The inter-arrival times of customers arriving at a HDB coffee shop were found to follow Exponential...

Here we enter these data into Excel with taking mid-point for each interval. And take mid point as a representative data in calculations for each interval.

Here we test that, the claim that the population mean inter-arrival time is equal to 2 minutes at 2.5% significance level.

Here Hypothesis is as

Null Hypothesis : H_o = mean inter-arrival time is equal to 2 min.

V/S Alternative Hypothesis : H₁ = mean inter-arrival time is not equal to 2 min.

Test Statistic :

here sample size is 9 (<30) so we use t-test as

Let,

S = 1.76

N = 100 and

Let,

Calculate p value as using EXCEL formula

p = TDIST(ABS(t) , N-1 , 2) = TDIST(0.34 , 99 , 2) = 0.7346

p = 0.7346

Here given significance level is 0.025. here p_calculated > 0.025

So we accept null hypothesis, That is population mean inter-arrival time is equal to 2 minutes.