Question

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 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 1.9 is x⎯⎯ = 50.573. If we let µ denote the mean of the breaking strengths of all possible trash bags of the new type and assume that σ equals 1.66:

(a) Calculate 95 percent and 99 percent confidence intervals for µ. (Round your answers to 3 decimal places.)

95 percent confidence intervals for µ is . [ , ]
99 percent confidence intervals for µ is . [ , ]

Answer 1

Solution :

Given that,

(a)

At 95%

Z_/2 = 1.96

Margin of error = E = Z_/2* ( /n)

= 1.96* (1.66 / 45)

= 0.485

At 95% confidence interval estimate of the population mean is,

- E < < + E

50.573 - 0.485 < < 50.573 + 0.485

50.088 < < 51.058

(50.088 , 5.058)

(b)

At 99%

Z_/2 = 2.576

Margin of error = E = Z_/2* ( /n)

= 2.576 * (1.66 / 45)

= 0.637

At 99% confidence interval estimate of the population mean is,

- E < < + E

50.573 - 0.637 < < 50.573 + 0.637

49.936 < < 51.210

(49.936 , 51.210)