AnswersStatisticsConducting a Chi-Square Test for Goodness of Fit

Conducting a Chi-Square Test for Goodness of Fit — Quiz Answers

10 verified answers3 views
1
Free Preview

A researcher would like to investigate if the distribution of the number of babies born is uniform across the days of the week. To investigate, the researcher selects a random sample of 350 babies and records on which day of the week they were born. He finds that 28 babies were born on Sundays, 65 on Mondays, 48 on Tuesdays, 56 on Wednesdays, 45 on Thursdays, 62 on Fridays, and 46 on Saturdays. The researcher would like to know if there is convincing evidence that the distribution of births is uniform across the days of the week. What is the value of the chi-square test statistic and the cap p -value of this test? Use the chi-square distribution table.

A
chi squared is equal to 18 point 6 8 , cap p -value is between 0 point 0 0 2 5 and 0 point 0 0 5
B
chi squared is equal to 18 point 6 8 , cap p -value is between 0 point 0 0 5 and 0 point 0 1
C
chi squared is equal to 24 point 7 0 , cap p -value is between 0 point 0 0 0 5 and 0 point 0 0 1
D
chi squared is equal to 24 point 7 0 , cap p -value is less than 0 point 0 0 0 5
2
Free Preview

A doctor used to believe that babies were equally likely to be born any day of the week, but with the rise in scheduled deliveries, the doctor now claims that babies are twice as likely to be born on a weekday (Monday through Friday) than on a weekend (Saturday and Sunday). To test this theory, she selects a random sample of 120 babies born this year and determines on which day of the week they were born. She would like to carry out a test of significance to test her claim. What is the name of the appropriate inference procedure?

A
one-sample t - test for a difference in means
B
two-sample z - test for a difference in proportions
C
two-sample t - test for a difference in means
D
chi-square test for goodness of fit
3

A researcher would like to investigate if the distribution of the number of babies born is uniform across the days of the week. To investigate, the researcher selects a random sample of 350 babies and records on which day of the week they were born. The researcher would like to know if there is convincing evidence that the distribution of births is uniform across the days of the week. Are the conditions for inference met?

A
No, the Large Counts condition is not met.
B
Yes, all of the conditions for inference are met.
C
No, the random condition is not met.
D
No, the 10 percent condition is not met.
4

After a product recall, a company solicits feedback from a random sample of 100 customers regarding their opinion about the company since the recall. Customers were asked, "Do you approve, disapprove, or have no opinion about the company?” The public relations department is concerned that the opinions may be equally distributed across these three options. They decide to carry out a test of significance. What are the appropriate hypotheses?

A
cap h sub 0 : Approximately 33 customers approve, approximately 33 disapprove, and approximately 33 customers have no opinion of the company. cap h sub A : At least one of these values differs from those stated in the null hypothesis.
B
cap h sub 0 : Customer opinion is not equally distributed across the three options. cap h sub A : Customer opinion is equally distributed across the three options.
C
cap h sub 0 : Customer opinion is equally distributed across the three options. cap h sub A : Customer opinion is not equally distributed across the three options.
D
cap h sub 0 : Approximately 34 customers approve, approximately 34 disapprove, and approximately 34 customers have no opinion of the company. cap h sub A : At least one of these values differs from those stated in the null hypothesis.
5

A company is started by four friends. The company was Erica’s idea, so she wants to fill 70 percent of the orders. Jen, Heather, and Tonya each agree to fill 10 percent of the orders. After a successful first year, Erica wants to determine if the distribution of the number of orders filled is adhering to the agreed-upon percentages. To do so, she selects a random sample of 100 orders from the large number of orders that were filled and determines who filled the order. What are the appropriate hypotheses for this test?

A
cap h sub 0 : p sub Erica is equal to 0 point 7 , p sub Jen is equal to 0 point 1 , p sub Heather is equal to 0 point 1 , p sub Tonya is equal to 0 point 1 cap h sub A : Not all of the p sub i 's are as stated.
B
cap h sub 0 : p sub Erica is equal to 0 point 7 , p sub Jen is equal to 0 point 1 , p sub Heather is equal to 0 point 1 , p sub Tonya is equal to 0 point 1 cap h sub A : p sub Erica is not equal to 0 point 7 , p sub Jen is not equal to 0 point 1 , p sub Heather is not equal to 0 point 1 , p sub Tonya is not equal to 0 point 1
C
cap h sub 0 : p sub Erica is not equal to 0 point 7 , p sub Jen is not equal to 0 point 1 , p sub Heather is not equal to 0 point 1 , p sub Tonya is not equal to 0 point 1 cap h sub A : p sub Erica is equal to 0 point 7 , p sub Jen is equal to 0 point 1 , p sub Heather is equal to 0 point 1 , p sub Tonya is equal to 0 point 1
D
cap h sub 0 : Not all of the p sub i 's are as stated. cap h sub A : p sub Erica is equal to 0 point 7 , p sub Jen is equal to 0 point 1 , p sub Heather is equal to 0 point 1 , p sub Tonya is equal to 0 point 1
6

A researcher would like to investigate if the distribution of the number of babies born is uniform across the days of the week. To investigate, the researcher selects a random sample of 350 babies and records on which day of the week they were born. The researcher would like to know if there is convincing evidence that the distribution of births is uniform across the days of the week. What is the name of the appropriate inference procedure?

A
chi-square test for goodness of fit
B
two-sample z - test for a difference in proportions
C
two-sample t - test for a difference in means
D
one-sample t - test for a difference in means
7

A doctor used to believe that babies were equally likely to be born any day of the week, but with the rise in scheduled deliveries, the doctor now claims that babies are twice as likely to be born on a weekday (Monday through Friday) than on a weekend (Saturday and Sunday). To test this theory, she selects a random sample of 120 babies born this year and determines on which day of the week they were born. She would like to carry out a test of significance to test her claim. Are the conditions for inference met?

A
Yes, all of the conditions for inference are met.
B
No, the Large Counts condition is not met.
C
No, the random condition is not met.
D
No, the 10 percent condition is not met.
8

A researcher would like to investigate if the distribution of the number of babies born is uniform across the days of the week. To investigate, the researcher selects a random sample of 350 babies and records on which day of the week they were born. The researcher would like to know if there is convincing evidence that the distribution of births is uniform across the days of the week. What are the appropriate hypotheses?

A
cap h sub 0 : The distribution of births is not uniform across the days of the week. cap h sub A : The distribution of births is uniform across the days of the week.
B
cap h sub 0 : The sample of 350 births is distributed so that 50 births occur each day of the week. cap h sub A : The sample of 350 births is not distributed so that 50 births occur each day of the week.
C
cap h sub 0 : The sample of 350 births is not distributed so that 50 births occur each day of the week. cap h sub A : The sample of 350 births is distributed so that 50 births occur each day of the week.
D
cap h sub 0 : The distribution of births is uniform across the days of the week. cap h sub A : The distribution of births is not uniform across the days of the week.
9

A doctor used to believe that babies were equally likely to be born any day of the week, but with the rise in scheduled deliveries, the doctor now claims that babies are twice as likely to be born on a weekday (Monday through Friday) than on a weekend (Saturday and Sunday). To test this theory, she selects a random sample of 120 babies born this year and determines on which day of the week they were born. She would like to carry out a test of significance to test her claim. What are the appropriate hypotheses?

A
cap h sub 0 : p sub Sun is equal to 1 over 12 , p sub Mon is equal to 1 sixth , p sub Tue is equal to 1 sixth , p sub Wed is equal to 1 sixth , p sub Thur is equal to 1 sixth , p sub Fri is equal to 1 sixth , p sub Sat is equal to 1 over 12 cap h sub A : Not all of the p sub i 's are as stated.
B
cap h sub 0 : Ten babies are born on each weekend day and 20 babies are born on each weekday. cap h sub A : The number of babies born on each weekend and weekday differ from what is stated in the null hypothesis.
C
cap h sub 0 : Not all of the p sub i 's are as stated. cap h sub A : p sub Sun is equal to 1 over 12 , p sub Mon is equal to 1 sixth , p sub Tue is equal to 1 sixth , p sub Wed is equal to 1 sixth , p sub Thur is equal to 1 sixth , p sub Fri is equal to 1 sixth , p sub Sat is equal to 1 over 12
D
cap h sub 0 : The number of babies born on each weekend and weekday differ from what is stated in the null hypothesis. cap h sub A : Ten babies are born on each weekend day and 20 babies are born on each weekday.
10

The chi-square test statistic is chi squared is equal to 18 point 6 8 and the cap p -value is between 0 point 0 0 2 5 and 0 point 0 0 5 What conclusion should the researcher make? Use A is equal to 0 point 0 5

A
Reject cap h sub 0 . There is convincing evidence that the distribution of births is not uniform across the days of the week.
B
Fail to reject cap h sub 0 . There is not convincing evidence that the distribution of births is not uniform across the days of the week.
C
Fail to reject cap h sub 0 . There is convincing evidence that the distribution of births is not uniform across the days of the week.
D
Reject cap h sub 0 . There is not convincing evidence that the distribution of births is not uniform across the days of the week.

Did you find these answers helpful?

More from this Course

Quiz
10 verified answers

Quiz

Quiz
10 verified answers

Quiz

Quiz
10 verified answers

Quiz