Question

A company has set a goal of developing a battery that lasts over 5 hours (300 minutes) in continuous use. A first test of 12 Of these batteries measured the following lifespans (in minutes): 321, 295, 332, 351, 281, 336, 311, 253, 270, 326, 311, and 288.

3.Provide the following information: Critical t-value ( for the 90% CI: Degrees of freedom of the T-model: Sample mean of lifespan: Sample standard deviation of lifespan

4. Interpret your 90% confidence interval.

5. Do you think the company has met their goal? Explain. (just yes or no answers without a reasonable explanation will receive 0 points)

Answer 1

3)

sample mean, xbar = 306.25
sample standard deviation, s = 29.3106
sample size, n = 12
degrees of freedom, df = n - 1 = 11

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, tc = t(α/2, df) = 1.7959

Critical value = 1.796

4)

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (306.25 - 1.7959 * 29.3106/sqrt(12) , 306.25 + 1.7959 * 29.3106/sqrt(12))
CI = (291.05 , 321.45)

Therefore, based on the data provided, the 90% confidence interval for the population mean is 291.05 < μ < 321.45 which indicates that we are 90% confident that the true population mean μ is contained by the interval (291.05 , 321.45)

5)

No, because confidence interval contains 300 minutes so, it does not meet their goal