- Problem 1 174 Green Beans Are Canned Into Bottles A Random Sample Of 25 Bottles Has The Following Weight In G 173 176 1 (38.17 KiB) Viewed 45 times
What is a power function? how is it calculated?
Problem 1 174 Green beans are canned into bottles. A random sample of 25 bottles has the following weight in g. 173 176 172 176 175 174 172 173 173 174 172 178 176 177 175 176 173 172 175 173 174 177 176 174 i = 174.4g and s = 1.756g. According to the manufacturer, the bottling plant operates with a standard deviation for the bottled beans of o=4g. Further, the weight is assumed to be normally distributed. a) Check whether the weight is less than 175 g at significance level = 0.05. Assume that the information of the manufacturer concerning is wrong. b) Repeat the test if it is known that o=4g. c) Compute the power function of the test in (b). d) How large is the probability that Ho in (b) will not be rejected, although H :u=174g is true? e) How large must be the sample size, so that the above test reveals a deviation from the target value (1758) down to Ig with a certainty of at least 97.5%. 1) For the filling weight 174g use the sample size calculated in part (e) to determine the probability of the second type error in the above test. rikast