A teacher conducted a study to know if blended leaming improves the students performances. A class of 25 students of Grade 11 was surveyed and found out that their mean score was 83 with a standard deviation of 3. A
study from other country revealed that = 80 with a standard deviation of 4. Test the hypothesis at 0.10 level of significance.
Difference of two independent normal variables
Let have a normal distribution with mean and variance
Let have a normal distribution with mean and variance
If and are independent, then will follow a normal distribution with mean and variance
The following null and alternative hypotheses need to be tested:
This corresponds to a two-tailed test, for which a t-test for one mean, with unknown population standard deviation, using the sample standard deviation, will be used.
Based on the information provided, the significance level is
degrees of freedom, and the critical value for a two-tailed test is
The rejection region for this two-tailed test is
The t-statistic is computed as follows:
Since it is observed that it is then concluded that the null hypothesis is not rejected.
Using the P-value approach:
The p-value for two-tailed is and since it is then concluded that the null hypothesis is not rejected.
Therefore, there is not enough evidence to claim that the population mean is different than 0, at the significance level.
Therefore, there is not enough evidence to claim that blended leaming improves the students performances, at the significance level.
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