A private tutoring company charges $20 for a 1-hour session. Currently, 300 students are each tutored for an hour each week. Sin
1 answer:
Answer:
$24 or $26
Step-by-step explanation:
If for each 50¢ increase, the estimate is that 5 fewer students will participate, for each $1 increase, the estimate is that 10 fewer students will participate.
Revenue is the product of the amount charged per hour by the number of students tutored for an hour each week. The revenue function, R(x), written as a function of the amount increased per lesson in dollars,x, is given by:
Since revenue needs to be $6,240 per week for the company to stay in business:
According to the sum & product of roots properties:
Therefore, either a $4.00 or a $6.00 increase would yield in a revenue of $6,240.
The price that must be charged for a 1-hour tutoring session is $24 or $26
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Answer:
A.
B. Z=2.255. P=0.01207.
C. Although it is not big difference, it is an improvement that has evidence. The scores are expected to be higher in average than without the review course.
D. P(z>0.94)=0.1736
Step-by-step explanation:
<em>A. state the null and alternative hypotheses.</em>
The null hypothesis states that the review course has no effect, so the scores are still the same. The alternative hypothesis states that the review course increase the score.
B. test the hypothesis at the a=.10 level of confidence. is a mean math score of 520 significantly higher than 514? find the test statistic, find P-value. is the sample statistic significantly higher?
The test statistic Z can be calculated as
The P-value of z=2.255 is P=0.01207.
The P-value is smaller than the significance level, so the effect is significant. The null hypothesis is rejected.
Then we can conclude that the score of 520 is significantly higher than 514, in this case, specially because the big sample size.
C. do you think that a mean math score of 520 vs 514 will affect the decision of a school admissions adminstrator? in other words does the increase in the score have any practical significance?
Although it is not big difference, it is an improvement that has evidence. The scores are expected to be higher in average than without the review course.
D. test the hypothesis at the a=.10 level of confidence with n=350 students. assume that the sample mean is still 520 and the sample standard deviation is still 119. is a sample mean of 520 significantly more than 514? find test statistic, find p value, is the sample mean statisically significantly higher? what do you conclude about the impact of large samples on the p-value?
In this case, the z-value is
In this case, the P-value is greater than the significance level, so there is no evidence that the review course is increasing the scores.
The sample size gives robustness to the results of the sample. A large sample is more representative of the population than a smaller sample. A little difference, as 520 from 514, but in a big sample leads to a more strong evidence of a change in the mean score.
Large samples give more extreme values of z, so P-values that are smaller and therefore tend to be smaller than the significance level.