Samples of two different types of automobiles were selected, and the actual speed for each car was determined when the speedometer registered 50 mph. the resulting 95% confidence intervals for true average actual speed were (51.7, 53.1) and (48.9, 50.1). assuming that the two sample standard deviations are identical, which confidence interval is based on the larger sample size?

The interval [48.9, 50.1] was based on the larger sample size.

Step-by-step explanation:

Hello!

To answer this I'll assume that both CI were constructed using statistic Z.

The formula is

                      x[bar]± * (δ/√n)

I'll not use the whole formula, just the semi amplitude (d) of the CI

                             d= * (δ/√n)

Then we rewrite the formula based on the sample size

                         d* =δ/√n

                         ⇒ (d* )² = δ²/n

                         ⇒ n*(d* )² = δ²

                         ⇒ n= δ²/(d*)²

First interval:

                         [51.7, 53.1]

Amplitude: a= Ls- Li = 53.1 - 51.7 = 1.4

Semi-amplitude: d=a/2 = 1.4/2 = 0.7

Replace the formula

n₁= δ²/(d*)²

⇒ n₁= δ²/(0.7*1.96)²

⇒ n₁= δ²/1.88

Second Interval

                         [48.9, 50.1]

Amplitude: a= Ls- Li = 50.1 - 48.9 = 1.2

Semi-amplitude: d=a/2 = 1.2/2 = 0.6

n₂= δ²/(d*)²

⇒ n₂= δ²/(0.6*1.96)²

⇒ n₂= δ²/1.38

Now, we compare the information we've got for the two intervals

n₁= δ²/1.88

n₂= δ²/1.38

See that I didn't put a subscript under the variance in both formulas, this is because the text says, both standard deviation are identical, meaning that the same happens with the variance. You can prove mathematically, that the formula with the lowest denominator will have the largest result.

>For example, let's say the standard deviation (δ) is 5, then:

n₁= 5²/1.88 = 13.29

n₂= 5²/1.38 = 18.12

The interval [48.9, 50.1] was based on the larger sample size.

I hope you have a SUPER day!

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.