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sweet-ann [11.9K]
3 years ago
8

The students at a High School earned money for an international animal rescue foundation. 82 seniors earned an average $26.75 pe

r student, 74 juniors earned an average $12.25 per student, 96 sophomores earned an average $15.50 per student, and 99 freshmen earned an average $10.85 per student. What was the average collection for a student in this school? A. $16.13 B. $5.37 C. $16.34 D. $16.63
Mathematics
1 answer:
Anon25 [30]3 years ago
4 0

Answer: A. $16.13

Step-by-step explanation:

Total students = 82+74+96+99 =351

Sum of earnings of 82 seniors  = $26.75  x 82= $2193.5

Sum of earnings of 74 juniors  = $12.25 x 74 = $906.5

Sum of earnings of 96 sophomores  = $15.50  x 96 = $1488

Sum of earnings of 99 freshmen  =  $10.85 x 99 = $1074.15

Total earnings =  $2193.5  + $906.5+  $1488 +$1074.15

= $5662.15

(Total earnings) ÷ (Total students )

= $5662.15÷ 351

= $16.13

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Fail to reject the null hypothesis

The conclusion

 There is no sufficient evidence to support the claim that the mean age of the cars is greater than that of taxi

Step-by-step explanation:

From the question we are told that

   The data is  

      Car Ages 4 0 8 11 14 3 4 4 3 5 8 3 3 7 4 6 6 1 8 2 15 11 4 1 6 1 8

     Taxi Ages 8 8 0 3 8 4 3 3 6 11 7 7 6 9 5 10 8 4 3 4

      The  level of significance \alpha = 0.05

 Generally the null hypothesis  is  H_o  :  \mu_1 - \mu_2  = 0

                  the alternative hypothesis is   H_a  :  \mu_1 - \mu_2 >  0

Generally the sample mean for the age of  cars is mathematically represented as

        \= x_1 = \frac{\sum x_i }{n}

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=>     \= x_1 = 5.56

Generally the standard deviation of age of  cars

     \sigma _1  = \sqrt{\frac{\sum (x_i - \= x)^2}{n_1} }

=>  \sigma _1  = \sqrt{\frac{(4 - 5.56)^2 + (0 - 5.56)^2+ (8 - 5.56)^2 + \cdots + 8}{ 27} }

=>  \sigma _1  =  3.88

Generally the sample mean for the age of taxi is mathematically represented as

        \= x_2 = \frac{\sum x_i }{n}

=>     \= x_2 = \frac{8 +8 +0  + \cdots + 4
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Generally the standard deviation of age of  taxi

\sigma _2  = \sqrt{\frac{\sum (x_i - \= x)^2}{n_1} }

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Generally the test statistics is mathematically represented as

   t = \frac{(\= x_ 1 - \= x_2 ) - 0}{\sqrt{\frac{\sigma^2_1}{n_1}  + \frac{\sigma^2_2}{n_2} }  }

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    p-value  =  P(t >  T) =  0.61722067

From the obtained values we see that the  p-value  >  \alpha hence we fail to reject the null hypothesis

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