Under which of the following circumstances should the null hypothesis be accepted when ?= 0.05?

Question

Options

• AWhen p is 0.00003
• BWhen p is 0.001
• CWhen p is 0.04
• DWhen p is 0.06

• A
  6% (2)
• B
  8% (3)
• C
  17% (6)
• D
  69% (25)

Explanation

The null hypothesis should be accepted when the p-value is greater than the alpha level, which is the significance level of the test. The p-value is the probability of obtaining a test statistic at least as extreme as the one observed in the sample, assuming that the null hypothesis is true. The alpha level is the probability of rejecting the null hypothesis when it is true, which is also known as In this case, the alpha level is 0.05, which means that there is a 5% chance of rejecting the null hypothesis when it is true. Therefore, to reject the null hypothesis, the p-value must be less than or equal to 0.05, which indicates that the test statistic is very unlikely to occur by chance under the null hypothesis. Conversely, to accept the null hypothesis, the p-value must be greater than 0.05, which indicates that the test statistic is not very unlikely to occur by chance under the null hypothesis. Among the four options, only option D has a p-value that is greater than 0.05 (p = 0.06). Therefore, option D is the correct answer. When p = 0.06, it means that there is a 6% chance of obtaining a test statistic at least as extreme as the one observed in the sample, assuming that the null hypothesis is true. This probability is not very low, and therefore does not provide enough evidence to reject the null hypothesis.

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