The coordinate system

"Immediately after a ban on using hand-held cell phones while driving was implemented, compliance with the law was measured. A r

sergiy2304 [10]

Answer:

(a) Null Hypothesis, $H_0$ : $p_1-p_2=0$ or $p_1= p_2$

Alternate Hypothesis, $H_A$ : $p_1-p_2\neq 0$ or $p_1\neq p_2$

(b) We conclude that there is a statistical difference in these two proportions measured initially and then one year later.

Step-by-step explanation:

We are given that a random sample of 1,250 drivers found that 98.9% were in compliance. A year after the implementation, compliance was again measured to see if compliance was the same (or not) as previously measured.

A different random sample of 1,100 drivers found 96.9% compliance."

Let $p_1$ = proportion of drivers that were in compliance initially

$p_2$ = proportion of drivers that were in compliance one year later

(a) Null Hypothesis, $H_0$ : $p_1-p_2=0$ or $p_1= p_2$ {means that there is not any statistical difference in these two proportions measured initially and then one year later}

Alternate Hypothesis, $H_A$ : $p_1-p_2\neq 0$ or $p_1\neq p_2$ {means that there is a statistical difference in these two proportions measured initially and then one year later}

The test statistics that will be used here is Two-sample z proportion statistics;

T.S. = $\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{ \frac{\hat p_1(1-\hat p_1)}{n_1} + \frac{\hat p_2(1-\hat p_2)}{n_2}} }$ ~ N(0,1)

where, $\hat p_1$ = sample proportion of drivers in compliance initially = 98.9%

$\hat p_2$ = sample proportion of drivers in compliance one year later = 96.9%

$n_1$ = sample of drivers initially = 1,250

$n_2$ = sample of drivers one year later = 1,100

(b) So, the test statistics = $\frac{(0.989-0.969)-(0)}{\sqrt{ \frac{0.989(1-0.989)}{1,250} + \frac{0.969(1-0.969)}{1,100}} }$

= 3.33

Now, P-value of the test statistics is given by;

P-value = P(Z > 3.33) = 1 - P(Z $\leq$ 3.33)

= 1 - 0.99957 = 0.00043

Since in the question we are not given with the level of significance so we assume it to be 5%. Now at 5% significance level, the z table gives critical values between -1.96 and 1.96 for two-tailed test.

Since our test statistics does not lies within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that there is a statistical difference in these two proportions measured initially and then one year later.

7 0

3 years ago

What are all the subsets of {5,9,13}

Naddika [18.5K]

All The Subsets

For theset {a,b,c}:

The empty set {} is a subset of {a,b,c}And these are subsets: {a}, {b} and {c}And these are also subsets: {a,b}, {a,c} and {b,c}And {a,b,c} is a subset of {a,b,c}

And when we list all the subsets of S={a,b,c} we get the Power Set of {a,b,c}:

P(S) = { {}, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c} }

Think of it as all the different ways we can select the items (the order of the items doesn't matter), including selecting none, or all.

Example: The shop has banana, chocolate and lemon ice cream.

What do you order?

Nothing at all: {}Or maybe just banana: {banana}. Or just {chocolate} or just {lemon}Or two together: {banana,chocolate} or {banana,lemon} or {chocolate,lemon}Or all three! {banana, chocolate,lemon}

Question: if the shop also has strawberry flavor what are your options? Solution later.

How Many Subsets

Easy! If the original set has n members, then the Power Set will have 2n members

Example: in the {a,b,c} example above, there are three members (a,b and c).

So, the Power Set should have 23 = 8, which it does!

Notation

The number of members of a set is often written as |S|, so when S has n members we can write:

|P(S)| = 2n

Example: for the set S={1,2,3,4,5} how many members will the power set have?

Well, S has 5 members, so:

|P(S)| = 2n = 25 = 32

You will see in a minute why the number of members is a power of 2

It's Binary!

And here is the most amazing thing. To create the Power Set, write down the sequence of binary numbers (using n digits), and then let "1" mean "put the matching member into this subset".

So "101" is replaced by 1 a, 0 b and 1 c to get us {a,c}

Like this:

abcSubset0000{ }1001{c}2010{b}3011{b,c}4100{a}5101{a,c}6110{a,b}7111{a,b,c}

Well, they are not in a pretty order, but they are all there.

Another ExampleLet's eat! We have four flavors of ice cream: banana, chocolate, lemon, and strawberry. How many different ways can we have them?Let's use letters for the flavors: {b, c, l, s}. Example selections include:{} (nothing, you are on a diet){b, c, l, s} (every flavor){b, c} (banana and chocolate are good together)etcLet's make the table using "binary": bclsSubset00000{}10001{s}20010{l}30011{l,s}...... etc ..... etc ...121100{b,c}131101{b,c,s}141110{b,c,l}151111{b,c,l,s}

And the result is (more neatly arranged):

P = { {}, {b}, {c}, {l}, {s}, {b,c}, {b,l}, {b,s}, {c,l}, {c,s}, {l,s}, {b,c,l}, {b,c,s},
{b,l,s}, {c,l,s}, {b,c,l,s} }

SymmetryIn the table above, did you notice that the first subset is empty and the last has every member?But did you also notice that the second subset has "s", and the second last subset has everything except "s"? In fact when we mirror that table about the middle we see there is a kind of symmetry.This is because the binary numbers (that we used to help us get all those combinations) have a beautiful and elegant pattern.A Prime Example

The Power Set can be useful in unexpected areas.

I wanted to find all factors (not just the prime factors, but all factors) of a number.

I could test all possible numbers: I could check 2, 3, 4, 5, 6, 7, etc...

That took a long time for large numbers.

But could I try to combine the prime factors?

Let me see, the prime factors of 510 are 2×3×5×17 (using prime factor tool).

So, all the factors of 510 are:

2, 3, 5 and 17,2×3, 2×5 and 2×17 as well, and2×3×5 and 2×3×17 and ..... aha! Just like ice cream I needed a Power Set!

And this is what I got:

2,3,5,17SubsetFactors of 51000000{ }110001{17}1720010{5}530011{5,17}5 × 17 = 8540100{3}350101{3,17}3 × 17 = 51 ... etc ...... etc ...... etc ...151111{2,3,5,17}2 × 3 × 5 × 17 = 510

And the result? The factors of 510 are 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255 and 510 (and −1, −2, −3, etc as well). See the All Factors Tool.

Automated

I couldn't resist making Power Sets available to you in an automated way.

So, when you need a power set, try Power Set Maker.

6 0

3 years ago

Read 2 more answers

(Will award Brainlies & many many points, please help!)

iren [92.7K]

Answer:

B] f(n) = 6(3)n − 1; f(5) = 486

Step-by-step explanation:

First, you have to identify which type of relation the points have. From the graph you can tell that it's an exponential growth. The x values change in the same amount every time, in this case by 1.

So if the relation is exponential, if we divide the y coordinates you should get the same result every time.

18 / 6 = 3

54 / 18 = 3

162 / 54 = 3

So the y value increases 3 times. That means that the next value should be 162*3 = 486.

3 0

3 years ago

Read 2 more answers

PLEASE HELP THIS IS DUE IN 10 MINUTES!!!!!

andreev551 [17]

<h3>Answer:</h3>

b1-h3, b2-h2, b3-h3.