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1 answer:
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Answer:
Now we can calculate the p value with this probability:
If we use a significance level os 0.05 we see that the p value is lower than the significance level so then we can conclude that the true proportion of students with jobs is higher than 0.35 for this case. If we decrease the significance level to 1% the result changes otherwise not.
Step-by-step explanation:
Information given
n=78 represent the random sample taken
X=36 represent the students with jobs
estimated proportion of students with jobs
is the value that we want to test
z would represent the statistic
represent the p value
Hypothesis to test
We want to test if the proportion of students with jobs is higher than 0.35, the system of hypothesis are:
Null hypothesis:
Alternative hypothesis:
The statistic is given by:
(1)
Replacing the info we got:
Now we can calculate the p value with this probability:
If we use a significance level os 0.05 we see that the p value is lower than the significance level so then we can conclude that the true proportion of students with jobs is higher than 0.35 for this case. If we decrease the significance level to 1% the result changes otherwise not.
We can write that as a function:
where is the number of price reductions. We can see that it is a quadratic function which has the biggest value at P = (p, q). It means that p is the number of reductions which results in the biggest profit.
It means that it's the best to make 2 price reductions for the company. The tickets should be sold for $200 - 2 * $20 = $160. It results in 2 * 50 more tickets sold which is 300 + 100 = 400.
Answer:
Ticket price: $160
Number of tickets: 400