Do faculty and students have similar perceptions of what types of behavior are i

Question

Do faculty and students have similar perceptions of what types of behavior are inappropriate in the classroom. Each individuals in a random sample of 173 students and 98 faculty members were asked to judge various behaviors on a scale from 1 (totally inappropriate) to 5(totally appropriate). Data from the behavior "Addressing instructor by first name" are given below. Is there sufficient evidence to conclude that the mean "appropriateness" score assigned to addressing an instructor by his or her first name is greater for students than for faculty? A. What is the appropriate test for this case: a. 2-sample t-test b. 2-sample paired t-test c. 2-sample z-test d. Chi-square test B. Carry out the test. Test statistic = and the p-value is: (round answers to 2 decimal places) C. There (is/is not) sufficient evidence to conclude that the mean "appropriateness" score assigned to addressing an instructor by his or her first name is greater for students than for faculty.

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: 1< 2

Alternative hypothesis: 1 > 2

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the difference between sample means is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = sqrt[(s12/n1) + (s22/n2)]

SE = 0.12643

DF = 269

t = [ (x1 - x2) - d ] / SE

t = 6.25

where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between the population means, and SE is the standard error.

Since we have a one-tailed test, the P-value is the probability that a t statistic having 269 degrees of freedom is more than - 6.25.

Thus, the P-value = less than 0.0001.

Interpret results. Since the P-value (0.0001) is less than the significance level (0.10), we cannot accept the null hypothesis.

There is sufficient evidence to conclude that the mean appropriateness score assigned to addressing an instructor by his or her first name is greater for students than for faculty.

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