Question

To follow up on our previous hypothesis test, a random graduate student instructor is selected and inspects the Moodle logs for all students enrolled in their section, and determines the sample proportion of those 104 students that have been viewing the asynchronous modules is 0.75. If they test the same hypotheses, what is the appropriate conclusion to a hypothesis test using this sample at the α=0.05 level ? a. We accept the null hypothesis and conclude that 80% of ST 311 students are viewing the asynchronous modules. b. We cannot perform this test because requisite assumptions have not been met. c. We fail to reject the null hypothesis and conclude that less than 80% of ST 311 students are viewing the asynchronous modules. d. We reject the null hypothesis and conclude that less than 80% of ST 311 students are viewing the asynchronous modules. e. We fail to reject the null hypothesis and cannot conclude that less than 80% of ST 311 students are viewing the asynchronous modules. f. We reject the null hypothesis and conclude that 75.00% of ST 311 students are viewing the asynchronous modules

Answer 1

The appropriate conclusion to a hypothesis test using a sample proportion of 0.75 is that we fail to reject the null hypothesis and conclude that less than 80% of ST 311 students are viewing the asynchronous modules.

Step-by-step explanation:

The random variable for this study is the sample proportion of graduate students viewing the asynchronous modules.

The null hypothesis for this study is that the proportion of ST 311 students viewing the asynchronous modules is greater than or equal to 80%, while the alternative hypothesis is that the proportion is less than 80%.

Using the sample proportion of 0.75 and a significance level of α=0.05, we fail to reject the null hypothesis and conclude that less than 80% of ST 311 students are viewing the asynchronous modules.

Answer 2

Based on a sample proportion of 0.75, comparing to a null hypothesis proportion of 0.80 at a significance level of 0.05, we either reject the null hypothesis and conclude that less than 80% of students are viewing the modules (if p-value < 0.05) or we fail to reject the null hypothesis without making a specific percentage conclusion (if p-value ≥ 0.05).

Step-by-step explanation:

In conducting a hypothesis test with the given sample proportion of 0.75 and the null hypothesis proportion of 0.80, we would use the sample size (104 students) to calculate the test statistic and corresponding p-value. Given the significance level (α) of 0.05, we compare the p-value to α to determine whether to reject the null hypothesis. If the test statistic results in a p-value less than 0.05, we would reject the null hypothesis, indicating sufficient evidence that less than 80% of ST 311 students are viewing the asynchronous modules. The correct conclusion based on the information provided would therefore be option d: We reject the null hypothesis and conclude that less than 80% of ST 311 students are viewing the asynchronous modules, assuming the p-value was indeed less than 0.05.

We would not conclude option f, as we cannot claim a specific percentage viewing the modules, only that it is less than the hypothesized proportion.

If the p-value is greater than 0.05, then we would fail to reject the null hypothesis (option e), as there would not be enough evidence to conclude that the proportion of students viewing the asynchronous modules is less than 80%.