(a) The null hypothesis "(H_0)" for the test is that the proportions are the same.
The alternate hypothesis "(H_1)" is that the proportions are not the same.
"H_0:p_1=p_2"
"H_1:p_1\\not=p_2"
Since the null hypothesis states that "p_1=p_2," we use a pooled sample proportion "p" to compute the standard error of the sampling distribution.
Given "n_1=300, n_2=200, p_1=0.56, p_2=0.48"
The test statistic is a z-score "(z)" defined by the following equation.
"z={(0.56-0.48)-0\\over \\sqrt{0.528(1-0.528)({1\\over 300}+{1\\over 200})}}\\approx1.755467"
Use p-value
Since p-value "p=0.079180>0.05=\\alpha" we fail to reject the null hypothesis.
The result is statistically nonsignificant.
(b)
"H_0:p_1\\leq p_2"
"H_1:p_1>p_2"
"z={(0.56-0.48)-0\\over \\sqrt{0.528(1-0.528)({1\\over 300}+{1\\over 200})}}\\approx1.755467"
Use p-value
Since p-value "p=0.039590<0.05=\\alpha," it is concluded that the null hypothesis is rejected.
Therefore, there is enough evidence to claim that Google Classroom is preferred by the first year students, at the 0.05 significance level.
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