Question

A travel agent claims that the average of the number of rooms in hotels in a large city is 500. At = 0.01, is the claim realistic? The data for a random sample of seven hotels are shown. 713 300 292 311 598 401 618

Answer 1

∑x = 3233

∑x² = 1680683

n = 7

Mean , x̅ = Ʃx/n = 3233/7 = 461.8571

Standard deviation, s = √[(Ʃx² - (Ʃx)²/n)/(n-1)] = √[(1680683-(3233)²/7)/(7-1)] = 176.7762

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Null and Alternative hypothesis:

Ho : µ = 500

H1 : µ ≠ 500

Test statistic:

t = (x̅ - µ)/(s/√n) = (461.8571 - 500)/(176.7762/√7) = -0.571

df = n-1 = 6

p-value = T.DIST.2T(ABS(-0.5709), 6) = 0.5888

Decision:

p-value > α, Do not reject the null hypothesis.

Conclusion:

There is not enough evidence to reject the claim that the average of the number of rooms in hotels in a large city is 500 at 0.01 significance level.