A driving school wants to find out which of its two instructors is more effective at preparing students to pass the state’s driv
er’s license exam. An incoming class of 100 students is randomly assigned to two groups, each of size 50. One group is taught by Instructor A; the other is taught by Instructor B. At the end of the course, 30 of Instructor A’s students and 22 of Instructor B’s students pass the state exam. Do these results give convincing evidence that Instructor A is more effective?A driving school wants to find out which of its two instructors is more effective at preparing students to pass the state’s driver’s license exam. An incoming class of 100 students is randomly assigned to two groups, each of size 50. One group is taught by Instructor A; the other is taught by Instructor B. At the end of the course, 30 of Instructor A’s students and 22 of Instructor B’s students pass the state exam. Do these results give convincing evidence that Instructor A is more effective?
1 answer:
Answer:
Yes, there is evidence to support that claim that instructor 1 is more effective than instructor 2
Step-by-step explanation:
We can conduct a hypothesis test for the difference of 2 proportions. If there is no difference in instructor quality, then the difference in proportions will be zero. That makes the null hypothesis
H0: p1 - p2 = 0
The question is asking whether instructor 1 is more effective, so if he is, his proportion will be larger than instructor 2, so the difference would result in a positive number. This makes the alternate hypothesis
Ha: p1 - p2 > 0
This is a right tailed test (the > or < sign always point to the critical region like an arrowhead)
We will use a significance level of 95% to conduct our test. This makes the critical values for our test statistic: z > 1.645.
If our test statistic falls in this region, we will reject the null hypothesis.
<u>See the attached photo for the hypothesis test and conclusion</u>
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Answer:
The third side is around 58.043
Step-by-step explanation:
Use the law of cosines:
Plug in the two sides we know (into a and b) and the angle we know (into angle C).
Thus:
Use a calculator:
(Note: Make sure you're in Degrees mode.)
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Answer:
<em>Here is the complete question:</em>
The ratio of the number of dogs to the number of cats is 4:5. There are 270 animals on the rescue farm. for each of the following statements, explain whether statements is true or false and why:
a. The number of dogs is 4/5 the number of cats.
b. 4/5 of the pets at the farm are dogs.
c. There are exactly 30 more cats than dogs.
d. There are exactly 30 dogs at the farm.
e. 5/9 of the pets at the farm are cats.
a,c and e are true statements.
Step-by-step explanation:
Let the number of dogs be "d' and number of cats be "c".
According to the question:
⇒ ...equation (i)
Arranging the ratio:
⇒
⇒
⇒ ...equation (ii)
Plugging (ii) in equation (i).
⇒
⇒
⇒
⇒
⇒
⇒
Number of dogs "d" = 120
Number of cats "c" = (270-120) = 150
Lets check each statement:
a.
The number of dogs is 4/5 the number of cats.
⇒
⇒
⇒
Statement is true.
b.
4/5 of the pets at the farm are dogs.
⇒
⇒
Number of dogs = 120
So the above statement is false.
c.
There are exactly 30 more cats than dogs.
⇒
⇒
Statement is true.
d.
There are exactly 30 dogs at the farm.
False, as there are 120 dogs
e.
5/9 of the pets at the farm are cats.
⇒
⇒
Statement is true.
So,
Statement a,c and e are true as we could observe in the explanation.