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Yakvenalex [24]
3 years ago
13

The following distribution shows the frequency of daily revenue for an Italian restaurant in Wilmington, Delaware. Revenue Frequ

ency Under $2,000 18 $2,000 to under $4,000 10 $4,000 to under $6,000 26 $6,000 to under $8,000 14 $8,000 to under $10,000 8 Over $10,000 4 What is the probability that a randomly selected day will generate more than $6,000 in revenue
Mathematics
1 answer:
sergejj [24]3 years ago
6 0

Answer:

The probability that a randomly selected day will generate more than $6,000 in revenue is 0.325.

Step-by-step explanation:

The frequency distribution of daily revenue for an Italian restaurant in Wilmington, Delaware is:

     <u>Revenue</u>      <u>Frequency</u>

   Under $2,000        18

$2,000 -  $4,000      10

$4,000 -  $6,000     26

$6,000 -  $8,000      14

$8,000 - $10,000       8

   Over $10,000           4

          Total                 80

The probability of an event <em>E</em> is defined as:

P(E)=\frac{n(E)}{N}

Here,

n (E) = favorable outcome

N = total outcomes

The favorable outcomes of the event <em>X</em> : "more than $6,000 in revenue" is defined as:

n (X) = 14 + 8 + 4 = 26

Total number of outcomes is, <em>N</em> = 80.

Compute the probability of the event <em>X</em> is:

P(X)=\frac{n(X)}{N}=\frac{26}{80}=0.325

Thus, the probability that a randomly selected day will generate more than $6,000 in revenue is 0.325.

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ehidna [41]

Answer:

Null hypothesis:p_{1} = p_{2}    

Alternative hypothesis:p_{1} \neq p_{2}    

z=\frac{0.410-0.350}{\sqrt{0.382(1-0.382)(\frac{1}{1000}+\frac{1}{900})}}=2.688    

p_v =2*P(Z>2.688)= 0.0072    

Comparing the p value with the significance level assumed \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to to reject the null hypothesis, and we can say that the proportions analyzed are significantly different at 5% of significance.

Step-by-step explanation:

Data given and notation    

X_{1}=410 represent the number of people indicating that their financial security was more than fair  in 2012

X_{2}=315 represent the number of people indicating that their financial security was more than fair in 2010

n_{1}=1000 sample 1 selected  

n_{2}=900 sample 2 selected  

p_{1}=\frac{410}{1000}=0.410 represent the proportion estimated of people indicating that their financial security was more than fair in 2012

p_{2}=\frac{315}{900}=0.350 represent the proportion estimated of people indicating that their financial security was more than fair in 2010  

\hat p represent the pooled estimate of p

z would represent the statistic (variable of interest)    

p_v represent the value for the test (variable of interest)  

\alpha=0.05 significance level given  

Part a: Concepts and formulas to use    

We need to conduct a hypothesis in order to check if is there is a difference between the two proportions, the system of hypothesis would be:    

Null hypothesis:p_{1} = p_{2}    

Alternative hypothesis:p_{1} \neq p_{2}    

Hypothesis testing

We need to apply a z test to compare proportions, and the statistic is given by:    

z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}   (1)  

Where \hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{410+315}{1000+900}=0.382  

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.    

Calculate the statistic  

Replacing in formula (1) the values obtained we got this:    

z=\frac{0.410-0.350}{\sqrt{0.382(1-0.382)(\frac{1}{1000}+\frac{1}{900})}}=2.688    

Statistical decision  

Since is a two sided test the p value would be:    

p_v =2*P(Z>2.688)= 0.0072    

Comparing the p value with the significance level assumed \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to to reject the null hypothesis, and we can say that the proportions analyzed are significantly different at 5% of significance.

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I hope this helps you



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