The presence of student-owned information and communication technologies (smartp
ID: 3127472 • Letter: T
Question
The presence of student-owned information and communication technologies (smartphones, laptops, tablets, etc.) in today's college classroom creates learning problems when students distract themselves during lectures by texting and using social media. Research on multitasking presents clear evidence that human information processing is insufficient for attending to multiple stimuli and for performing simultaneous tasks. To collect data on how multitasking with these technologies interferes with the learning process, a carefully-designed study was conducted at a mostly residential large public university in the Northeast United States. Junco, R. In-class multitasking and academic performance. Computers in Human Behavior (2012) At the beginning of a semester a group of students who were US residents admitted through the regular admissions process and who were taking the same courses were selected based on their high use of social media and the similarities of their college GPA's. The selected students were randomly assigned to one of 2 groups: group 1 students were told to text and use Facebook during classes in their usual high-frequency manner; group 2 students were told to refrain from any use of texting and Facebook during classes. At the conclusion of the semester the semester GPA's of the students were collected. The results are shown in the table below. IN-CLASS MUTLITASKING STUDY Frequent Facebook Use and Texting No Facebook Use or Texting x1 = 2.87 x2 = 3.16 s1 = 0.67 s2 = 0.53 n1 = 65 n2 = 65 Do texting and Facebook use during class have a negative affect on GPA? To answer this question perform a hypothesis test with H0: 12 = 0 where 1 is the mean semester GPA of all students who text and use Facebook frequently during class and 2 is the mean semester GPA of all students who do not text or use Facebook during class. Question 1. What is the value of the test statistic for this hypothesis test? test statistic Question 2. What is the P-value for this hypothesis test? P-value (use 4 decimal places) Question 3. What is the correct conclusion for this hypothesis test? (1 submission allowed) Do not reject the null hypothesis; there is no significant difference between the mean GPA of students who frequently text and use Facebook during class and the mean GPA of students who do not text and use Facebook during class. Reject the null hypothesis and conclude that the mean GPA of students who frequently text and use Facebook during class is less than the mean GPA of students who do not text and use Facebook during class. Reject the null hypothesis and conclude that the mean GPA of students who do not text and use Facebook during class is less than the mean GPA of students who frequently text and use Facebook during class. Question 4. Calculate a 95% confidence interval for 12 where 1 is the mean semester GPA of all students who text and use Facebook frequently during class and 2 is the mean semester GPA of all students who do not text or use Facebook during class. lower limit of confidence interval (use 2 decimal places) upper limit of confidence interval (use 2 decimal places).
Explanation / Answer
1. What is the value of the test statistic for this hypothesis test?
Formulating the null and alternative hypotheses,
Ho: u1 - u2 >= 0
Ha: u1 - u2 < 0
At level of significance = 0.05
As we can see, this is a left tailed test.
Calculating the means of each group,
X1 = 2.87
X2 = 3.16
Calculating the standard deviations of each group,
s1 = 0.67
s2 = 0.53
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):
n1 = sample size of group 1 = 65
n2 = sample size of group 2 = 65
Also, sD = 0.105960806
Thus, the t statistic will be
Z = [X1 - X2 - uD]/sD = -2.736861036 [ANSWER, TEST STATISTIC]
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2.
where uD = hypothesized difference = 0
Also, using p values,
p = 0.003101424 [ANSWER, P VALUE]
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3.
As P value is very low, then
OPTION B: Reject the null hypothesis and conclude that the mean GPA of students who frequently text and use Facebook during class is less than the mean GPA of students who do not text and use Facebook during class.
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4.
For the 0.95 confidence level, then
alpha/2 = (1 - confidence level)/2 = 0.025
Z(alpha/2) = 1.959963985
lower bound = [X1 - X2] - Z(alpha/2) * sD = -0.497679363
upper bound = [X1 - X2] + Z(alpha/2) * sD = -0.082320637
Thus, the confidence interval is
( -0.497679363 , -0.082320637 )
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