In a random sample of 25 samples of gasoline sold as 87 octane, the mean (R+M)/2 octane rating was 87.3 with a standard deviation of 0.59. Use this sample to test the claim that, for all gasoline sold as 87 octane, the mean (R+M)/2 octane rating is 87. Use a 0.01 significance level.
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- A manufacturer wants to increase the shelf life of a line of cake mixes. Past records indicate that the average shelf life of the mix is 231 days. After a revised mix has been developed, a sample of nine boxes of cake mix gave these shelf lives (in days): 230,233, 235, 236, 233, 240, 240, 241, and 237. Using α = 0.025, has the shelf life of the cake mix increased? Multiple Choice Yes, because computed t is greater than the critical value. Yes, because computed t is less than the critical value. No, because computed t lies in the region of acceptance. No, because 236.11 is quite close to 231.The amount of coffee poured from a dispenser into a glassobeys the normal law whose average is 300 mL and the deviationtype 5 mL.a) What proportion of the glasses of coffee served by this dispenser contain less than 292 mL of coffee?b) If the glasses have a maximum capacity of 310 mL, whatproportion of glasses overflowing when usedwith this distributor?c) What should be the capacity of the glasses so that only 1% of them overflow when used?with this distributor?A. For this test, what is the critical value of an a-level of 0.05?
- A researcher wishes to test the claim that the average cost of tuition and fees at a four year public college is greater than $5700. She selects a random sample of 36 four-year public colleges and finds the mean to be $5950. The population standard deviation is $659. Is there evidence to support the claim at 0.05? STEP 2. The critical value (s) is/are: z1 = z2 = (IF THERE IS ONLY ONE CRITICAL VALUE ENTER IT IN THE LEFT BOX AND ENTER NA IN THE RIGHT BOX.)What is the critical value? (Round to three decimal places)Suppose that a loss follows log-normal distribution with the parameters μ=3μ=3 and σ=2σ=2. Find the 95% relative VaR.
- Suppose the incidence rate of myocardial infarction (MI)was 5 per 1000 among 45- to 54-year-old men in 2000.To look at changes in incidence over time, 5000 men in thisage group were followed for 1 year starting in 2010. Fifteennew cases of MI were found. Q.)Suppose that 25% of patients with MI in 2000 died within24 hours. This proportion is called the 24-hour case-fatalityrate. 7.14 Of the 15 new MI cases in the preceding study,5 died within 24 hours. Test whether the 24-hour casefatality rate changed from 2000 to 2010. 7.15 Suppose we eventually plan to accumulate 50 MIcases during the period 2010–2015. Assume that the24-hour case-fatality rate is truly 20% during this period.How much power would such a study have in distinguishingbetween case-fatality rates in 2000 and 2010–2015 if atwo-sided test with significance level .05 is planned? 7.16 How large a sample is needed in Problem 7.15 toachieve 90% power?You are conducting a two-tailed test of a claim about a population proportion .If α=0.02, find the positive critical value, to two decimal places. _____________Suppose the incidence rate of myocardial infarction (MI)was 5 per 1000 among 45- to 54-year-old men in 2000.To look at changes in incidence over time, 5000 men in thisage group were followed for 1 year starting in 2010. Fifteennew cases of MI were found. Suppose that 25% of patients with MI in 2000 died within24 hours. This proportion is called the 24-hour case-fatalityrate. >Suppose we eventually plan to accumulate 50 MIcases during the period 2010–2015. Assume that the24-hour case-fatality rate is truly 20% during this period.How much power would such a study have in distinguishingbetween case-fatality rates in 2000 and 2010–2015 if atwo-sided test with significance level .05 is planned?
- About ______% of the area is between z= -1 and z= 1 (or within 1 standard deviations of the mean).what are the critical values r =?Let x = red blood cell (RBC) count in millions per cubic millimeter of whole blood. For healthy females, x has an approximately normal distribution with mean ? = 5.6 and standard deviation ? = 0.4. (d) Convert the z interval, z < −1.44, to an x interval. (Round your answer to one decimal place.) x < _________ (e) Convert the z interval, 1.28 < z, to an x interval. (Round your answer to one decimal place.) _______ < x (f) Convert the z interval, −2.25 < z < −1.00, to an x interval. (Round your answers to one decimal place.) _________ < x < ____________