Decide whether to accept or reject the null hypothesis. What type of error might you have committed?

Question

Test the hypothesis: Ho: u = 60 against the alternative hypothesis H 1: u > 60 at the 5% level of significance given that a SAMPLE MEAN based on a sample of size n = 36 yielded a value of 62.5. The POPULATION standard deviation is known to be 6.2.

Decide whether to accept or reject the null hypothesis. What type of error might you have committed?

Answer 1

First, note that the hypotheses are incorrect.

If Ha is >60, then H0 must be <= 60

If H0 is = 60, Ha must be != 60

I'm assuming the first, a one-tailed test.

We can use the normal distribution because the standard deviation is known and the sample size is >= 30.

Standard error of the mean is 6.2/sqrt(36) = 1.033.

The test statistic is Z = (62.5 - 60) / 1.033 = 2.42

The critical value (the boundary of 45% of the area under the normal curve to the right of the mean -- from a standard normal table) = 1.645.

Since the test statistic exceeds the critical value, we can reject the null hypothesis and presume that the true mean is greater than 60, However, there is some chance that this was just a weird sample (which does happen sometimes). If that's the case, we will have made a Type I error.