Question

]It is widely known that alcohol related car accidents can have a big impact on people’s lives. One widely reported statistic is that the mean number of “years of potential life lost” among men is 32, but it was computed several years ago. Researchers want to know if this statistic has changed since the data were first compiled, with a significance level of 5%. A random sample of 24 alcohol related fatalities from this moth had a mean “years of potential life lost” of 33.8 and a standard deviation of 6 years.

a. [7 points] Construct a confidence interval around the sample mean at 95% Confidence Level.

b. [7 points] Based on the confidence interval, how would you decide about the hypothesis that the mean statistic of “years of potential life lost” has remained the same (at 5% level of significance)?

Answer 1

a. [7 points] Construct a confidence interval around the sample mean at 95% Confidence Level.

The provided sample mean is 33.8 and the sample standard deviation is s = 6 . The size of the sample is n = 24 and the required confidence level is 95%.

The number of degrees of freedom are df = 24 - 1 = 23 , and the significance level is α=0.05.

Based on the provided information, the critical t-value for α=0.05 and df = 23 degrees of freedom is t_c = 2.069

The 95% confidence for the population mean is computed using the following expression

Therefore, based on the information provided, the 95 % confidence for the population mean is

CI = (31.266,36.334)

which completes the calculation.

b. [7 points] Based on the confidence interval, how would you decide about the hypothesis that the mean statistic of “years of potential life lost” has remained the same (at 5% level of significance)?

Since the confidence interval include 32 hence the mean statistic of “years of potential life lost” has remained the same