1 answer

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

Question:

The inter-arrival times of customers arriving at a HDB coffee shop were found to follow Exponential distribution L H Frequenc
The inter-arrival times of customers arriving at a HDB coffee shop were found to follow Exponential distribution L H Frequency The grouped data shows frequency counts of sampled inter- 0 1 41 arrival times occurring greater than or equal to L minutes and 1 2 21 less than H minutes. A total of 100 sample inter-arrival times 23 19 were measured. Use the mid-point as a representative data in calculations for each interval. Test the claim that the population mean inter-arrival time is equal to 2 minutes at 2.5% significance level. Calculate the 8 9 1 p-value of the test statistic, and hence use p-value to 9 10 conclude the hypothesis test.

Answers

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 : Ho = 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

t = \frac{\bar{x}-\mu}{S/\sqrt{N}}

Let,

194 = N-_ 100-1.94 100

X.F2 Σ.2 * F _ (Σ.urg 683 376.36 3.0974 s2

S = 1.76

N = 100 and \mu = 2

Let, 1.94 2 t = 176/ 10 =-0.34 1

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 pcalculated > 0.025

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

.

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