We suspect that Method 1 for detecting impurities in iron ingots yields higher results than Method 2 for finding such impurities. We want to give a 95% confidence interval for the difference in the average number of impurities detected by the two methods. In order to obtain the confidence interval, we measured the impurities of 3 ingots, employing both methods for each ingot. The results are presented in the table below. We let 1 denote the population average number of defects for Method 1 and 2 denotes the population average number of defects for Method 2. We wish to develop a confidence interval for ??=?1−?2μd=μ1−μ2 Give the margin of error for the 95% confidence interval for ??=?1−?2μd=μ1−μ2 Ingot 1 Ingot 2 Ingot 3 Method 1 16 32 12 Method 2 12 26 10

We consider the problem of improving lithium car batteries. A research group is makıng great advances using a new type anode and they claim that the mean life is greater than 1600 recharge cycles. To support this claim, they create 36 new batteries and subject them to recharge cycles until they fail. The claim will be established if the sample mean lifetime is greater than 1640 cycles. Otherwise, the claim will not be established and further improvements are needed. Assume that the population standard deviation o = 192 cycles is known. (a) Find the probability of a Type I error. (b) Find the probability of a Type II error when u = 1680 cycles.

K For parts a and b, use technology to estimate the following. a) The critical value of t for a 90% confidence interval with df = 5. b) The critical value of t for a 99% confidence interval with df = 104.

A baseball team claims that the mean length of its games is 2.4 hours. State H0 and Ha in words and in symbols. Then determine whether the hypothesis test for this claim is​ left-tailed, right-tailed, or​ two-tailed. Explain your reasoning.       State the null hypothesis in words and in symbols. Choose the correct answer below.     A. The null hypothesis expressed in words​ is, "the mean length of a baseball​ team's games is at most 2.4 ​hours." The null hypothesis is expressed symbolically​ as, ​"H0​: μ≤2.4​."   B. The null hypothesis expressed in words​ is, "the mean length of a baseball​ team's games is more than 2.4 ​hours." The null hypothesis is expressed symbolically​ as, ​"H0​: μ≠2.4​."   C. The null hypothesis expressed in words​ is, "the mean length of a baseball​ team's games is at least 2.4 ​hours." The null hypothesis is expressed symbolically​ as, ​"H0​: μ≥2.4​."   D. The null hypothesis expressed in words​ is, "the mean length of a baseball​…