Consider the following sample data drawn independently from normally distributed

Question

Consider the following sample data drawn independently from normally distributed populations with equal population variances. Use Table 2.

1 is the population mean for individuals with a CFA designation and 2 is the population mean of individuals with MBAs.

a. Construct the relevant hypotheses to test if the mean of the second population is greater than the mean of the first population.

b-1. Calculate the value of the test statistic. (Negative values should be indicated by a minus sign. Round all intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

Test statistic            

b-2. Calculate the critical value at the 5% level of significance. (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)

Critical value            

b-3. Using the critical value approach, can we reject the null hypothesis at the 5% significance level?

c. Using the critical value approach, can we reject the null hypothesis at the 10% level?

Sample 1 Sample 2 12.0 9.7 10.1 12.2 7.6 12.8 11.8 11.2 8.7 11.2 11.5 11.5 8.7 11.2 10.1 13.2

Explanation / Answer

a) H0: 1 2 0; HA: 1 2 < 0

b)

here

degree of freedom =n1+n2-2=14

S1=S2=((n-1)s12+(n-1)s22)/(n1+n2-2))1/2 =pooled std deviation

also std error =(S12+S22/n2)1/2=0.6953

b-1)test stat=(x1-x2)/std error =-2.247

b-2) critical value at the 5% level of significance=-1.761

b-3)Yes since value of test stat is less then critcal value

c)

S. no child adult 1 12 9.7 2 10.1 12.2 3 7.6 12.8 4 11.8 11.2 5 8.7 11.2 6 11.5 11.5 7 8.7 11.2 8 10.1 13.2 total 80.500 93.000 mean 10.063 11.625 std deviation(S) 1.631 1.099

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