The following sample is drawn from a distribution with expected value mu and sta
ID: 3207205 • Letter: T
Question
The following sample is drawn from a distribution with expected value mu and standard deviation sigma: x = 1.3, 2.1, 0.4, 1.3, 0.5, 0.2, 1.8, 2.5, 1.9, 3.2. Perform all tests at the 0.05 significance level. What is the sample mean? What is the sample variance? Test the hypothesis mu greaterthanorequalto 2.0. Test the hypothesis mu = 0.7. Suppose are using the sample mean to test the null hypothesis H_0: mu greaterthanorequalto 0 using a one tail T test. If the significance level of your test increases from 0.05 to 0.10 are you more or less likely to reject H_0? If the sample size increases, will the power of your increases or decreases against the alternative hypothesis H_ = mu = 3?Explanation / Answer
4
(a) When the significance level is increased, the range of accepted values decreases, so it becomes more and more likely that the null hypothesis will get rejected.
This is equivalent to saying that the confidence interval decreases as the significance level increases. Due to the decrease in confidence level, the chances of rejection also increase.
(b) Increasing the sample size decreases the standard deviation.of the sampling distribution. As a result the curve gets more and more concentrated towards the mean value. But this has no effect on the power of estimator. This is because the difference of sample mean and sampling distribution's mean is not changed, and our chances of accepting or rejecting a hypothesis remains independant of sample size.
But it should be noted that if sample size exceeds 30, then we have to switch over to z-statistic instead of t-statistic.