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Katyanochek1 [597]
3 years ago
9

A recent survey of 8,000 high school students found that the mean price of a prom dress was $195.00 with a standard deviation of

$12.00. Alyssa thinks that her school is more fashion conscious and spent more than $195.00. She collected data from 20 people in her high school and found that the average price spent on a prom dress was $208.00. Which of the following is the correct z-statistic for this situation?
Mathematics
1 answer:
KiRa [710]3 years ago
5 0

To calculate the z-statistic, we must first calculate the standard error.

Standard error is standard deviation divided by the square root of the population. In this case, it is equal to 2.68.

The z-score is defined the distance from the sample to the population mean in units of standard error.

z = (195 – 208)/2.68 = -4.86

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Step-by-step explanation:

Part A:

To complete the square, we will do the first few steps all at once, since they are necessary but not complicated to follow all at once.  Set the function equal to 0 first, then move the constant over to the other side:

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On the right is simple addition, but on the left side, during this process we created a perfect square binomial that will reflect the h coordinate of the vertex.  We will state that binomial and do the addition on the right both at the same time:

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If you FOIL out the (t + 3)(t + 3) you will get back the polynomial t^2+6t+9

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Because this is a positive parabola that opens upwards, the function will have a minimum value (if it was negative and opened upside down, it would have a minimum value).  In other words, you know the vertex is a minimum because this is a positive parabola that opens upwards.

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