribution is 24.9958
True
False
Question
A walk-in medical clinic believes that arrivals are uniformly distributed over weekdays (Monday through Friday). It has collected the following data based on a random sample of 100 days.
Frequency
Mon
25
Tue
22
Wed
19
Thu
18
Fri
16
Total
100
Assuming that a goodness-of-fit test is to be conducted using a 0.10 level of significance, the critical value is:
7.7794
9.4877
11.0705
9.2363
Question.
A walk-in medical clinic believes that arrivals are uniformly distributed over weekdays (Monday through Friday). It has collected the following data based on a random sample of 100 days.
Frequency
Mon
25
Tue
22
Wed
19
Thu
18
Fri
16
Total
100
To conduct a goodness-of-fit test, what is the expected value for Friday?
20
25
100
16
( expected value = 100/5 =20)
Question
A walk-in medical clinic believes that arrivals are uniformly distributed over weekdays (Monday through Friday). It has collected the following data based on a random sample of 100 days.
Frequency
Mon
25
Tue
22
Wed
19
Thu
18
Fri
16
Total
100
Based on these data, conduct a goodness-of-fit test using a 0.10 level of significance. Which conclusion is correct?
Arrivals are uniformly distributed over the weekday because (test statistic) > (critical value).
Arrives are uniformly distributed over the weekday because (test statistic) < (critical value).
Arrivals are not uniformly distributed over the weekday because (test statistic) > (critical value).
Arrivals are not uniformly distributed over the weekday because (test statistic) > (critical value).
observed
expected
O - E
(O - E)² / E
25
20.000
5.000
1.250
22
20.000
2.000
0.200
19
20.000
-1.000
0.050
18
20.000
-2.000
0.200
16
20.000
-4.000
0.800
100
100.000
0.000
2.500
2.50
chi-square
4
df
Question
We are interested in determining whether the opinions of the individuals on gun control (as to Yes, No, and No Opinion) are uniformly distributed.
A sample of 150 was taken and the following data were obtained.
Do you support gun control
Number of Responses
Yes
40
No
60
No Opinion
50
The conclusion of the test with alpha = 0.05 is that the views of people on gun control are:
inconclusive.
uniformly distributed.
not uniformly distributed.
None of the above
observed
expected
O - E
(O - E)² / E
40
50.000
-10.000
2.000
60
50.000
10.000
2.000
50
50.000
0.000
0.000
150
150.000
0.000
4.000
4.00
chi-square
2
df
.1353
p-value
Question
The goodness-of-fit test is always a one-tail test with the rejection region in the upper tail.
True
False
Question
A survey was recently conducted in which males and females were asked whether they owned a laptop personal computer. The following data were observed:
Males
Females
Have Laptop
120
70
No Laptop
50
60
Given this information, if having a laptop is independent of gender, the expected number of males with laptops in this survey is 150.
True
False
Expected=(170*190)/300 =107.66
Question
The logic behind the chi-square goodness-of-fit test is based on determining how far the actual observed frequencies are from the expected frequencies.
True
False
Question
The Conrad Real Estate Company recently conducted a statistical test to determine whether the number of days that homes are on the market prior to selling is normally distributed with a mean equal to 50 days and a standard deviation equal to 10 days. The sample of 200 homes was divided into 8 groups to form a grouped data frequency distribution. The degrees of freedom for the test will be 7.
True
False
Question
Consider a goodness-of-fit test with a computed value of chi-square = 1.273 and a critical value = 13.388, the appropriate conclusion would be to:
reject H0.
take a larger sample.
take a smaller sample.
fail to reject H0.
Question
A walk-in medical clinic believes that arrivals are uniformly distributed over weekdays (Monday through Friday). It has collected the following data based on a random sample of 100 days.
Frequency
Mon
25
Tue
22
Wed
19
Thu
18
Fri
16
Total
100
What is the value of the test statistic needed to conduct a goodness-of-fit test?
7.7794
2.46
8.75
2.50
Goodness of Fit Test
observed
expected
O - E
(O - E)² / E
25
20.000
5.000
1.250
22
20.000
2.000
0.200
19
20.000
-1.000
0.050
18
20.000
-2.000
0.200
16
20.000
-4.000
0.800
100
100.000
0.000
2.500
2.50
chi-square
4
df
.6446
p-value
Question
A walk-in medical clinic believes that arrivals are uniformly distributed over weekdays (Monday through Friday). It has collected the following data based on a random sample of 100 days.
Frequency
Mon
25
Tue
22
Wed
19
Thu
18
Fri
16
Total
100
Based on this information how many degrees for freedom are involved in this goodness of fit test?
4
99
100
5
Question
If the test statistic for a chi-square goodness-of-fit test is larger than the critical value, the null hypothesis should be rejected.
True
False
Question
A survey was recently conducted in which males and females were asked whether they owned a laptop personal computer. The following data were observed:
Males
Females
Have Laptop
120
70
No Laptop
50
60
Given this information, if an alpha level of .05 is used, the critical value for testing whether the two variables are independent is x2= 3.8415.
True
False
Question
A researcher is using a chi-square test to determine whether there are any preferences among 4 brands of orange juice. With alpha= 0.05 and n = 30, the critical region for the hypothesis test would have a boundary of:
8.17
7.81
42.25
8.71
( df=3)
Question 20
A survey was recently conducted in which males and females were asked whether they owned a laptop personal computer. The following data were observed:
Males
Females
Have Laptop
120
70
No Laptop
50
60
Given this information, if an alpha level of .05 is used, the sum of the expected cell frequencies will be equal to the sum of the observed cell frequencies.
True
False
| 60 | |
| 20 | |
|
| 33 |
| 30 |
