b Determine the appropriate critical? value(s). &10.1.7-T Question Help The data
ID: 3055506 • Letter: B
Question
b Determine the appropriate critical? value(s).
&10.1.7-T Question Help The data to the right show the average retirement ages for a random sample of workers in Country A and a random sample of workers in Country B. Complete parts a and b Country A 63.5 years 40 Country B 66.2 years 40 Sample mean Sample size Population standard deviation 4.8 years 5.3 years a. Perform a hypothesis test using ?= 0.10 to determine if the average retirement age in Country B is higher than it is in Country A. Let population 1 be the workers in Country A and population 2 be the workers in Country B. Identify the null and alternative hypotheses. Choose the correct answer below Calculate the appropriate test statistic The test statistic is Round to two decimal places as needed.)Explanation / Answer
Solution:
T statistic can be calculated as follows
Ttest = ((x1bar -x2bar) - (mean1-mean2))/Sqrt( (s12 /n)+(s22/n2))
Ttest = (63.5-66.2)/ sqrt((4.8*4.8/40)+(5.3*5.3/40))
Ttest = -2.7/sqrt(0.576+0.70325)
Ttest = -2.7/sqrt(1.27935)
Ttest= -2.7/1.131
Ttest = -2.3872
Df =40+40-2 =78
P-value can be calculated from t table for one tailed test which is 0.009
Which is less than alpha value so in this case we will reject the null hypothesis in favour of alternate hypothesis.
Tcritical value at df =78 and alpha =0.10 and for one tailed test
Tcrit = -1.29
Here we can see that tcrit>tstat and this is left tailed test so we will reject null hypothesis.
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