In order to compare the means of two populations, independent random samples of 395 observations are selected from each population, with the results found in the table to the right. Complete pans • through e.
Sample I Sample 2 ch xi- 5.285 x- 20-5.245 si = 155 s2= 210
Use a 95% confidence interval to estimate the difference between the population means (pi — p2). Interpret the confidence interval.
— _ al al sf sf A confidence interval is found by (x1 — x2) Xs/eV, _ „'2) where 6(;1_;2)'' —n + 712 s' 4 andVVV x. s are the means and standard deviations of the samples respectively. 999Before finding the confidence interval, you must find z,./ z = 2.025. While either technology or a standard normal distribution table can be used. for this problem we will use a table. Use a standard normal tabk to find zo2= Z.02s.
z„f2= z,02a = 1.96
Use the above equation to find the correct confidence interval, rounding to one decimal place.
— si sf Or - x2) ± Zan —4 — nt n2
1552 2102 (5,285 - 5,245) ± I.% —+ 395 395
= 40325.7
The confidence interval in interval notation is (14.3
Substitute.
Simplify.
Nate) do 14/vave, az, tarn To interpret the meaning of the confidence interval, think about what percent confidence interval you fated and what value you are confident will fall within the interval. ()Test the null hypothesis 110:(pc — p2) = 0 versus the alternative hypothesis 11.: (pi — p2) ot). Give the significance level of the test, and interpret the result.
— — fa — z2) —(µ —µ ) Begin by finding the test statistic, z = whereµ is the population mean and o is the 2 2 ÷ nt n2
population standard deviation.
Use the above equation to find the test statistic z rounded to two decimal places.