8.3. Testing a Mean Hypothesis http://www.ck12.org
- When setting the critical regions for this hypothesis, it is important to consider the repercussions of the
decision. Since there does not appear to be major financial or health repercussions of this decision, a more
conservative alpha level need not be chosen. With an alpha level of.05 and a sample size of 256, we find the
area under the curve associated in thez-distribution and set the critical regions accordingly. With this alpha
level and sample size, the critical regions are set at 1.96 standard scores above and below the mean. - With a calculated test statistic of 2.463, we reject the null hypothesis since it falls beyond the critical values
established with an alpha level of.05. This means that the probability that the observed sample mean would
have occurred by chance if the null hypothesis is true is less than 5%. - Yes, because the sample size is below 120, in most cases thet-distribution would be the appropriate distribu-
tion to use and what you have issnott. - The critical values for this scenario using thet-distribution are 2.045 standard scores above and below the
mean. With a calculatedt-test statistic of 0.8425, we do not reject the null hypothesis. Therefore, we
can conclude that the probability that the observed sample mean could have occurred by chance if the null
hypothesis was true is greater than 5%. - You would need a larger difference because the standard error of the mean would be greater with a sample
size of 30 than with a sample size of 256. - (a) one-tailed test (b).05 level of significance (c)n= 144