Trash Bag Case Consider the trash bag problem. Suppose that an independent labor

Question

Trash Bag Case
Consider the trash bag problem. Suppose that an independent laboratory has tested trash bags and has found that no 30-gallon bags that are currently on the market have a mean breaking strength of 50 pounds or more. On the basis of these results, the producer of the new, improved trash bag feels sure that its 30-gallon bag will be the strongest such bag on the market if the new trash bag's breaking strength can be shown to be at least 50 pounds. The mean and the standard deviation of the sample of 40 trash bag breaking strengths are X (sample mean) = 50.575 and s = 1.65. If we let m denote the mean of the breaking strengths of all possible trash bags of the new type,
a. Calculate 95 percent and 99 percent confidence intervals for µ.
b. Using the 95 percent confidence interval, can we be 95 confident that µ is at least 50 pounds? Explain.
c. Using the 99 percent confidence interval, can we be 99 confident that µ is at least 50 pounds? Explain.
d. Based on your answers to parts b and c, how confident are you that the new 30-gallon trash bag is the strongest on the market.

Explanation / Answer

Consider the trash bag problem. Suppose that an independent lab has tested trash bags and had found that no 30-gallon bags that are currently on the market have a mean breaking strength of 50 pounds or more. On the basis of these results, the producer of the news, improved trash bag feels sure that its 30 gallon bag will be the strongest such bag on the market if the new trash bag’s mean breaking strength can be shown to be at least 50 pounds. The mean of the sample of 40 trash bag breaking strengths in Table 1.9 is the sample mean x (with a line over the x)= 50.575. If we let µ denote the mean of the breaking strengths of all possible trash bags of the all possible trash bags of the new type and assume that o equals 1.65:

a. Calculate 95 percent and 99 percent confidence intervals for µ

CI at 95% is: 50.575±z(0.025)*1.65/v40 =50.575±1.96*1.65/v40=(50.064,51.086)
CI at 99% is: 50.575±z(0.005)*1.65/v40 = 50.575±2.576*1.65/v40=(49.903,51.247)

b. Using the 95 percent confidence interval, can we be 95 percent confident the µ is at least 50 pounds? Explain.

Yes , because 50 is not in the interval,( we have a 95% confidence that u is greater)

c. Using the 99 percent confidence interval, can we be 99 percent confident that µ is at least 50 pounds? Explain.

No, because 50 is in the interval (49.903,51.247)

d. Based on your answers to parts b and c, how convinced are you that the new 30 gallon trash bag is the strongest such bag on the market?

Using c) we are 95% convinced that the new 30 gallon trash bag is the strongest such bag on the market Consider the trash bag problem. Suppose that an independent lab has tested trash bags and had found that no 30-gallon bags that are currently on the market have a mean breaking strength of 50 pounds or more. On the basis of these results, the producer of the news, improved trash bag feels sure that its 30 gallon bag will be the strongest such bag on the market if the new trash bag’s mean breaking strength can be shown to be at least 50 pounds. The mean of the sample of 40 trash bag breaking strengths in Table 1.9 is the sample mean x (with a line over the x)= 50.575. If we let µ denote the mean of the breaking strengths of all possible trash bags of the all possible trash bags of the new type and assume that o equals 1.65:

a. Calculate 95 percent and 99 percent confidence intervals for µ

CI at 95% is: 50.575±z(0.025)*1.65/v40 =50.575±1.96*1.65/v40=(50.064,51.086)
CI at 99% is: 50.575±z(0.005)*1.65/v40 = 50.575±2.576*1.65/v40=(49.903,51.247)

b. Using the 95 percent confidence interval, can we be 95 percent confident the µ is at least 50 pounds? Explain.

Yes , because 50 is not in the interval,( we have a 95% confidence that u is greater)

c. Using the 99 percent confidence interval, can we be 99 percent confident that µ is at least 50 pounds? Explain.

No, because 50 is in the interval (49.903,51.247)

d. Based on your answers to parts b and c, how convinced are you that the new 30 gallon trash bag is the strongest such bag on the market?

Using c) we are 95% convinced that the new 30 gallon trash bag is the strongest such bag on the market Consider the trash bag problem. Suppose that an independent lab has tested trash bags and had found that no 30-gallon bags that are currently on the market have a mean breaking strength of 50 pounds or more. On the basis of these results, the producer of the news, improved trash bag feels sure that its 30 gallon bag will be the strongest such bag on the market if the new trash bag’s mean breaking strength can be shown to be at least 50 pounds. The mean of the sample of 40 trash bag breaking strengths in Table 1.9 is the sample mean x (with a line over the x)= 50.575. If we let µ denote the mean of the breaking strengths of all possible trash bags of the all possible trash bags of the new type and assume that o equals 1.65:

a. Calculate 95 percent and 99 percent confidence intervals for µ

CI at 95% is: 50.575±z(0.025)*1.65/v40 =50.575±1.96*1.65/v40=(50.064,51.086)
CI at 99% is: 50.575±z(0.005)*1.65/v40 = 50.575±2.576*1.65/v40=(49.903,51.247)

b. Using the 95 percent confidence interval, can we be 95 percent confident the µ is at least 50 pounds? Explain.

Yes , because 50 is not in the interval,( we have a 95% confidence that u is greater)

c. Using the 99 percent confidence interval, can we be 99 percent confident that µ is at least 50 pounds? Explain.

No, because 50 is in the interval (49.903,51.247)

d. Based on your answers to parts b and c, how convinced are you that the new 30 gallon trash bag is the strongest such bag on the market?

Using c) we are 95% convinced that the new 30 gallon trash bag is the strongest such bag on the market

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