a local bank claims that the waiting time for its customers to be served is the

Question

a local bank claims that the waiting time for its customers to be served is the lowest in the area. a competitors bank checks the waiting time at both banks. the sample statistics are listed below. test the banks claim assuming the variances are not equal.   use a= 0.05

(1)what is the Ha?, (2)What is the Ho?   (3)What is the claim Ho? or Ha?   (4)what is critical value?   (5)what is standardized test statistic ? (6)what is the descision?

local bank competitor bank n1 = 15 n2 = 16 x bar1 = 5.3 x bar2 = 5.6 S1 = 1.1 S2 = 1.0

Explanation / Answer

Here we have to test the hypothesis that,

H0 : mu1 - mu2 = 0 Vs Ha : mu1 - mu2 < 0

where mu1 is population mean for local bank.

mu2 is population mean for competitor bank.

Given that,

There are two samples which has sample size less than 30 and population variance are unknown.

So we use t-test for two samples.

Assume variances are not equal.

alpha = level of significance = 0.05

This we can done by using TI-83 calculator.

steps :

STAT --> TESTS --> 4: 2-SampTTest --> ENTER --> Highlight on Stats --> ENTER --> Input all the values of x1bar, Sx1, n1, x2bar, Sx2, n2 --> 5.--> select alternative < mu2 --> Enter --> Pooled : No --> Calculate --> ENTER

Output is,

t = -0.7929

P = 0.2172

df = 28.26

Critical value we can find by using EXCEL syntax is,

=TINV(probability, deg_freedom)

where, probability is alpha.

deg_freedom = n1 + n2 - 2 = 15 + 16 - 2 = 29

critical value = 2.0452

t < critical value

Accept H0 at 5% level of significance.

Conclusion : Population mean for local bank and competitor bank is equal.

n1 = 15 n2 = 16 x bar1 = 5.3 x bar2 = 5.6 S1 = 1.1 S2 = 1.0

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.