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GuDViN [60]
2 years ago
11

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
Mathematics
1 answer:
9966 [12]2 years ago
7 0

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 = \frac{p-P}{\sqrt{\frac{PQ}{n} } }

           Z = \frac{0.174-0.24}{\sqrt{\frac{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

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