The management of New Country Bank claims that the mean waiting time for all cus
ID: 3153735 • Letter: T
Question
The management of New Country Bank claims that the mean waiting time for all customers at its branches is less than that at the Public Bank, which is its main competitor. A business consulting firm took a sample of 100 customers from the New Century Bank and found that they waited an average of 3.8 minutes before being served. Another sample of 150 customers taken from the Public Bank showed that these customers waited an average of 4.3 minutes before being served, Assume that the standard deviations for the two populations are 1.2 and 1.5 minutes, respectively. a. what is the point estimate of mu_1 - mu_2? b. Make a 99% confidence interval for the difference between the two population means c. Test at a 1% significance level whether the claim of the management of the New Century Bank is true. d. Calculate the P-value for the test. Based on this P-value, would you reject the null hypothesis if alpha =,01? what if alpha =.05?Explanation / Answer
We are given that,
X1bar = 3.8
n1 = 100
n2 = 150
X2bar = 4.3
sigma1 = 1.2
sigma2 = 1.5
C-level = 99% = 0.99
The point estimate of mu1 - mu2 is X1bar - X2bar.
X1bar - X2bar = 3.8 - 4.3 = -0.5
99% confidence interval for mu1-mu2 we can find by using TI-83 calculator.
steps :
STAT --> TESTS --> 9 : 2-SampZInt --> ENTER --> Highlight on stats --> ENTER --> Input all the values --> Calculate --> ENTER
Output is :
99% confidence interval for mu1-mu2 is,
(-0.9417, -0.0583)
Conclusion : We are 99% confident that the difference of population mean is lies between -0.9417 and -0.0583.
Assume alpha = 1% = 0.01
Here we have to test the hypothesis that,
H0 : mu1 = mu2 Vs H1 : mu1 < mu2
This testing also we can done using TI-83 calculator.
STAT --> TESTS --> 3:2-SampZTest --> ENTER --> Highlight on Stats --> ENTER --> Input all the values --> select alternative "<mu2" --> ENTER --> Calculate --> ENTER
The test statistic is,
z = -2.916
P-value = 0.002
P-value < alpha
Reject H0 at 1% level of significance.
COnclusion : There is sufficient evidence to say that population mean mu1 is less than population mean mu2.
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