STAT_'l ZB_P review Score: 5.7/10 5/7 answered Go to the DCMP Sompiing Distribution of the Sample Mean (Continuous Population) tool at Mp5:lldcmathpathwaysshinyappsio/SampDist cont/ 5. You will use this data analysis tool to simulate random samples of colleges and examine the mean annual cost of attendance for each sample. Enter the following inputs: - Select Population Distribution: Real Population Data - Select Example: College Cost The population distribution shown is the distribution of the average annual costs of attending college {in U.S. dollars) fora population of 1,909 public and private four-year US. colleges. Score on last try: 1 0\" pts. See Details for more. > Next question What shape is the population distribution of the average annual costs of attending college? Uniform Bell-shaped, or approximately normal Skewed left Skewed right 66 E Calculator STAT_1 ZB_P review Score: 6.7110 5/7 answered 0 Question 2 v Next question You can retry this question below Generate 1,000 random samples of size n = 20. According to your 1,000 samples (looking at the statistics on the third graph): What is the mean of the sampling distribution ofthe sample mean? 33 7 What is the standard deviation of the sampling distribution of the sample mean? :5 7 Part A: The histogram labeled "Data Distribution (Histogram from last generated sample)" is a histogram of the last randomly generated sample. What is the sample mean for this sample? $|7 '0' Part B: The same sample mean generated from the last randomly generated sample should be shown on the sampling distribution of the sample mean. Use the mean and standard deviation of the simulated sampling distribution of the sample mean (from the 1,000 simulated samples) to calculate a z-score for the last observed sample mean. Write a sentence interpreting this value. z = (rounded to the nearest hundredth) Interpretation(fill in the blanks): The observed sample mean annual cost of attending college of $ is standard deviations above v '/ $ Part C: Write a sentence interpreting the value of the standard deviation of the sampling distribution of the sample mean that you used to calculate the zscore in Part B. A typical sample mean college annual cost for samples of size 20 will fall about 55 away from the overall mean of $ E Calculator STAT_'l ZB_P review Score: 6.7/10 5/7 answered 0 Question 3 v When we calculate a z-score for a statistic, as in Question 'I, Part B, we call this a standardized statistic. Question 1 used simulation to estimate the mean and standard deviation ofthe sample mean. Mathematically, though, we know the exact formulas for these values. The standardized sample mean is E[meanofi] :Ep z _ std. deviation of 5: _ i as where i is the sample mean, ,u is the population mean, 0' is the population standard deviation, and n is the sample size. The statistic is "standardized" since it is centered to have a mean of O and scaled to have a standard deviation of'l. If the population distribution is normal or the sample size is sufficiently large, this standardized statistic will follow a standard normal distributiona normal distribution with a mean of 0 and a standard deviation of 1. Score on last try: 0.5 of 1 pts. See Details for more. > Next question You can retry this question below What are the population mean and population standard deviation of the variable average annual cost of attending college? Use appropriate statistical notation. These values are displayed in the main title ofthe Population Distribution in the tool. (population mean) u v V =5;- (population standard deviation) 0 v " =$ E Calculator STAT_1 ZB_P review Store: 6.7/10 5/7 answered X Question 4 v Next question You can retry this question below Using the values from Question 3, calculate the mean and standard deviation of the sampling distribution of the sample mean for samples of size 20. Mean of the sample mean = $- Standard deviation of the sample mean = $- (to the nearest dollar) E Calculator