Done 9 myopenmath.com AA C', -2, the sample mean is unusual. 0 Because the z-score is between -2 and 2 (but not equal), the sample mean is not unusual. 0 Because the z-score is greater than or equal to 2, the sample mean is unusual. Another way to decide if a sample mean is statistically significant is to look at the probability of a random sample mean being at least as extreme as the one you have. One rule is to say that if that probability is less than 5% (or 0.05), then the value is statistically significant. Use the normal probability computed above to determine if the sample mean (:2 = 56.79) is statistically significant. 0 Because the probability is not less than 5% (0.05), the low value of the sample mean for the Prius ECO is not statistically significant. 0 Because the probability is less than 5% (0.05), the low value of the sample mean for the Prius ECO is statistically significant. Check Answer B myopenmath.com A machine cans 12 ounce sodas, so the population mean is supposed to be p = 1202. There is understandable variation in this, and so the population standard deviation is advertised as 0.13 Suppose we test a random sample of 51 soda cans from this machine, and observe a mean of 11.97 ounces. We would like to use the normal distribution to determine if the value is unusually low for this machine. Are the criteria for approximate normality satisfied for the distribution of sample means from samples of size n = 51? No, the criteria are not satisfied. Yes the criteria are satisfied because the sample size is greater than 30. 0 Yes the criteria are satisfied because the population we're sampling from is normal. Part 2 of 2 Give the mean of all possible sample means: pi = l:] Give the standard error (deviation) for the distribution of all possible sample means. Keep 4 places after the decimal. From the sample mentioned above, the sample mean is :E = 11.97. If we need to know if this value is statistically significant, we can compute Pct 17.8), We begin by computing the z-score of the sample mean. Using the rounded standard error (deviation) computed above, determine this z-score. Round to two places after the decimal. Use the z-score to state whether the sample mean is unusually high. 0 Because the z-score is less than or equal to -2, the sample mean is unusual. 0 Because the zscore is between -2 and 2 (but not equal), the sample mean is not unusual. 0 Because the z-score is greater than or equal to 2, the sample mean is unusual. Another way to decide if a sample mean is statistically significant is to look at the probability of a random sample mean being at least as extreme as the one you have. One rule is to say that if that probability is less than 5% (or 0.05), then the value is statistically significant. Can we use the normal distribution to compute this probability? 0 We can, regardless of whether the criteria were satisfied. 0 We cannot because the criteria for approximate normality were not satisfied. B myopenmath.com Part 1 of 3 In a population of values, x, with mean ,u and standard deviation 0', we wish to compute a sample mean from a sample of size n. The collection of all possible sample means, 93, from samples of size n, is the sampling distribution for this statistic. We know the following about this sampling distribution: Center: The mean of sample means is the mean of the population we're sampling from, so Hi =.U- Shape: The distribution of sample means is approximately normal if either (1) the sample size is greater than 30 (n > 30) or (2) the population we're sampling from is normal. One of the two criteria must be met for approximate normality. Spread: The standard error (deviation) of sample means is Suppose we gather a sample of size 20 from a population with mean ,1]. = 15.5 and standard deviation 0 = 5.1. Are the criteria for approximate normality satisfied for the distribution of sample means from samples of size n = 20? 0 Yes the criteria are satisfied because the population we're sampling from is normal. 0 Yes the criteria are satisfied because the sample size is greater than 30. O No, the criteria are not satisfied. Part 2 of 3