Computing the pooled standard deviation. An experiment was run to compare three timed-release fertilizers in terms of plant growth. The sample sizes were 23, 21, and 27 plants, and the corresponding estimated standard deviations were 4, 5, and 7 centimeters. (a) Is it reasonable to use the assumption of equal standard deviations when we analyze these data? Give a reason for your answer. (b) Give the values of the variances for the three groups. (c) Find the pooled variance. (d) What is the value of the pooled standard deviation?

Chapter 11 --- Means (Sampling Distribution, Confidence Intervals, Hypothesis Tests) Sampling Distribution of a Sample Mean Example 1: The Arm and Hammer Company wants to ensure that their laundry detergent actually contains 100 fluid ounces, as indicated on the label. Historical summaries from the filling process indicate the mean amount per container is 100 fluid ounces and the standard deviation is 3 fluid ounces when the process is working properly. The data on fill amounts tend to follow a normal distribution. The quality technician takes random samples periodically to check if the process is working properly. The measure of quality that we will look at here is whether or not the process mean fill amount is 100 ounces. If the process is either overfilling or unde