1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
tekilochka [14]
3 years ago
6

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

andom 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."
a. State an appropriate null and alternative hypothesis for testing whether or not there is any statistical difference in these two proportions measured initially and then one year later.
b. Conduct the test of hypothesis you stated in part a). Be sure to check the conditions for your test. State the P-value of your test and your conclusion.
Mathematics
1 answer:
sergiy2304 [10]3 years ago
7 0

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."

<em />

<em>Let </em>p_1<em> = proportion of drivers that were in compliance initially</em>

p_2<em> = proportion of drivers that were in compliance one year later</em>

(a) <u>Null Hypothesis</u>, 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}

<u>Alternate Hypothesis</u>, 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 <u>Two-sample z proportion statistics</u>;

                     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, <u><em>the test statistics</em></u>  =  \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

<u>Now, P-value of the test statistics is given by;</u>

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

                                            = 1 - 0.99957 = <u>0.00043</u>

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.

<em>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 </em><u><em>we reject our null hypothesis.</em></u>

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

You might be interested in
An investor has an account with stock from two different companies. Last year, her stock in Company A was worth $2690 and her st
Mrac [35]

Answer:

<h2> 14.7 %</h2>

Step-by-step explanation:

let us total the amount in her portfolio

Company A was worth $2690

Company B was worth $2980.

Total = $5670

when The stock in Company A decreases by 20%  she will have

$2690 *0.8=  $2152

Company A will worth $2152

when The stock in Company B decreases by 10%  she will have

$2980 *0.9=  $2682

Company A will worth  $2682

In all after the decline in are portfolio is $2152+$2682= $4834

the difference for the original amount in her investment is = $5670-$4834

= $836

The total percentage decrease in the investor's stock account

= (836/5670)*100= 0.147*100= 14.7 %

3 0
3 years ago
If f(x)=x*−81 and g(x)=(x−9)−1(x+9), find g(x)×f(x).
Nostrana [21]
F(x) = x²-81

g(x) = (x-9) -1(x+9)

= (x-9) -x-9


g(x) • f(x)



= [x²-81 ] • [ (x-9) -x-9 ]

=[ x²-81 ] • [ (x-x -9-9) ]
= [ x²-81 ] •[0-18]
= [ x²-81] •[ -18]

= -18•x² +-81•-18
= -18x²+1458
7 0
3 years ago
211135.711111 write this in cash price (dollars)
aleksklad [387]
211,135.71 merry christmas
5 0
2 years ago
Simplify each expression by combining like terms. <br>7a - 6 + 8a ​
anygoal [31]

=7a - 6 + 8

=7a + 8a - 6 =15a - 6

5 0
3 years ago
Angle CMW and angle WML together form angle CML. Angle CMW is a right angle. What must be true about angle CML?
ANTONII [103]
CML must be an obtuse angle.

Since CMW and WML together form CML, and CMW is a right angle, then CML must be larger than a right angle, which makes it obtuse.
3 0
3 years ago
Other questions:
  • Use the formula A = Ibh find the height to the nearest tenth of a triangle with a base of 15 and an area of 200.​
    13·1 answer
  • Simplify. (-2)^-3<br> A.-8<br> B.-1/8<br> C.1/8<br> D.8
    15·1 answer
  • 3Pounds = How many ounces is in a 3Pounds?​
    8·2 answers
  • A=16, c=14 find the length of b if necessary round to the nearest tenth
    10·1 answer
  • What is the standard form of a line that has a slope of 3 and passes through the point (–4, –5)?
    7·1 answer
  • Enter the missing numbers in the boxes to complete the table of equivalent ratios.
    8·2 answers
  • Y - 0.8x = 0.5<br> 5y - 2.5 = 4x<br> *Substitution
    8·2 answers
  • Please help i no not know
    13·2 answers
  • 6. All 20 spaces in the LCS parking lot are filled with vehicles. Some are occupied by two wheeled
    7·1 answer
  • What decimal part of $1 is 6 pennies​
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!