3. The mean and the standard deviation of the sample of 40 trash bag breaking st

Question

3. The mean and the standard deviation of the sample of 40 trash bag breaking strengths in the Table -are-50.575 and s = 1.6438. Use the Excel output in Figure 8.15 to calculate a t-based 95 percent confidence interval for u, the mean of the breaking strengths of all possible new trash bags. Are we 95 percent confident that ? is at least 50 pounds? (12 points) a. Descriptive Statistics for Strength i Mean Standard Error 50.575 0.2599 50.65 50.9 1.6438 2.7019 -0.2151 -0.0549 7.2 46.8 s Median e Mode Standard Deviation a Sample Variance s Kurtosis 1o Skewness Range 12 Minimum 1a Maximum 14 Sum s Count 1.6 Confidence Level(95.0%) 0.5257

Explanation / Answer

Given that,

sample size (n) = 40

Sample mean (Xbar) = 50.575

standard deviation (sd) = 1.6438

95% confidence interval for population mean (mu) is,

Xbar - E < mu < Xbar + E

where E is margin of error.

E = tc * se

se = sd / sqrt(n)

tc is the critical value for t-distribution.

c is the confidence level = 95% = 0.95

We can find one sample t-interval in ti-83 calculator.

steps :

STAT --> TESTS --> 8:TInterval --> ENTER --> Highlight on STATS --> ENTER --> Input all the values --> Calculate --> ENTER

95% confidence interv, for population mean is (50.049, 51.101)

We are 95% confident that the population mean is lies between 50.049 and 51.101.

Yes we are 95% confident that mu is atleast 50 pounds.

Since is lies between 50.049 and 51.101.

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