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1 year ago

Marcus is comparing the costs of two cellular phone services.

Mathematics

1 answer:

kolbaska11 [484]1 year ago

7 0

The true statements about Marcus graph are:

The initial cost of phone service 1 is greater than the initial cost of phone service 2
The unit rate of phone service 2 is greater than the unit rate of phone service 2

<h3>How to determine the true statement</h3>

From the complete question, we have the following parameters:

<u>Phone service 1</u>

Initial cost: $40
Rate: $8.50 per service

<u>Phone service 2</u>

Initial cost: $30
Rate: $10.50 per service

By comparing the above parameters:

The initial cost of phone service 1 is greater than the initial cost of phone service 2
The unit rate of phone service 2 is greater than the unit rate of phone service 2

The above statements represent the true statements about the Marcus' graph

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Step-by-step explanation:

1) Data given and notation

$\bar X=8300$ represent the sample mean

$\sigma=1200$ represent the population standard deviation

$n=64$ sample size

$\mu_o =800$ represent the value that we want to test

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

z would represent the statistic (variable of interest)

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

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We need to conduct a hypothesis in order to check if the mean is higher than 8000, the system of hypothesis are :

Null hypothesis: $\mu \leq 8000$

Alternative hypothesis: $\mu > 8000$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-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".

3) Calculate the statistic

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

$z=\frac{8300-8000}{\frac{1200}{\sqrt{64}}}=2$

4) P-value

Since is a one-side upper test the p value would given by:

$p_v =P(Z>2)=0.0228$

5) Conclusion

If we compare the p value and the significance level assumed, for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the mean is significantly higher than $8000.

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