Consider the trash bag problem:

Suppose an independent laboratory has tested trash bags and found that no 30-gallon bags currently on the market have a mean breaking strength of 50 pounds or more. Based on these results, the producer of a new, improved trash bag feels confident that their 30-gallon bag will be the strongest on the market if its mean breaking strength can be shown to be at least 50 pounds.

The mean of the sample of 45 trash bag breaking strengths in Table 1.10 is [tex] T = 50.574 [/tex]. If we let [tex] \mu [/tex] denote the mean of the breaking strengths of all possible trash bags of the new type and assume that [tex] \sigma [/tex] equals 1.69:

(a) Calculate the 95 percent and 99 percent confidence intervals for [tex] \mu [/tex]. (Round your answers to 3 decimal places.)

- 95 percent confidence interval for [tex] \mu [/tex] is:
- 99 percent confidence interval for [tex] \mu [/tex] is:

(b) Using the 95 percent confidence interval, can we be 95 percent confident that [tex] \mu [/tex] is at least 50 pounds?

(c) Using the 99 percent confidence interval, can we be 99 percent confident that [tex] \mu [/tex] is at least 50 pounds?

Question

15-03-2024
Mathematics

High School

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Consider the trash bag problem:

Suppose an independent laboratory has tested trash bags and found that no 30-gallon bags currently on the market have a mean breaking strength of 50 pounds or more. Based on these results, the producer of a new, improved trash bag feels confident that their 30-gallon bag will be the strongest on the market if its mean breaking strength can be shown to be at least 50 pounds.

The mean of the sample of 45 trash bag breaking strengths in Table 1.10 is [tex] T = 50.574 [/tex]. If we let [tex] \mu [/tex] denote the mean of the breaking strengths of all possible trash bags of the new type and assume that [tex] \sigma [/tex] equals 1.69:

(a) Calculate the 95 percent and 99 percent confidence intervals for [tex] \mu [/tex]. (Round your answers to 3 decimal places.)

- 95 percent confidence interval for [tex] \mu [/tex] is:
- 99 percent confidence interval for [tex] \mu [/tex] is:

(b) Using the 95 percent confidence interval, can we be 95 percent confident that [tex] \mu [/tex] is at least 50 pounds?

(c) Using the 99 percent confidence interval, can we be 99 percent confident that [tex] \mu [/tex] is at least 50 pounds?

Answer :

Final answer:

To calculate the confidence intervals for u, we use the sample mean, sample size, standard deviation, and desired level of confidence. The formula for calculating the confidence interval is provided along with the corresponding Z-scores. Plugging in the values, we can calculate the confidence intervals for u.

Explanation:

To calculate the confidence intervals for u, we need to use the sample mean (T), the sample size (n), the standard deviation (o), and the desired level of confidence. The formula for calculating the confidence interval is:

For 95% confidence interval: u ± Z * (o / √n)
For 99% confidence interval: u ± Z * (o / √n)

Where Z is the Z-score corresponding to the desired level of confidence. For a 95% confidence interval, the Z-score is 1.96, and for a 99% confidence interval, the Z-score is 2.576. Plugging in the values, we can calculate the confidence intervals for u.

Learn more about confidence intervals here:

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Answer :

Final answer:

Explanation:

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