Question

Based on data collected 5 years ago, a hotel expects that 24% of all guests will request smoking rooms. The hotel suspects that this proportion has decreased. To test this hypothesis, the hotel takes a random sample of 223 guests. Out of this sample, 39 guests requested smoking rooms. Conduct a test to check for evidence that the proportion of guests requesting smoking rooms has in fact decreased. Use a significance level of

Answer 1

The calculated value Z = 2.3084 > 1.96 at 5% level of significance

Null hypothesis is rejected

Alternative hypothesis is accepted

The hotel does not expects that 24% of all guests will request smoking rooms

Explanation:

Step(i):-

Given the hotel takes a random sample of 223 guests. Out of this sample, 39 guests requested smoking rooms.

Sample proportion

p = x/n = 39/223 = 0.174

Given Population proportion 'P' = 0.24

Given random sample size 'n' = 223

Level of significance ∝ =0.05

The critical value Z₀.₀₅ = 1.96

Null Hypothesis (H₀) : P=0.24

Alternative Hypothesis (H₁) : P≠ 0.24

Step(ii):-

Test statistic

`Z = \frac{p-P}{\sqrt{(PQ)/(n) } }`

`Z = \frac{0.174-0.24}{\sqrt{(0.24 X 0.76)/(223) } }`

|Z| = | -2.3084|= 2.3084

The calculated value Z = 2.3084 > 1.96 at 5% level of significance

Null hypothesis is rejected

Alternative hypothesis is accepted

The hotel does not expects that 24% of all guests will request smoking rooms