In constructing a confidence interval from a manageable sample in order to estimate a population mean at a 0.10 level of significance, the null hypothesis formulated could not be rejected. Therefore, the company assumed that the value hypothesized is useful for its decision making. However, if the test had been conducted at a 0.05 level of significance, the same null hypothesis would have been rejected. Why would this be? What is involved in deciding the level of confidence and how does it relate to the sample size and the resources that the Company should dedicate to hypothesis testing?
In constructing a confidence interval from a manageable sample in order to estimate a population mean at a 0.10 level of significance, the null hypothesis formulated could not be rejected. Therefore, the company assumed that the value hypothesized is useful for its decision making. However, if the test had been conducted at a 0.05 level of significance, the same null hypothesis would have been rejected. Why would this be? What is involved in deciding the level of confidence and how does it relate to the
We had the level of significance to be 0.10 where the null hypothesis could not be rejected.
While when the level of significance is changed to 0.05 that is decreased from 0.10 to 0.05.
We may expect our test statistic value to fall in the critical region when the level of significance is decreased to 0.05 and thus, reject the null hypothesis.
Thus, we can say that the critical region becomes larger when the confidence level decreases.
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