Question

The written work for the following problem must be submitted to receive credit. The formulas and numbers that have been used in the formula must be shown to receive credit.

A local bank claims that the waiting time for its customers to be served is the lowest in the area. A competitor bank checks the waiting times at both banks. The sample statistics are listed below. Test the local bank’s claim. Use the information given below. Use a significance level of .05 and assume the variances are equal.

Sample statistics for a local bank and a competitor's bank

Sample Size	Local Bank	Competitor Bank
	N1= 46	N2= 50
Avg Waiting time	X1 = 2.3 min	X2= 2.6 min
Sample Standard Deviation	S1 = 1.1 min	S2 = 1.0 min

Are the samples dependent or independent?

State your Null/Alternative hypotheses

What is the test-statistic?

What is the p-value?

What are the critical values?

Does the test-statistic lie in the rejection region?

Interpret the Result?

Does the result change for a different value of alpha? Explain?

Answer 1

Ans:

Independent samples

pooled standard deviation=SQRT(((46-1)*1.1^2+(50-1)*1^2)/(46+50-2))=1.049

standard error for difference=1.049*sqrt((1/46)+(1/50))=0.2143

Test statistic:

t=(2.3-2.6)/0.2143

t=-1.400

df=46+50-2=94

p-value=tdist(1.40,94,1)=0.0824

critical t value=-1.661

No,test statistic does not lie in rejection region.

Fail to reject null hypothesis.

There is not sufficient evidence to support the local bank's claim that waiting time is lower for local bank.

If alpha=0.1,then we reject the null hypothesis(As p-value<0.1),so result will change for alpha 0.1.