Answer:
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
Step-by-step explanation:
<u><em>Step(i):</em></u>-
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
<u><em>Null Hypothesis</em></u> (H₀) : P=0.24
<u><em>Alternative Hypothesis</em></u> (H₁) : P≠ 0.24
<u><em>Step(ii)</em></u>:-
<em>Test statistic </em>
|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