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konstantin123 [22]
3 years ago
5

Steve and Michele and celebrating their 30th anniversary by having a reception at the local reception hall. they have a budget o

f 3,500, the reception hall charges a 50 dollar clean up fee plus 31 dollars per person. find the greatest number of people they can invite and stay within their budget
Mathematics
1 answer:
serious [3.7K]3 years ago
3 0
$3,500 budget minus $50 clean up fee equals $3,450.
3500 - 50 = 3450

$3,450 divided by $31 per person equals 111.29
3450 / 31 = 111.29

111 people multiplied by $31 equals $3,441 plus $50 clean up fee equals $3,491
111 x 31 = 3441
3441 + 50 = 3491

They can invite 111 people and will have $9 to spare
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Answer:

p_v =P(z>1.82)=0.034  

Assuming a standard significance level of \alpha=0.05 the best conclusion for this case would be:

4. There is not enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.034).

Because p_v

If we select a significance level lower than 0.034 then the conclusion would change.

Step-by-step explanation:

Data given

n=300 represent the random sample taken

X=120 represent the people who have a smart phone

\hat p=\frac{120}{300}=0.4 estimated proportion of people who have a smart phone

p_o=0.35 is the value that we want to test

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)  

System of hypothesis

We need to conduct a hypothesis in order to test the claim that the true proportion of people who have a smart phone is higher than 0.35, the system of hypothesis are.:  

Null hypothesis:p\leq 0.35  

Alternative hypothesis:p > 0.35  

The statistic is given by:

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

z=\frac{0.4 -0.35}{\sqrt{\frac{0.35(1-0.35)}{300}}}=1.82  

Statistical decision  

Since is a right tailed test the p value would be:  

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Assuming a standard significance level of \alpha=0.05 the best conclusion for this case would be:

4. There is not enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.034).

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