Question

5. Using z-scores with the distribution of sample means On each trial of a digit span memory task, the partiapant is asked to read aloud a string of random digits. The partidpant must then repeat the digits in the correct order. If the participant is successful, the length of the next string is increased by one. For instance, if the partidpant repeats four digits successfully, she will hear five random digits on the next trial. The partiipant's score is the longest string of digits she can successfully repeat. A professor of cognitive psydhology is interested in the number of digits successfully repeated on the digit span task among college students. She measures the number of digits successfully repeated for 64 randomly selected students. The professor knows that the distribution of scores is normal, but she does not know that the true average number of digits sucessuly repeated on the digit span task among college students is 7.06 digits with a standard deviation of 1.610 digits (Hint: Use the population The expected value of the mean of the 64 randomly selected students, M, is mean and/or standard deviation just given to calculate the expected value of M.) . (Hint: Use the population mean and/or standard deviation just given to The standard error of M is calculate the standard error.) The DataView tool that foilows displays a data set consisting of 200 potential samples (each sample has 64 observations) Sample ariables 2 Observations 200 Statistics for 200 Random Samples in 64) drawn from a normal distribution R was used to generate the samples. Observations Variable Type ▽ Form ValuesMissing Sample Means Quantitative Numeric 200 200 Sample SD Quantitative Numeric Variable Variable Correlation Correlation

Answer 1