A sample of 50 items is selected to determine whether or not to accept the hypothesis that a population means differs from a value of 20. The sample mean and standard deviation are 18 and 7, respectively. The null hypothesis is not rejected, which of the following is a possible value for the level of significance associated with this test?
8%
10%
1%
5%
Im not sure how to approach this? Help would be appreciated.
To determine a possible value for the level of significance associated with this test, we need to look at the critical region and the p-value.
First, let's define our null and alternative hypotheses:
- Null hypothesis (H0): The population mean is equal to 20.
- Alternative hypothesis (H1): The population mean is not equal to 20.
Since the null hypothesis is not rejected, it means that the sample evidence does not provide sufficient evidence to conclude that the population mean differs from 20. In other words, the sample mean of 18 could reasonably occur if the population mean is 20.
To determine the level of significance, we need to compare the p-value with a pre-determined significance level (also known as alpha). The significance level is typically set before conducting the test and represents the maximum acceptable probability of making a Type I error (rejecting a true null hypothesis).
If the p-value is less than or equal to the significance level, we reject the null hypothesis. If it is greater than the significance level, we fail to reject the null hypothesis.
Unfortunately, you haven't provided the p-value for this test. Without knowing the p-value, we cannot determine the level of significance associated with this test. The possible values (8%, 10%, 1%, 5%) are just examples of commonly used significance levels, but we cannot know for sure which one applies to this particular test without the p-value.
To find the p-value, you would need additional information such as the test statistic (e.g., t-value) and the degrees of freedom. With these additional details, one could calculate the p-value and compare it to the significance level to determine if the null hypothesis should be rejected or not.
Thus, without the p-value or additional information, we cannot determine the exact level of significance associated with this test.