A single observation is to be used to test the nullhypothesis that the mean waiting time between tremors recorded at a seismological station (the mean of an expo-nential population) is θ = 10 hours against the alternative that θ Z 10 hours. If the null hypothesis is to be rejected ifand only if the observed value is less than 8 or greaterthan 12, find(a) the probability of a type I error;(b) the probabilities of type II errors when θ = 2, 4, 6, 8,12, 16, and 20.Also plot the power function of this test criterion.

A consumer group plans a comparative study of the mean life of four different brands of batteries. Ten batteries of each brand will be randomly selected and the time until the energy level falls below a pre-specified level is measured. a) Which of the following is the appropriate alternative hypothesis for the null hypothesis: H0: μa = μb = μc = μd? (In this problem, μa = mean time of Brand A, μb = mean time of Brand B, etc.) Ha: none of the means are equal Ha: μa ≠ μb ≠ μc ≠ μd Ha: μa ≠ μb, μa ≠ μc, μa ≠ μd, μb ≠ μc, μb ≠ μd, μc ≠ μd Ha: at least one of the means is different b)In order to analyze the data with ANOVA, we need to satisfy the condition of randomization. How do we know that this condition has been met? -One SRS of batteries is selected from a collection of batteries of all brands. -The batteries are randomly allocated to the four brands. -Separate random samples of batteries are selected from each brand.

A prescription allergy medicine is supposed to contain an average of 245 parts per million (ppm) of active ingredient. The manufacturer periodically collects data to determine if the production process is working properly. A random sample of 64 pills has a mean of 250 ppm with a standard deviation of 12 ppm. Let u denotes the average amount of the active ingredient in pills of this allergy medicine. The null and alternative hypotheses are as Ho: μ = 245, Hau #245. The level of significance is 1%. The t-test statistic is 3.33 with a P-value of 0.0014. What is the correct conclusion? The mean amount of active ingredient in pills of this allergy medicine is greater than 245 ppm. The mean amount of active ingredient in pills of this allergy medicine is equal to 250 ppm. The mean amount of active ingredient in pills of this allergy medicine is equal to 245 ppm. moon amount of active ingredient in pills of this allergy medicine is not equal to 245 ppm.

A certain model of car can be ordered with either a large or small engine. The mean number of miles per gallon for cars with a small engine is 6.8. An automotive engineer thinks that the mean for cars with the larger engine is higher than this. State the appropriate null and alternate hypotheses. The null hypothesis is Hoμ (Choose one) The alternate hypothesis is H₁ μu (Choose one) ×