Is it true that the best students sit in the front of the classroom, or is that

ID: 2909595 • Letter: I

Question

Is it true that the best students sit in the front of the classroom, or is that a false stereotype? In surveys done by two statistics classes at the University of California at Davis, students reported their grade point averages and also answered the question “Where do you typically sit in a classroom? Front, middle, or back?” The ANOVA output is displayed below.

(a) (3 points) Write null and alternative hypotheses for this problem. State the hypotheses using proper statistical notation. To what populations do these hypotheses apply? Be specific to this situation.

(b) (3 points) What values are given in the output for the F-statistic and the p-value? What conclusion can be reached about the hypotheses you wrote in part (a)?

(c) (2 points) On the basis of the 95% confidence intervals given for the population means, describe the differences among the age groups.

(d) (2 points) Is the assumption of equal population standard deviations reasonable for these data? Briefly explain

(2 points) In a chi-square goodness-of-fit test, is it possible for all of the expected counts to be larger than the corresponding observed counts? Explain. (10 points) Is it true that the best students sit in the front of the classroom, or is that a false stereotype? In surveys done by two statistics classes at the University of California at Davis, students reported their grade point averages and also answered the question "Where do you typically sit in a classroom? Front, middle, or back?" The ANOVA output is displayed below (a) (3 points) Write null and alternative hypotheses for this problem. State the hypotheses using proper statistical notation. To what populations do these hypotheses apply? Be specific to this situation. Analysis of Variance for GPA DF MS Seat Error Total 2 3.994 1.997 6.69 0.001 381 113 7750299 383 117.769 individual 95% C is For Mean Based on Pooled StDev Mean 88 3.2029 0.549 StDev Front Middle 218 2.9853 05577 78 2.9194 0.5105 Back Pooled StDe 0.5465 2.85 3.00 3.15 330 (b) (3 points) What values are given in the output for the F-statistic and the p-value? What conclusion can be reached about the hypotheses you wrote in part (a)? (c) (2 points) On the basis of the 95% confidence intervals given for the population means, describe the differences among the age groups (d) (2 points) Is the assumption of equal population standard deviations reasonable for these data? Briefly explain.

Explanation / Answer

Part a

The null and alternative hypotheses for the given ANOVA are given as below:

Null hypothesis: H0: The average GPA for the students sitting at front, middle, and back is same.

Alternative hypothesis: Ha: The average GPA for the students sitting at front, middle, and back is not same.

Let µ1 = Average GPA for students sitting at front

µ2 = Average GPA for students sitting at middle

µ3 = Average GPA for students sitting at back

In symbolic notation,

H0: µ1 = µ2 = µ3 vs. Ha: µ1 ? µ2 ? µ3 or at least one µ is different or µ1 is greater.

(For ANOVA, we use multiple alternative hypotheses.)

Above hypotheses will be applied to the population of statistics classes at the University of California at Davis.

Part b

From given ANOVA output, the value of F test statistic is given as 6.69 and the p-value for this ANOVA is given as 0.001. This p-value is less than default level of significance or alpha value 0.05, so we reject the null hypothesis that the average GPA for the students sitting at front, middle, and back is same. There is sufficient evidence to conclude that the average GPA for the students sitting at front, middle, and back is not same.

Part c

From the given output for the 95% confidence intervals, it is observed that the mean for the students sitting at front is more than the students who sits at middle or back. Also, it is observed that the mean for students sitting at middle is more than the mean for students sitting at back. The average GPA for students sits at back is minimum among three groups and it is maximum for students sits at front.

Part d

The assumption of equal population standard deviations is reasonable for given data, because values for standard deviations for the GPA scores for students sitting at front, middle, and back is approximately same or close to each other.

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