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Let x1 and x2 be the distributions of the lifetime of brand I and brand 2 batteries used in small ashlights. A random sample of 111 = 42 small ashlights were installed with brand 1 batteries and left on until the batteries failed. The brand 1 batteries gave sample mean lifetime of 21 = 9. 8 hours. Previous study shows population standard deviation 0'1 2 2.2 hours. A random sample of n: = 38 small flashlights were installed with brand 2 batteries and left on until the batteries failed. The brand 2 batteries gave sample mean lifetime of 22 = 3.1 hours. Previous study shows population standard deviation 02 = 3. 5 hours. Use a 5% level of significance to test the claim that the mean population life of brand 1 battery is larger than the mean population life of brand 2 battery. a. [2 points] State the null and alternate hypothesis. Note the value of it. Which tailed test is it ? Null hypothesis | Alternate hypothesis | Level of signicance b. [2 points] Choose one of the correct options below as \"Yes\" or \"No\". - Do you have x1 and x2 distributions as normal distributions, or, Yes No are two samples of sizes in 2 3D and n2 2 30 obtained from 2:1 and x2 ? - Are the above obtained two samples independent? Yes No a Are the sample means 171 and flprovidecl or, can we calculate them? Yes No a Are the standard deviations 01 and 02 of the x1 and 172 known to us ? Yes No c. [1 point] Compute the sample test statistic \"2E1 :32\" , and convert it to a \"2\" value. d. [1 point] Determine the P-value. e. [1 point] Conclude the Test and interpret your conclusion: 1". [1 point] Calculate the maximal error estimate E for a 90% condence interval. 9. [1 point] Find a 90% condence interval for "p11 #2"- h. [1 point] Interpret the result in the given problem's context