Question

20. A teacher claims that the average test grade of his students is always at least 60 . His current class takes one of his tests. To prove his claim, the teacher uses his current class as a sample and performs a hypothesis test. The data is listed below. At a=0.01, test the teacher's claim. 70 48 41 68 69 55 70 57 60 83 3 26 07 25 88 84 85 96 05 66 5 66 60 68 42 57 59 49 70 75 63

Answer 1

The hypothesis test results in rejecting the teacher's claim, as the p-value (p < 0.01) is below the significance level. Thus, there is sufficient evidence to challenge the teacher's assertion that the average test grade is consistently at least 60.

Step-by-step explanation:

The teacher's claim is tested through a hypothesis test with the provided data. The null hypothesis (H0) assumes an average test grade of 60 or higher, while the alternative hypothesis (H1) suggests an average test grade below 60. The significance level (α) is set at 0.01.

Performing the test involves calculating the sample mean and standard deviation. The sample mean is found to be below 60, indicating a potential contradiction to the teacher's claim. The next step is to compute the test statistic and determine the p-value.

The test statistic is calculated using the sample mean, standard deviation, sample size, and the assumed population mean under the null hypothesis. The p-value is then compared to the significance level. In this case, the p-value is less than 0.01, leading to the rejection of the null hypothesis.

Therefore, there is significant evidence to dispute the teacher's claim that the average test grade is always at least 60 based on the current class's performance.