Given the following values: = 10,M = 8, = 0.5,conduct a one-sample z test at a .05 level of significance.What is the decision for a two-tailed test?
A)to reject the null hypothesis
B)to retain the null hypothesis
C)There is not enough information since the sample size is not given.

Question

Given the following values:  = 10,M = 8,  = 0.5,conduct a one-sample z test at a .05 level of significance.What is the decision for a two-tailed test?
A)to reject the null hypothesis 
B)to retain the null hypothesis 
C)There is not enough information since the sample size is not given.

Quizplus · Accepted Answer

Since we are conducting a one-sample z-test, we need to have the sample size (n). However, since the sample size is not given, we cannot calculate the test statistic.

Assuming that we have a large enough sample size, our hypotheses would be:

Null hypothesis: μ = M
Alternative hypothesis: μ ≠ M

Our level of significance is α = .05, which means our critical z-score is ±1.96.

If we calculate the test statistic (z-score) and it falls within the rejection region (±1.96), we would reject the null hypothesis. Otherwise, we would retain the null hypothesis.

Without the sample size, we cannot perform the calculation, but given the options, the best choice is to reject the null hypothesis.

Given the Following Values: = 10,M = 8