1. When do you use a t-test instead of a z-test? 2. We know in the U.S. that the population average ACT score is 22 with a standard deviation of 6. A professor believes that his introductory psychology course is significantly different from the average. He checks his students ACT scores and finds the following: 16 19 16 35 19 18 20 11 19 19 24 11 21 19 17 13 17 27 25 20 21 11 11 14 18 21 23 15 14 16 Conduct a z-test and use the table in your book to find the critical cutoff z-scores. Find out if the professors intro psych course mean ACT is within or outside the 95% probable limits given a population with a mean of 22 and standard deviation of 6. [Z-obtained is found by taking the mean of sample minus the mean of population divided by the Standard Error (M), which is calculated by dividing the standard deviation of the population by the square root of n (M = / n)]. a) Show your calculations for Z obtained score: z = (M- ) / M ZObtained value (answer from above) (2 points): _____ ZCritical value. Find in z table in your book (Also, it is the cutoff for a 95% CI). b) Draw the normal curve and mark where the professors class mean would fall (where is its z- score?). Is it within the 95% probable limits or outside of the z critical cut-off scores? c) What do your results show in terms of the professors students ACT scores? Are they significantly different from average? How are they different? g. Write a summary statement of your results and include APA format. This means write a sentence summarizing the differences before and after the history test. Report the t statistic, degrees of freedom, and p value. You can use this APA Format Template for a One Sample T-test: Results from a one-sample t-test showed that the students average IQ score before taking the history of Psychology class (M = comparison mean score) was (or was not) significantly different from the average IQ score after taking the class (M = new mean score). t(df) = t-score, p < p-value..