Question

City A requires that bills be paid within 30 days. A sample of 100 bills shows a mean of 33 days and a standard deviation of 17. a. Is it possible that the sample mean of 33 days could be drawn from a population with a true mean of 30? Show your work. In other words, Is the sample mean of 33 days statistically different from 30 days? Show your work. b. Construct a confidence interval with a 95% confidence level.

Answer 1

given data are:-

sample mean () = 33

sample size (n) = 100

sample sd (s) = 17

a).hypothesis:-

the test statistic be:-

df = (n-1) = (100-1) = 99

the p value = 0.0807

[ in any blank cell of excel type =T.DIST.2T(1.7647,99) ]

decision:-

p value = 0.0807 > 0.05 (alpha)

we fail to reject the null hypothesis and conclude that the sample mean of 33 days is not statistically different from 30 days.i.e, there is enough evidence to claim that the sample mean of 33 days could be drawn from a population with a true mean of 30.

b).t critical value for alpha=0.05, df=99,both tailed test be:-

[ using t distribution table ]

the 95% confidence interval for the true population mean is:-

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