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3 years ago

At the city museum, child admission is

Mathematics

2 answers:

Elina [12.6K]3 years ago

6 0

99 child tickets were sold hope that helps

Vlad1618 [11]3 years ago

5 0

Let's make
A = adult tickets sold
C = child tickets sold
A + C = 162
5.90C + 9.50A = 1182.60

if .. A+C = 162 then A = 162 - C
substitute (162 - C) for A in the other equation.

5.9C + 9.5(162-C) = 1182.6
5.9C + 1539 - 9.5C = 1182.6
-3.6C + 1539 = 1182.6
-3.6C = 1182.6 - 1539
-3.6C = -356.4
C = -356.4/-3.6
C = 99 tickets

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a) Null hypothesis: $\mu \leq 15$

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Data given and notation

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$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

And the sample deviation is:

$s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

$\bar X=17$ represent the sample mean

$s=4$ represent the sample standard deviation

$n=35$ sample size

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$\alpha=0.01$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

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We need to conduct a hypothesis in order to check if the mean is less or equal than 15, the system of hypothesis would be:

Null hypothesis: $\mu \leq 15$

Alternative hypothesis: $\mu > 15$

Since we don't know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Part b Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{17-15}{\frac{4}{\sqrt{35}}}=2.958$

Part c P-value

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Part d Conclusion

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