Consider the following changes that might occur in the context of carrying out either a one or two sample z test. For each, first answer:

Will we be MORE likely or LESS likely to reject the null hypothesis if this happens?

Then explain your answer...

(a) if the sample size gets bigger in a one-sample z test

(b) if the standard deviation of the box gets smaller in a one-sample z test

(c) if the observed value of the statistic gets closer to the value in the null hypothesis in a one-sample z test

(d) if the difference between the two statistics in a two-sample z test gets bigger

(e) if we use a lower threshold for the p-value (e.g. 1% instead of 5%)