Deck 12: Tests With Qualitative Data

Question 1

For the following observed and expected frequencies, compute the value of

A) 11.070
B) 9.488
C) 8.260
D) 5.900

Answer 1

5.900

Question 2

For the given table of observed frequencies: i). Compute the row totals, the column totals, and the grand total.
ii). Construct the corresponding table of expected values.
iii). Compute the value of the chi-square test statistic.
iv). Perform a test for independence, using the level of significance.

Answer 2

i).
ii). Expected Values:

Question 3

The number of visits to a certain web site were counted each day of a particular week. The results are given in
the following table. Test the hypothesis that the web site visits are equally likely to occur on any day of the week. Use the
level of significance.

Answer 3

Expected frequency for each day: 127.142857
Reject H₀ The visits do not appear to be equally likely.

Question 4

A psychology instructor gave a five-question true-false quiz to her class of 201 students. The results were as follows. The instructor thinks that the students may have answered the questions by guessing, so that the probability that
Any given answer is correct is 0.5. Under the null hypothesis, the number of correct answers has a binomial
Distribution with 5 trials and success probability 0.5.
Perform a chi-square test of this hypothesis. Can you reject H₀ at the =0.01 level?

A) No
B) Yes

Question 5

A) 31.667
B) 11.070
C) 9.488
D) 30.308

Question 6

The number of drunk-driving arrests were counted each month by the Millville police department. The results are given in the following table. Test the hypothesis that drunk-driving arrests are equally likely to occur in any month. Use the = 0.05 level Of significance.

A) Do not reject H₀. The arrests may be equally likely.
B) Reject H₀. The arrests do not appear to be equally likely

Question 7

Following are observed frequencies. The null hypothesis is H₀: p₁=0.3, p₂=0.2, p₃=0.2, p₄=0.15, p₅=0.15 .

i). Compute the expected frequencies.
ii). Compute the value of X².
iii). How many degrees of freedom are there?
iv). Test the hypothesis that the distribution of the observed frequencies is as given by the null hypot] the =0.01 level of significance.

Question 8

The number of visits to a certain web site were counted each day of a particular week. The results are given in the following table. Test the hypothesis that web site visits are equally likely to occur on any day of the week. Use the = 0.05 Level of significance.

A) Do not reject H₀. The visits may be equally likely
B) Reject H₀. The visits do not appear to be equally likely

Question 9

A biology professor claims that, on the average, 15% of her students get a grade of A, 20% get a B, 40% get a C, 15% get a D, and 10% get an F. The grades of a random sample of 135 students were
Recorded. The following table presents the results. What is the value of ?

A) 9.488
B) 37.333
C) 11.143
D) 36.321

Question 10

Following are observed frequencies. The null hypothesis is H₀: p₁=0.4, p₂=0.2, p3=0.15,p₄=0.1, p₅=0.15

Compute the expected frequencies.

A) 0.384,0.263,0.182,0.04,0.131
B) 38,26,18,4,13
C) 39.6,19.8,14.85,9.9,14.85
D) 19.8,19.8,19.8,19.8,19.8

Question 11

Following are observed frequencies. The null hypothesis is H₀: p₁=0.35, p₂=0.3, p₃=0.1,p₄=0.15, p₅=0.1

Test the hypothesis that the distribution of the observed frequencies is as given by the null hypothesis level of significance.

A) Do not reject H₀
B) Reject H₀

Question 12

A biology professor claims that, on the average, 10% of her students get a grade of A, 30% get a B, 35% get a C, 10% get a D, and 15% get an F. The grades of a random sample of 113 students were Recorded. The following table presents the results.

Compute the expected frequencies.

A) 3,34,38,12,26
B) 0.027,0.301,0.336,0.106,0.23
C) 11.3,33.9,39.55,11.3,16.95
D) 22.6,22.6,22.6,22.6,22.6

Question 13

The number of drunk-driving arrests were counted each month by the Millville police department. The results
are given in the following table. Test the hypothesis that drunk-driving arrests are equally likely to occur in any month. Use the = 0.05 level
of significance.

Question 14

Find the area to the right of 23.337 under the chi-square distribution with 12 degrees of freedom.

A) 0.0125
B) 0.975
C) 0.025
D) 0.0375

Question 15

A psychology instructor gave a five-question true-false quiz to her class of 193 students. The results were as follows. The instructor thinks that the students may have answered the questions by guessing, so that the probability that any given answer is correct is 0.5. Under the null hypothesis, the number of correct answers has a binomial distribution with 5 trials and success probability 0.5.
Perform a chi-square test of this hypothesis. Can you reject H₀ at the =0.01 level?

Question 16

Following is a set of observed and expected frequencies:
Test the hypothesis that the distribution of the observed frequencies is as given by the expected frequ Use the level of significance.

A) Do not reject H₀
B) Reject H₀

Question 17

For the given table of observed frequencies, perform a test for independence, using the α = 0.01 level of significance.

A) Do not reject H₀
B) Reject H₀

Question 18

A biology professor claims that, on the average, 15% of her students get a grade of A, 30% get a B, 30% get a C, 10% get a D, and 15% get an F. The grades of a random sample of 105 students were
Recorded. The following table presents the results. Test the hypothesis that the grades follow the distribution claimed by the professor. Use the level of
Significance.

A) Reject
B) Do not reject

Question 19

Find the critical value for the chi-square statistic with 13 degrees of freedom.

A) 4.107
B) 27.688
C) 29.819
D) 26.217

Question 20

A biology professor claims that, on the average, 20% of her students get a grade of A, 30% get a B,
35% get a C, 10% get a D, and 5% get an F. The grades of a random sample of 137 students were
recorded. The following table presents the results. i). Compute the expected frequencies.
ii). What is the value of ?
iii). How many degrees of freedom are there?
iv). Test the hypothesis that the grades follow the distribution claimed by the professor. Use the = 0.05
level of significance.

Question 21

The following table presents the numbers of cucumber seeds, by brand, that germinated or failed to germinate 14 days after planting. Can you conclude that the germination rate is related to the brand of seed? Use the level of significance.

Question 22

A sample of 149 university students who recently moved off-campus were polled to see whether they agree that off-campus living is preferable to on-campus living. In addition, each was asked how many people live in
Their current off-campus residence. The results are summarized in the following contingency table. Perform a test for independence, using the level of significance. What do you conclude?

A) Do not reject H₀. There is insufficient evidence to conclude that the survey responses and the number of roommates are dependent.
B) Reject H₀ It appears that the survey responses and the number of roommates are dependent.

Question 23

The following table presents the numbers of customers who - after 2 weeks of use - were satisfied or dissatisfied with their newly-purchased computers. Can you conclude that the satisfaction rate is related to the brand of computer? Use the level of Significance.

A) Do not reject H₀. There is insufficient evidence to conclude that the satisfaction rate differs among the computer brands.
B) Reject H₀ It appears that the satisfaction rates differ among the computer brands.

Question 24

The following table presents the numbers of customers who - after 2 weeks of use - were satisfied or dissatisfied with their newly-purchased computers. Can you conclude that the satisfaction rate is related to the brand of computer? Use the level of significance.

Question 25

A sample of 178 university students who recently moved off-campus were polled to see whether they agree
that off-campus living is preferable to on-campus living. In addition, each was asked how many people live in
their current off-campus residence. The results are summarized in the following contingency table. i). Compute the row totals, the column totals, and the grand total.
ii). Construct the corresponding table of expected values.
iii). Compute the value of the chi-square test statistic.
iv). Perform a test for independence, using the level of significance. What do you conclude?

Question 26

The following table presents the numbers of cucumber seeds, by brand, that germinated or failed to germinate 14 days after planting. Can you conclude that the germination rate is related to the brand of seed? Use the level of Significance.

A) Reject H₀. It appears that the germination rates differ among the seed brands.
B) Do not reject H₀. There is insufficient evidence to conclude that the germination rate differs among the seed brands.