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Which Delivery Method Is Best? At a community college, the
Chapter 1, Problem 15AYU(choose chapter or problem)
Problem 15AYU
Which Delivery Method Is Best?
At a community college, the mathematics department has been experimenting with four different delivery mechanisms for content in their Intermediate Algebra courses. One method is the traditional lecture (method I), the second is a hybrid format in which half the class time is online and the other half is face-to-face (method II), the third is online (method III), and the fourth is an emporium model from which students obtain their lectures and do their work in a lab with an instructor available for assistance (method IV). To assess the effectiveness of the four methods, students in each approach are given a final exam with the results shown next. Do the data suggest that any method has a different mean score from the others?
(a) Write the null and alternative hypotheses.
(b) State the requirements that must be satisfied to use the oneway ANOVA procedure.
(c) Assuming the requirements stated in part (b) are satisfied, use the following StatCrunch output to test the hypothesis of equal means at the α = 0.05 level of significance.
(d) Shown are side-by-side boxplots drawn in StatCrunch of each delivery method. Do these support the results obtained in part (c)?
(e) Interpret the P-value.
(f ) Verify the residuals are normally distributed.
Questions & Answers
QUESTION:
Problem 15AYU
Which Delivery Method Is Best?
At a community college, the mathematics department has been experimenting with four different delivery mechanisms for content in their Intermediate Algebra courses. One method is the traditional lecture (method I), the second is a hybrid format in which half the class time is online and the other half is face-to-face (method II), the third is online (method III), and the fourth is an emporium model from which students obtain their lectures and do their work in a lab with an instructor available for assistance (method IV). To assess the effectiveness of the four methods, students in each approach are given a final exam with the results shown next. Do the data suggest that any method has a different mean score from the others?
(a) Write the null and alternative hypotheses.
(b) State the requirements that must be satisfied to use the oneway ANOVA procedure.
(c) Assuming the requirements stated in part (b) are satisfied, use the following StatCrunch output to test the hypothesis of equal means at the α = 0.05 level of significance.
(d) Shown are side-by-side boxplots drawn in StatCrunch of each delivery method. Do these support the results obtained in part (c)?
(e) Interpret the P-value.
(f ) Verify the residuals are normally distributed.
ANSWER:
Problem 15AYU
Answer:
Step1:
a). Consider the null and alternative hypotheses are
: there is no difference in the mean score per method.
: at least one of the mean score is different from the others.
With = 0.05 level of significance
b).The requirements that must be satisfied to use the oneway ANOVA procedure:
1).There must be k simple random samples, one from each of k populations or a randomized experiment with k treatments.
2).The k samples must be independent of each other
3).The populations must be normally distributed.
4).The populations must have the same variance
c).We have
From the above given MINITAB we have F calculated value it is F = 0.9629275, we need to find F critical value it can be obtained by using statistical table
Now,
=
=
= 2.60