A study by a bank compared the average savings of customers who were depositors
ID: 3324711 • Letter: A
Question
A study by a bank compared the average savings of customers who were depositors for three years or less with those who had been depositors for more than three years. The results of a sample are: 5. 3 Years 1-3 Years Mean Savings Balance $1.200 S1.250 Population Standard Deviation$100 100 $150 150 Sample Size a. To test that the two groups of customers have equal savings rates, what is the critical value of z using = 0.05? b. What is the computed test statistic? Round to two decimal places c. To test that the two groups of customers have equal savings rates, what is the p-value for a two-tailed test?Explanation / Answer
To test whether the group means are significantly different we go for z test
z = (x1- x2-)/sqrt(12/n1+22/n2)
(a) this is two-tailed test and critical z(0.05)=1.96
(b)z=|(1200-1250)|/sqrt(100*100/100 + 150*150/150)=3.16
(c) two -tailed p-value=0.0004 ( P(Z>3.16)/2)
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