Please help me with this problem Suppose that an independent laboratory has test

Question

Please help me with this problem Suppose that an independent laboratory has tested trash bagsand has foudn that no 30-gallon bags that are currently on themarket have a mean breaking strength of 50 pounds or more. Onthe basis of these results, the producer of the new, improved trashbag feels sure that its 30 gallon bag will be in the strongest suchbag on the market if the new trash bag's mean breaking strength canbe shown to be at least 50 pounds. If we let denotethe mean of the breaking strengths of all possible trash bags ofthe new type and assume that equals 1.65: a. Calculate 95 percent and 99 percent confidenceintervals for . b. Using the 95 percent confidence interval, can we be95 percent confident that is at least 50 pounds?Explain c. Using the 99 percent confidence interval, can we be99 percent confident that is at least 50 pounds?Explain d. Based on your answer to parts b and c, how convincedare you that the new 30-gallon trash bag is the strongest such bagon the market? Please help me with this problem Suppose that an independent laboratory has tested trash bagsand has foudn that no 30-gallon bags that are currently on themarket have a mean breaking strength of 50 pounds or more. Onthe basis of these results, the producer of the new, improved trashbag feels sure that its 30 gallon bag will be in the strongest suchbag on the market if the new trash bag's mean breaking strength canbe shown to be at least 50 pounds. If we let denotethe mean of the breaking strengths of all possible trash bags ofthe new type and assume that equals 1.65: a. Calculate 95 percent and 99 percent confidenceintervals for . b. Using the 95 percent confidence interval, can we be95 percent confident that is at least 50 pounds?Explain c. Using the 99 percent confidence interval, can we be99 percent confident that is at least 50 pounds?Explain d. Based on your answer to parts b and c, how convincedare you that the new 30-gallon trash bag is the strongest such bagon the market?

Explanation / Answer

As mentioned in the Question that = 1.65 n = 30 and the mean is 50 pounds The formula to calculate the 95% confidence itnerval is ±z/2 (/n) Where z/2 = z0.05/2 =1.96 (Which is obtained from normal table values) Plugin the values we have 50 ±1.96(1.65/30) = (49.4096,50.5904) Similarly for 99% the normal table value is changed to 1.96 to2.56 i.e., 50 ±2.56(1.65/30) = (49.2288,50.7712) b) From the above we can say that 95% of all the observationslies in the above interval Yes we are 95% confident that is at least 50pounds c) From the above we can say that 99% of all the observationslies in the above interval Yes we are 99% confident that is at least 50pounds d) Based on the parts b and c, we are 95% and 99%confident that the new 30-gallon trash bag is the strongest suchbag on the market respectively

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