The graph shows the profit, y, of a community fundraiser, with respect to the number

Choose the correct interpretation of the above confidence interval. Note: 2 submissions allowed.

abruzzese [7]

Answer:

Step-by-step explanation:

Hello!

Full Text:

As part of its "It Can Wait" campaign to discourage texting while driving, AT&T recently released the results of separate surveys concerning the extent of texting while driving among adults twd_commutor_survey and among teens att_teen_survey_executive . In the survey of the adults, 496 of n1 = 1,011 adult drivers (49.06%) said they text while driving. In the survey of the teens, 516 of n2 = 1,200 (43%) said they text while driving.

Question 1. Calculate a 98% confidence interval for the difference padult - pteen in the proportions of adults that text while driving and the proportion of teens that text while driving. (use 4 decimal places in your answers) lower bound upper bound

Be:

X₁: Number of adult drivers that text while driving, out of 1011.

n₁= 1011

x₁= 496

p₁'= 496/1011= 0.4906

X₂: Number of teen drivers that text while driving, out of 1200.

n₂= 1200

x₂= 516

p₂'= 516/1200= 0.43

For the 98% CI for p₁-p₂

$Z_{1-\alpha /2}= Z_{0.99}= 2.326$

(p₁'-p₂')± $Z_{1-\alpha /2}$ * $\sqrt{\frac{p'_1(1-p'_1)}{n_1} +\frac{p'_2(1-p'_2)}{n_2} }$

(0.4906-0.43)±2.326* $\sqrt{\frac{0.4906(1-0.4906)}{1011} +\frac{0.43(1-0.43)}{1200} }$

0.0606±2.326*0.0212

[0.011; 0.11]

Using a 98% confidence level, you'd expect that the interval [0.011; 0.11] contains the difference between the population proportion of adults that text while driving and the population proportion of teens that ext while driving.

Question 2. Choose the correct interpretation of the above confidence interval. Note: 2 submissions allowed.

To decide over a hypothesis test using a confidence interval there are several conditions that should be met:

1) The hypotheses should be two-tailed:

H₀: p₁ - p₂= 0

H₁: p₁ - p₂≠ 0

2) The confidence level of the interval and the significance level of the test should be complementary, this means that if the interval was constructed with a level 1 - α: 0.98 then the test should be made using α: 0.02.

Naturally, the hypotheses and the CI should be made for the same parameters.

If all conditions are met, the decision criteria is as follows:

If the CI contains the value stated in the null hypothesis, the decision is to not reject the null hypothesis.

If the CI doesn't contain the value stated in the null hypothesis, the decision is to reject the null hypothesis.

In this case, the value stated in the null hypothesis is "zero" and is not included in the interval, so the decision is to reject the null hypothesis. You can conclude that the population proportions of adults and teens that text while driving are different.

Considering that the CI is positive, we can think that the proportion of adults that text while driving is grater than the proportion of teens that text while driving.

Options:

1) Since 0 is not in the confidence interval, the surveys provide evidence that the proportion of teens that text while driving is greater than the proportion of adults that text while driving.

2) Since the confidence interval is entirely positive, the surveys provide evidence that the proportion of teens that text while driving is greater than the proportion of adults that text while driving.

3) Since the confidence interval is entirely positive, the surveys provide evidence that the proportion of adults that text while driving is greater than the proportion of teens that text while driving.

4) Since 0 is not in the confidence interval, the surveys provide evidence that there is no significant difference between the proportions of adults and teens that text while driving.

The correct option is: "3"

I hope this helps!

3 0

3 years ago

In a class of 28 students, 11 have a brother and 9 have a sister. There are 2 students

Westkost [7]

Answer:

$\displaystyle P(A\mid B)=\frac{2}{11}$

Step-by-step explanation:

Conditional Probability

Is a measure of the probability of the occurrence of an event, given that another event has already occurred. If event B has occurred, then the probability that event A occurs is given by:

$P(A\mid B)={\frac {P(A\cap B)}{P(B)}}$

Where $P(A\cap B)$ is the probability that both events occur and P(B) is the probability that B occurs.

Let's define events A and B for the question. There are 11 students that have a brother and 9 that have a sister. Two of those students have a brother and a sister.

We are given the fact that the selected student has a brother: this is the event that has already occurred, thus:

B = A student has a brother

A = A student has a sister

The probability that a student has a brother is:

$\displaystyle P(B)=\frac{11}{28}$

The probability that the student has a brother and a sister is:

$\displaystyle P(A\cap B)=\frac{2}{28}$

Thus, the conditional probability is:

$P(A\mid B)={\frac {\frac{2}{28}}{\frac{11}{28}}}$

Simplifying:

$\mathbf{\displaystyle P(A\mid B)=\frac{2}{11}}$

4 0

3 years ago

April and Bill went to the grocery store to buy chocolate bars. April bought 4 small chocolate bars and 6 large chocolate bars ,

Elena-2011 [213]

Step-by-step explanation:

To do this equation, we could put it in terms of algebra, lets say the large chocolate bars are represented by L and the small bars by S

April

4S + 6L = $16.50

Bill

4S + 3L = $11.25

Looking at this, we can see that the difference between the two purchases is that Bill bought three less large chocolate bars, this means the difference in total cost equals three large chocolate bars. Using this knowledge.

$16.50 minus $11.25 = $5.25

$5.25 = Three Large Bars

Divide this by three to get the cost of one large bar.

$1.75 is the cost of one single large bar.

8 0

3 years ago

Read 2 more answers

Pleaseee help! i need the answer for x (look at picture)

Semenov [28]

Answer:

180 - 133

Step-by-step explanation: