Wednesday, June 18, 2008

Statistic questions I got wrong

LL- the first one is one of the percentiles I keep getting wrong. I however NOW know what I did wrong. Let me tell you what I did. I emailed the teacher this, (Copy and paste from my sent email… yea… I am insane!) "Dear Sir (his name removed for privacy reasons) I need to make an appointment for you and I to sit down and have you talk to me like I have never seen a number before!"

Question 1) (Taken from Hawks learning software that accompanies my Hawks Beginning Statistics book) And I do have the correct answers to these.

The total of all the frequencies in a frequency table is 384. If a section in a pie chart corresponds to an item with a frequency of 138, what is the size of the angle of the corresponding circular wedge? (round to the nearest degree)

Question 2) ( and I missed all five sections to this!) But again, I have the right answer now and I know what I did wrong.

A sample of 116 motels is selected from a large urban area and the price for a night of lodging for a single room was determined for each motel. The mean rate is computed to be $85 and the standard deviation is $13. One motel charged $55 per night which is the 15th percentile. Another motel charged $119 per night which is the 75th percentile.

  1. What is the z-score for a motel charging $106 per night? Round your answer 2 decimals
  2. How many motels charged at least $119 per night? Round your answer to the nearest integer
  3. How many motels charged at least $55 per night? Round your answer to the nearest integer
  4. If the z-score for a motel is -0.5, what is the price of a single room at the motel (in dollars)?
  5. The median rate is at most $55 True or False?

Question 3) ( just for shits and giggles, I also got this one wrong) But, aha… I got know why and I got the answers

Find the chebyshev interval for which at least 75% of the data will fall if the mean is 450 and the standard deviation is 15

LL- just remember, you asked!

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Blogger LL said...

Hmmmm... been a long time since I took sadistics, and we never had to do pie charts, or figure angles... but...

Number 1, I'd think would be 138/384=36% which corresponds to approximately 129 degrees of the pie chart.

The others... well... I'm too far removed from. Let's see if memory serves... 99% of the samples fall within +/- 3 sd's so... so we've got 85 + 39 which gives us the upper boundary of 124, while the lower boundary is 85 - 39 which would be 46.

Now... if memory still serves 95% of the sample falls within +/- 2 sd's, so... that gives us 85 + 26 which is 111 upper and 59 lower so... If I could remember what a z-score is or how to figure it, I might be a little closer, but just off the top of my head (not using a calculator here) I'd have to say that...

$106 per night would be around the 93% mark.

The $119 motels would fall in the top 97% or so, so that would mean that around 3% of the sample or 3.48 motels charged at least 119 so we'll call it 3. But... we know that 119 is the 75th percentile, so we're not dealing with a standard bell curve, so... that means that 25% of the 116 motels charged 119 or better so around 29...

That also means that 106 is not around the 93% because it would be less than 119, so...

I have no clue what a chebyshev interval is...

What it all boils down to is that I can't remember how to figure a z-score. It has been over 15 years since I used any of this crap so... I think I'm actually doing all right! Thanks for posting it anyway. It's a good mental exercise.

6/18/08, 9:10 PM  
Blogger JennyC&F said...

1) 138/384 answer times 360
3)answ 420,480
chebshev is (m-2r), (m+ 2r)
(450-2(15), (450+2(15)

6/19/08, 7:05 PM  

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