# two peer replies must be 100 words each

Instructions: Responses should be a minimum of 100 words and may include direct questions. In the peer responses, pick a confidence level other than 95% , i.e. 90%, 99%, 97%, any other confidence level is fine. Have fun and be creative with it and calculate another T-confidence interval and interpret your results. Compare my results to that of the initial 95% of the two peers, how much do they differ? How useful can this type of information be when you go to buy a new car, or even a house?

Peer 1 (Stacia ):

T-Critical Value

To find the 95% T-Critical Value, I first found 1-.95, which was .05. Since we have to both add and subtract from .05, I divided .05/2 = .025. I then subtracted .025 from 1, to get a probability of .975. Then I needed to find the degree of freedom. The degrees of freedom, which is our sample size minus 1. (10-1=9). Now that I have found those two, I can insert them into my formula in Excel.

=T.INV(.975,9)= 2.26215716

I then plug this number into the equation: Ì…xÂ± Tâˆ— ( SD/âˆš N)

37,149.40 + 2.26215716 * (10038.59662/3.16227766) = \$44,330

37,149.40 – 2.26215716 * (10038.59662/3.16227766) = \$29,968

This concludes that there is a 95% confidence that the sample price of cars will be between \$29,968 and \$44,330.

Z- Critical Value

For the Z Critical Value, I need to use my p and q from week 3.

p = 0.60

q = 0.40

To find the 95% confidence interval, I will subtract .95 from 1, to give me .05. Since we will be adding and subtracting, I will divide .05/2, to give me .025. In order to use Excel, I need to subtract 1-.025, which gives me .975. The formula I will use in Excel is =NORM.S.INV(.975). This gives me a Z-Critical Value of 1.96 (rounded).

Now, I will plug everything into the equation: Ì‚pÂ± Zâˆ— (âˆš Ì‚pâˆ— Ì‚q /n )

.60 + 1.96*(âˆš.6*.4/10) = 90.36418943, or 90.4%

.60 – 1.96 *(âˆš.6*.4/10) = 29.63581057, or 29.6%

This means that there is a 95% confidence that proportion of cars sampled that falls below the average goes from 29.6% to 90.3%.

I was not surprised by the intervals. After looking through all of my data from the car prices, it all made sense.

Peer 2 ( Martine):

1. T-Critical Value: In order to find the 95% T-Critical Value, I subtracted .95 from 1 to get .05. then divided that by 2 to receive .025, and after subtracting that from 1, I end with a final result of .975. In order to find the degree of freedom, I subtracted 1 from the sample size of 10, resulting in a total of 9.

Using this data within Excel, the formula then looks like this =T.INV(0.975,9) = 2.2621571628

I then take the number and insert it, along with other data from week 1 into the following formula: Ì…xÂ± Tâˆ— ( SD/âˆš N) which ends up looking like so:

a. 41,117+2.2621571628*(16,398/âˆš10) = 52847.42254411

and

b. 41,117-2.2621571628*(16,398/âˆš10) = 29386.57745588

Therefore, there is a 95% confidence that the sample price of vehicles will be between \$29,386.57 and \$52,847.42.

2. Z-Critical Value: To find this, weâ€™ll look back to week 3 when we found these values:

Success (p) = 0.6

Failure (q) = 0.4

I will use the same intro as I did for the T-Critical Value but I will switch the Excel formula to Norm.S.Inv and end with =NORM.S.INV(0.975), giving us a result of 1.9599639845.

Now I will plug all of my values into the following formula Ì‚pÂ± Zâˆ— (âˆš Ì‚pâˆ— Ì‚q /n ) which gives us:

a. 0.6+1.9599639845*(âˆš0.6*0.4/10) = 0.9036

and

b. 0.6-1.9599639845*(âˆš0.6*0.4/10) = 0.2964

Therefore, there is a 95% confidence that the proportion of cars sampled which fall below the average ranges from 90.36% and 29.64%.

I wouldnâ€™t say I felt surprised by any of these results, as I worked the data and equations it kind of all seemed to fall in line.