A cell phone company charges by the minute (and partial minute) for a phone call. Arionna’s plan includes 300 minutes in the $20
base cost. If she uses more than 300 minutes, there is a $5 overage fee and an additional charge of $0.25 per minute. Which graph represents the cost of her plan per minute, where x represents the minutes used and y represents the cost?
A B C D
A B C D
2 answers:
Answer: First Graph A will be the correct graph for given function.
Explanation: Since, According to the given questions there are two conditions
1- Arionna’s plan includes 300 minutes in the $20 base cost.
That is, function f(x) =20, when
2- If she uses more than 300 minutes, there is a $5 overage fee and an additional charge of $0.25 per minute.
That is, function f(x)= 20+5+0.25x ⇒ f(x)= 25+0.25x, when x>300
Thus, we can say that there is a piece wise function of the entire given situation.
Which is
Since, after mapping the graph of above situation we found that It is similar to option A.
Note: according to graph B there is no charge for minutes less than 300 which is wrong. So, it can not be the graph of given situation.
In graph C until completing 300 minutes the charge is continuously increasing. But according to question it is fixed to 20 dollar. So, it can not be the graph of given situation.
In graph D except charge of per minute there is no overage fee for more than 300 minutes. which is also wrong.So, it can not be the graph of given situation.
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Answer:
Part A:
The null and alternative hypothesis are:
Part B:
- A Type I error is when the null hypothesis is rejected although it is true. In this case, it would mean that we conclude that the hiring process is discriminatory, when in reality it is a random result and the process is not discriminatory.
- A Type II error is when the null hypothesis fails to be rejected although it is false. In this case, the hiring process is discriminatory, but statistically the result is not significant enough to prove that.
Part C:
A reduction in the significance level causes a reduction in the power of the test.
Part D:
The power of the test is increased with a larger sample.
Step-by-step explanation:
We have a restaurant with hire a proprotion of 15 % of people in the age ragne of 30-50 years. The expected proportion, according to the applicants, is 50%.
The test will tell us if the actual 15% is a result of a discriminatory practice or a random result.
Part A:
The null and alternative hypothesis are:
Part B:
- A Type I error is when the null hypothesis is rejected although it is true. In this case, it would mean that we conclude that the hiring process is discriminatory, when in reality it is a random result and the process is not discriminatory.
- A Type II error is when the null hypothesis fails to be rejected although it is false. In this case, the hiring process is discriminatory, but statistically the result is not significant enough to prove that.
Part C:
The power of an hypothesis test is the probability that the test rejects the null hypothesis (H_0) when a specific alternative hypothesis (H_1) is true.
If the significance level is reduced (from 5% to 1%), the rejection region is reduced, so the probability of rejecting the null hypothesis is also reduced.
Then, a reduction in the significance level causes a reduction in the power of the test.
Part D:
A bigger sample size gives robustness to the sample statistic. Then, if the alternative hypothesis is true, the probabilities of detecting the effect are increased with increased sample size.
Then, the power of the test is increased with a larger sample.
